practice and homework lesson 1.11 answer key grade 5

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Go Math! 5 Common Core, Grade: 5 Publisher: Houghton Mifflin Harcourt

Go math 5 common core, title : go math 5 common core, publisher : houghton mifflin harcourt, isbn : 547587813, isbn-13 : 9780547587813, use the table below to find videos, mobile apps, worksheets and lessons that supplement go math 5 common core., textbook resources.

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Comparing and Contrasting Data Distributions

11.1: Math Talk: Mean (5 minutes)

CCSS Standards

Routines and Materials

Instructional Routines

• MLR8: Discussion Supports

This is the first math talk activity in the course. See the launch for extended instructions for facilitating this activity successfully.

The purpose of this Math Talk is to expand students’ strategies for finding a mean beyond following an algorithm to reasoning that the mean of the values in a symmetric data set is the middle value. The third item is designed to illustrate that this technique only works for symmetric data sets. These understandings help students develop fluency and will be helpful later in this lesson when students will need to use symmetry to match a mean to the distribution.

This Math Talk provides an opportunity for students to notice and make use of the symmetric structure (MP7) of the values to determine the mean. While participating in these activities, students need to be precise in their word choice and use of language (MP6).

Monitor for students who:

• use the standard algorithm for finding mean (sum and divide)
• use the symmetry of the data set

This is the first time students do the  math talk  instructional routine, so it is important to explain how it works before starting.

Explain the math talk routine: one problem is displayed at a time. For each problem, students are given a few minutes to quietly think and give a signal when they have an answer and a strategy. The teacher selects students to share different strategies for each problem, and might ask questions like “Who thought about it a different way?” The teacher records students' explanations for all to see. Students might be asked to provide more details about why they decided to approach a problem a certain way. It may not be possible to share every possible strategy for the given limited time; the teacher may only gather two or three distinctive strategies per problem. 

Consider establishing a small, discreet hand signal that students can display to indicate that they have an answer they can support with reasoning. This signal could be a thumbs-up, a certain number of fingers that tells the number of responses they have, or another subtle signal. This is a quick way to see if the students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.

Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.

Student Facing

Evaluate the mean of each data set mentally.

61, 71, 81, 91, 101

0, 100, 100, 100, 100

0, 5, 6, 7, 12

Student Response

For access, consult one of our IM Certified Partners .

Anticipated Misconceptions

If students struggle to use symmetry as a method for finding the mean, consider asking them to find the mean for the values: 1, 2, 3, 4, 5.

Activity Synthesis

Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:

• “Who can restate ___’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to __’s strategy?”
• “Do you agree or disagree? Why?”

Although all correct methods for solving for the mean are valid, highlight the use of symmetry in the data. In previous lessons, students learned that symmetric distributions have a mean in the center of the data. When symmetry is present, it can be used to quickly discover the mean.

11.2: Describing Data Distributions (15 minutes)

Building On

Building Towards

• MLR7: Compare and Connect

Required Materials

• Pre-printed slips, cut from copies of the blackline master

In this activity students take turns with a partner matching data displays with distribution characteristics and determine what measure of center is most appropriate for the data. Students trade roles explaining their thinking and listening, providing opportunities to explain their reasoning and critique the reasoning of others (MP3).

Arrange students in groups of 2. Demonstrate how to set up and and find matches. Choose a student to be your partner. Mix up the cards and place them face-up. Point out that the cards contain either a data display or a written statement. Select one of each style of card and then explain to your partner why you think the cards do or do not match. Demonstrate productive ways to agree or disagree, for example, by explaining your mathematical thinking or asking clarifying questions. Give each group a set of cut-up cards for matching. Ask students to pause after completing the matching for a whole-class discussion. Give students five minutes to work the second question then pause for a whole-class discussion.

Tell students that the appropriate measure of center may not be the one given on the cards.

• For each match that you find, explain to your partner how you know it’s a match.
• For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
• After matching, determine if the mean or median is more appropriate for describing the center of the data set based on the distribution shape. Discuss your reasoning with your partner. If it is not given, calculate (if possible) or estimate the appropriate measure of center. Be prepared to explain your reasoning.

Much discussion takes place between partners. Once all groups have completed the matching, discuss the following:

• “Which matches were tricky? Explain why.” (The box plot in row 6 was tricky because I had to use process of elimination to figure out that it was the one that was uniform.)
• “Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?” (Yes. I realized that I thought incorrectly that skewed left meant that most of the data was on the left. However, I learned that skewed left means that there is data to the left of where most of the data is located.)
• “Can you determine the median using only a histogram? Why or why not?” (No, but you can determine the interval that contains the median.)
• “Can you determine if a distribution is uniform from a box plot? Why or why not?” (No. You can determine that the data could possibly be symmetric based on the distribution of the five number summary, but beyond that you would not be able to know that the data is uniform using only a box plot.)

The purpose of the second part of the activity is to discuss the relationship between mean and median based on the shape of the distribution and to make the connection to measures of variability. Ask:

• “If the mean is the appropriate measure of center, should we use the MAD or the IQR to measure variability?” (MAD)
• “If the median is the appropriate measure of center, should we use the MAD or the IQR to measure variability?” (IQR)

11.3: Visual Variability and Statistics (10 minutes)

• MLR2: Collect and Display

This activity prompts students to compare variability in several data sets by analyzing the distributions shown on box plots and dot plots. Some students may reason about variability by observing the shapes and features of the data displays. Others may try to quantify the variability by finding the IQR from each box plot, or by estimating the MAD from each dot plot. Look for students who approach the task quantitatively.

Arrange students in groups of 2. Give students five minutes to work through the questions then pause for a whole-group discussion.

Each box plot summarizes the number of miles driven each day for 30 days in each month. The box plots represent, in order, the months of August, September, October, November, and December.

• The five box plots have the same median. Explain why the median is more appropriate for describing the center of the data set than the mean for these distributions.
• The five dot plots have the same mean. Explain why the mean is more appropriate for describing the center of the data set than the median.

Are you ready for more?

 These two box plots have the same median and the same IQR. How could we compare the variability of the two distributions?

Description: <p>Two box plots on the same number line. From 2 to 20, by 2s.<br> <br> Bottom box plot has whisker from 2 to 8. Box from 8 to 13 with vertical line at 9. Whisker from 13 to 20.<br> <br> Top box plot has whisker from 6 to 8. Box from 8 to 13 with vertical line at 9. Whisker from 13 to 18.</p>

These two dot plots have the same mean and the same MAD. How could we compare the variability of the two distributions?

Students may have forgotten what variability means or which statistic to use to determine the variability in a data set. Refer them to previous work or ask them what measure is useful in determining a data set's tendency to have different values.

The purpose of this discussion is to make the connection between the shape of the distribution and the use of either IQR or MAD to quantify variability. Another goal is to make sure students understand that a greater value from IQR or MAD means greater variability. Display the box plots in order of variability with the IQR included, and then display the dots plots in order of variability with the MAD included.

The IQR for the data in distributions A through E are {40, 60, 50, 40, 20} and the MAD for the data in distributions F through J are approximately {1.56, 1.10, 2.68, 2.22, 0}. Here are some questions for discussion:

• “What are the IQR and MAD measuring?” (They are measuring the spread or variability of the data)
• “Which plots were the most difficult to arrange?” (The dot plots were more difficult because it was easy to find the IQR for the box plots.)
• “Do the orders given by the IQR and MAD match your order?” (Yes, except for the box plots A and D which had the same IQR and I didn’t know how to arrange them.)
• “What do you notice about the values for IQR and MAD?” (The values for the MAD were higher than I thought except for distribution J. I did not know that the MAD could be equal to zero.)
• “What advantages are offered by using IQR and MAD versus visual inspection?” (The IQR and MAD are values that can be easily sorted.)

If some students already arranged the plots using IQR or MAD you should ask them, “Why did you choose to arrange the plots by IQR or MAD?” (I knew that IQR and MAD were measures of variability so I used them.)

Lesson Synthesis

In this lesson, students investigated variability using data displays and summary statistics.

• “One data set’s measure of center is best represented by a median of 7 and another data set by a median of 10. How would you determine which data set has greater variability?” (You calculate the IQR. Whichever one has a larger IQR is more variable.)
• “How do you determine which of two roughly symmetric distributions has less variability?” (You calculate the MAD. Whichever one has a lower MAD has less variability.)
• “What does it mean to say that one data set or distribution has more variability than another?” (The appropriate measure of variability for one data set is greater than the other. Using a data display, one distribution is more spread apart than the other.)

11.4: Cool-down - Which Menu? (5 minutes)

Student lesson summary.

The mean absolute deviation, or MAD, is a measure of variability that is calculated by finding the mean distance from the mean of all the data points. Here are two dot plots, each with a mean of 15 centimeters, displaying the length of sea scallop shells in centimeters.

Notice that both dot plots show a symmetric distribution so the mean and the MAD are appropriate choices for describing center and variability. The data in the first dot plot appear to be more spread apart than the data in the second dot plot, so you can say that the first data set appears to have greater variability than the second data set. This is confirmed by the MAD. The MAD of the first data set is 1.18 centimeters and the MAD of the second data set is approximately 0.94 cm. This means that the values in the first data set are, on average, about 1.18 cm away from the mean and the values in the second data set are, on average, about 0.94 cm away from the mean. The greater the MAD of the data, the greater the variability of the data.

The interquartile range, IQR, is a measure of variability that is calculated by subtracting the value for the first quartile, Q1, from the value for the the third quartile, Q3. These two box plots represent the distributions of the lengths in centimeters of a different group of sea scallop shells, each with a median of 15 centimeters.

Notice that neither of the box plots have a symmetric distribution. The median and the IQR are appropriate choices for describing center and variability for these data sets. The middle half of the data displayed in the first box plot appear to be more spread apart, or show greater variability, than the middle half of the data displayed in the second box plot. The IQR of the first distribution is 14 cm and 10 cm for the second data set. The IQR measures the difference between the median of the second half of the data, Q3, and the median of the first half, Q1, of the data, so it is not impacted by the minimum or the maximum value in the data set. It is a measure of the spread of the middle 50% of the data.

The MAD is calculated using every value in the data while the IQR is calculated using only the values for Q1 and Q3.

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Go Math Practice - 5th Grade 1.1 - Place Value and Patterns Worksheet Freebie

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Go Math Grade 5 Chapter 1 Answer Key Pdf Place Value, Multiplication, and Expressions

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Place Value, Multiplication, and Expressions Go Math Grade 5 Chapter 1 Answer Key Pdf

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Lesson 1: Investigate • Place Value and Patterns

• Place Value and Patterns – Page No. 7
• Place Value and Patterns Lesson Check – Page No. 8

Lesson 2: Place Value of Whole Numbers

• Place Value of Whole Numbers – Page No. 11
• Place Value of Whole Numbers Lesson Check – Page No. 12

Lesson 3: Algebra • Properties

• Properties – Page No. 15
• Properties Lesson Check – Page No. 16

Lesson 4: Algebra • Powers of 10 and Exponents

• Powers of 10 and Exponents – Page No. 18
• Powers of 10 and Exponents Lesson Check – Page No. 19
• UNLOCK the Problem – Page No. 20

Lesson 5: Algebra • Multiplication Patterns

• Multiplication Patterns – Page No. 22
• Multiplication Patterns Lesson Check – Page No. 23
• Multiplication Patterns Lesson Check 1 – Page No. 24

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 25
• Mid-Chapter Checkpoint Lesson Check – Page No. 26

Lesson 6: Multiply by 1-Digit Numbers

• Multiply by 1-Digit Numbers – Page No. 29
• Mult iply by 1-Digit Numbers Lesson Check- Page No. 30

Lesson 7: Multiply by Multi-Digit Numbers

• Multiply by Multi-Digit Numbers – Page No. 33
• Multiply by Multi-Digit Numbers Lesson Check – Page No. 34

Lesson 8: Relate Multiplication to Division

• Relate Multiplication to Division – Page No. 37
• Relate Multiplication to Division Lesson Check – Page No. 38

Lesson 9: Problem Solving • Multiplication and Division

• Multiplication and Division – Page No. 41
• Multiplication and Division Lesson Check – Page No. 42

Lesson 10: Algebra • Numerical Expressions

• Numerical Expressions – Page No. 45
• Numerical Expressions Lesson Check – Page No. 46

Lesson 11: Algebra • Evaluate Numerical Expressions

• Evaluate Numerical Expressions – Page No. 49
• Evaluate Numerical Expressions Lesson Check – Page No. 50

Lesson 12: Algebra • Grouping Symbols

• Grouping Symbols – Page No. 53
• Grouping Symbols Lesson Check – Page No. 54

Review/Test

• Review/Test – Page No. 55
• Review/Test – Page No. 56
• Review/Test – Page No. 57
• Review/Test – Page No. 58

Place Value and Patterns – Share and Show – Page No. 7

Complete the sentence.

Question 1. 500 is 10 times as much as ______

Explanation: Let the unknown number is S. 500 = 10S S = 500/10 = 50. 500 is 10 times as much as 50.

Question 2. 20,000 is \(\frac{1}{10}\) of ______

Answer: 2,00,000

Explanation: Let the unknown number is S. 20,000 = \(\frac{1}{10}\) S S = 20,000 X 10 = 2,00,000

Go Math 5th Grade Lesson 1.1 Homework Answers Question 3. 900 is \(\frac{1}{10}\) of ______

Answer: 9,000

Explanation: Let the unknown number is S. 900 = \(\frac{1}{10}\) S S = 900 X 10 = 9,000

Question 4. 600 is 10 times as much as ______

Explanation: Let the unknown number is S. 600 = 10S S = 600/10 = 60.

Use place-value patterns to complete the table

Question 5.

Explanation: 1. 10 is 10 times as much as ______ Let the unknown number is S. 10 = 10S S = 10/10 = 1. 10 is 10 times as much as 1. 10 is \(\frac{1}{10}\) of ______ Let the unknown number is S. 10 = \(\frac{1}{10}\) S S = 10 X 10 = 100. 2. 3,000 is 10 times as much as ______ Let the unknown number is S. 3,000 = 10S S = 3,000/10 = 300. 3,000 is 10 times as much as 300. 3,000 is \(\frac{1}{10}\) of ______ Let the unknown number is S. 3,000 = \(\frac{1}{10}\) S S = 3,000 X 10 = 30,000. 3. 800 is 10 times as much as ______ Let the unknown number is S. 800 = 10S S = 800/10 = 80. 800 is 10 times as much as 80. 800 is \(\frac{1}{10}\) of ______ Let the unknown number is S. 800 = \(\frac{1}{10}\) S S = 800 X 10 = 8,000. 4. 50 is 10 times as much as ______ Let the unknown number is S. 50 = 10S S = 50/10 = 5. 50 is 10 times as much as 5. 50 is \(\frac{1}{10}\) of ______ Let the unknown number is S. 50 = \(\frac{1}{10}\) S S = 50 X 10 = 500.

Question 6.

Explanation: 1. 400 is 10 times as much as ______ Let the unknown number is S. 400 = 10S S = 400/10 = 40. 400 is 10 times as much as 40. 400 is \(\frac{1}{10}\) of ______ Let the unknown number is S. 400 = \(\frac{1}{10}\) S S = 400 X 10 = 4,000. 2. 90 is 10 times as much as ______ Let the unknown number is S. 90 = 10S S = 90/10 = 9. 90 is 10 times as much as 9. 90 is \(\frac{1}{10}\) of ______ Let the unknown number is S. 90 = \(\frac{1}{10}\) S S = 90 X 10 = 900. 3. 6,000 is 10 times as much as ______ Let the unknown number is S. 6,000 = 10S S = 6,000/10 = 600. 6,000 is 10 times as much as 600. 6,000 is \(\frac{1}{10}\) of ______ Let the unknown number is S. 6,000 = \(\frac{1}{10}\) S S = 6,000 X 10 = 60,000. 4. 200 is 10 times as much as ______ Let the unknown number is S. 200 = 10S S = 200/10 = 20. 200 is 10 times as much as 20. 200 is \(\frac{1}{10}\) of ______ Let the unknown number is S. 200 = \(\frac{1}{10}\) S S = 200 X 10 = 2,000.

Complete the sentence with 100 or 1,000.

Question 13. 200 is ______ times as much as 2

Answer: 200 is 100 times as much as 2

Explanation: Let the unknown number is S. 200 = 2S S = 200/2 = 100

Math Expressions Grade 5 Pdf Answer Key Question 14. 4,000 is ______ times as much as 4

Answer: 4,000 is 1000 times as much as 4

Explanation: Let the unknown number is S. 4,000 = 2S S = 4,000/2 = 1,000

Question 15. 700,000 is ______ times as much as 700

Answer: 700,000 is 1,000 times as much as 700

Explanation: Let the unknown number is S. 700,000 = 700S S = 700,000/700 = 1,000

Question 16. 600 is ______ times as much as 6

Answer: 600 is 100 times as much as 6

Explanation: Let the unknown number is S. 600 = 6S S = 600/6= 100

Question 17. 50,000 is ______ times as much as 500

Answer: 50,000 is 100_ times as much as 500

Explanation: Let the unknown number is S. 50,000 = 500S S = 50,000/500= 100

Question 18. 30,000 is ______ times as much as 30

Answer: 30,000 is 1,000 times as much as 30

Explanation: Let the unknown number is S. 30,000 = 30S S = 30,000/30 = 1,000

Question 19. Explain how you can use place-value patterns to describe how 50 and 5,000 compare. Type below: __________

Answer: 5,000 is 100 times as much as 50

Explanation: 5,000/50 = 100

Place Value and Patterns – Problem Solving – Page No. 8

Sense or Nonsense?

Answer: Robyn’s model makes sense. Because the given data 300 is 100 times as much as 3. It clearly states that there are 100 model-blocks and one model blocks should take to solve the problem.

Question 20. Explain how you would help Mark understand why he should have used small cubes instead of longs. Type below: __________

Answer: Mark’s drew 100 model-blocks and 10 model-blocks which. To get 300 is 100 times as much as 3, he needs to do 300/3 = 100 model blocks.

Place Value of Whole Numbers – Share and Show – Page No. 11

Complete the place-value chart to find the value of each digit.

Explanation: 7 x 1,000,000 = 7,000,000 3 x 100,000 = 300,000 3 x 1,000 = 3000 8 x 100 = 800 2 x 10 = 20

Write the value of the underlined digit.

Question 2. 1,57 4 ,833 __________

Answer: 4,000

Explanation: (1 x 1,000,000) + (5 x 1,00,000) + (7 x 10,000) + (4 x 1,000) + (8 x 100) + (3 x 10) + (3 x 1) 4 x 1,000 = 4 thousands = 4,000

Go Math 5th Grade Lesson 1.11 Homework Answers Question 3. 598, 1 02 __________

Answer: 100

Explanation: (5 x 1,00,000) + (9 x 10,000) + (8 x 1,000) + (1 x 100) + (0 x 10) + (2 x 1) 1 x 100 = 4 hundreds = 100

Question 4. 7,0 9 3,455 __________

Answer: 90,000

Explanation: (7 x 1,000,000) + (0 x 1,00,000) + (9 x 10,000) + (3 x 1,000) + (4 x 100) + (5 x 10) + (5 x 1) 9 x 10,000 = 9 ten-thousands = 90,000

Question 5. 3 01,256,878 __________

Answer: 3,00,000,000

Explanation: (3 x 1,00,000,000) + (0 x 10,000,000) + (1 x 1,000,000) + (2 x 1,00,000) + (5 x 10,000) + (6 x 1,000) + (8 x 100) + (7 x 10) + (8 x 1) 3 x 1,00,000,000 = 3 hundred- millions = 3,00,000,000

Write the number in two other forms.

Question 6. (8 × 100,000) + (4 × 1,000) + (6 × 1) = __________

Answer: 80,4006 Eight Hundred Four Thousand Six

Explanation: (8 × 100,000) + (4 × 1,000) + (6 × 1) = 800,000 + 4,000 + 6 = 80,4006

Question 7. seven million, twenty thousand, thirty-two __________

Answer: 7,020,032 Seven Million Twenty Thousand Thirty-Two

Explanation: seven million = 7,000,000 twenty thousand = 20,000 thirty-two = 32

On Your Own

Question 8. 8 4 9,567,043 __________

Answer: 40,000,000

Explanation: (8 x 1,00,000,000) + (4 x 10,000,000) + (9 x 1,000,000) + (5 x 1,00,000) + (6 x 10,000) + (7 x 1,000) + (0 x 100) + (4 x 10) + (3 x 1) 4 x 10,000,000 = 4 ten- millions = 40,000,000

Question 9. 9, 4 22,850 __________

Answer: 4,00,000

Explanation: (9 x 1,000,000) + (4 x 1,00,000) + (2 x 10,000) + (2 x 1,000) + (8 x 100) + (5 x 10) + (0 x 1) 4 x 1,00,000 = 4 Hundred Thousand = 4,00,000

Question 10. 9 6,283 __________

Explanation: (9 x 10,000) + (6 x 1,000) + (2 x 100) + (8 x 10) + (3 x 1) 9 x 10,000 = 9 ten-thousands = 90,000

Question 11. 4 98,354,021 __________

Answer: 4,00,000,000

Explanation: (4 x 1,00,000,000) + (9 x 10,000,000) + (8 x 1,000,000) + (3 x 1,00,000) + (5 x 10,000) + (4 x 1,000) + (0 x 100) + (2 x 10) + (1 x 1) 4 x 1,00,000,000 = Four Hundred Million = 4,00,000,000

Lesson 1.1 Numerical Expressions Answer Key Question 12. 791, 3 50 __________

Answer: 300

Explanation: (7 x 1,00,000) + (9 x 10,000) + (1 x 1,000) + (3 x 100) + (5 x 10) + (0 x 1) 3 x 100 = 3 hundred = 300

Question 13. 2 7 ,911,534 __________

Answer: 7,000,000

Explanation: (2 x 10,000,000) + (7 x 1,000,000) + (9 x 1,00,000) + (1 x 10,000) + (1 x 1,000) + (5 x 100) + (3 x 10) + (4 x 1) 7 x 1,000,000 = Seven Million = 7,000,000

Question 14. 105,9 8 0,774 __________

Answer: 80,000

Explanation: (1 x 1,00,000,000) + (0 x 10,000,000) + (5 x 1,000,000) + (9 x 1,00,000) + (8 x 10,000) + (0 x 1,000) + (7 x 100) + (7 x 10) + (4 x 1) 8 x 10,000 = 8 ten-thousand = 80,000

Question 15. 8,26 5 ,178 __________

Answer: 5,000

Explanation: (8 x 1,000,000) + (2 x 1,00,000) + (6 x 10,000) + (5 x 1,000) + (1 x 100) + (7 x 10) + (8 x 1) 5 x 1,000 = 5 one-thousand = 5,000

Question 16. 345,000 Type below: __________

Answer: Three Hundred Forty-Five Thousand (3 x 1,00,000) + (4 x 10,000) + (5 x 1,000) + (0 x 100) + (0 x 10) + (0 x 1)

Question 17. 119,000,003 Type below: __________

Answer: One Hundred Nineteen Million Three (1 x 100,000,000) + (1 x 10,000,000) + (9 x 1,000,000) + (0 x 1,00,000) + (0 x 10,000) + (0 x 1,000) + (0 x 100) + (0 x 10) + (3 x 1)

Place Value of Whole Numbers – Problem Solving – Page No. 12

Use the table for 18–19.

Answer: Saturn

Explanation: Saturn = 1,427,000/10 = 142,700 which is 10 times as far as Earth

Question 19. Which planet is about \(\frac{1}{10}\) of the distance Uranus is from the Sun? __________

Answer: Mars

Explanation: Mars = 227,900 \(\frac{1}{10}\) x 2,871,000 = 287,100 Which planet is about \(\frac{1}{10}\) of the distance Uranus is from the Sun

Question 20. What’s the Error? Matt wrote the number four million, three hundred five thousand, seven hundred sixty-two as 4,350,762. Describe and correct his error. Type below: __________

Answer: Matt switched 2 digits in the thousands period: 4,305,762

Place Value And Patterns Lesson 1.1 Answers Question 21. Explain how you know that the values of the digit 5 in the numbers 150,000 and 100,500 are not the same. Type below: __________

Answer: In 150,000, the digit 5 is in the ten-thousands place, So, its value is 50,000; in 100,500, the digit 5 is in the hundreds place. So, its value is 500.

Question 22. Test Prep In the number 869,653,214, which describes how the digit 6 in the ten-millions place compares to the digit 6 in the hundred-thousands place? Options: A. 10 times as much as B. 100 times as much as C. 1,000 times as much as D.\(\frac{1}{10}\) of

Answer: B. 100 times as much as

Explanation: 869,653,214 (8 x 100,000,000) + (6 x 10,000,000) + (9 x 1,000,000) + (6 x 1,00,000) + (5 x 10,000) + (3 x 1,000) + (2 x 100) + (1 x 10) + (4 x 1) 6 x 10,000,000 = 60,000,000 6 x 1,00,000 = 6,00,000 60,000,000/6,00,000 = 100

Properties – Share and Show – Page No. 15

Use properties to find 4 × 23 × 25.

Question 1. 23 × × 25 ________ Property of Multiplication 23 × ( × ) ________ Property of Multiplication 23 × __________ ____

Answer: 23 x 4 x 25; Commutative Property of Multiplication 23 x (4 x 25); Associative Property of Multiplication 23 x 100 2,300

Use properties to find the sum or product.

Question 2. 89 + 27 + 11 = ____

Answer: 89 + (27 + 11); Associative Property of Addition 89 + 38 127

Question 3. 9 × 52 = ____

Answer: 468

Explanation: 9 x 52 Write 52 = (50 + 2) 9 x (50 + 2) (9 x 50) + (9 x 2); Distributive Property of Multiplication 450 + 18 468

Question 4. 107 + 0 + 39 + 13 = ____

Answer: 107 + 0 + 39 + 13 (107 + 0) + (39 + 13); Associative Property of Addition 107 + 0 = 107; Identity Property of Addition 107 + 52 = 159

Complete the equation, and tell which property you used.

Question 5. 9 × (30 + 7) = (9 × ____) + (9 × 7)

Answer: 9 × (30 + 7) = (9 ×30) + (9 × 7) Distributive Property of Multiplication

Explanation: 9 x (30 + 7) (9 x 30) + (9 x 7); Distributive Property of Multiplication 270 + 63 = 333

Question 6. 0 + ____ = 47

Answer: 47; Identity Property of Addition

Explanation: 0 + 47 = 47; Identity Property of Addition

Question 6. Describe how you can use properties to solve problems more easily. Type below: __________

Answer: Using Properties of Addition and Properties of Multiplication, we can solve problems more easily. Simplifying problems is easy with the properties.

Practice: Copy and Solve Use properties to find the sum or product.

Question 7. 3 × 78 = ____

Answer: 234, Associative Property of Multiplication

Explanation: Write 78 as 6 x 13 3 x 6 x 13 (3 x 6) x 13; Associative Property of Multiplication 18 x 13 = 234

Go Math Grade 5 Lesson 1.1 Question 8. 4 × 60 × 5 = ____

Answer: 1,200; Associative Property of Multiplication

Explanation: 4 x 60 x 5 4 x (60 x 5); Associative Property of Multiplication 4 x 300 = 1,200

Question 9. 21 + 25 + 39 + 5 = ____

Answer: 90; Associative Property of Addition

Explanation: (21 + 25) + (39 + 5); Associative Property of Addition 46 + 44 = 90

Question 10. 11 + (19 + 6) = (11 + ____) + 6

Answer: 11 + (19 + 6) = (11 + 19) + 6; Associative Property of Addition

Question 11. 25 + 14 = ____ + 25

Answer: 25 + 14 = 14 + 25; Commutative Property of Addition

Question 12. Show how you can use the Distributive Property to rewrite and find (32 × 6) + (32 × 4). ____

Answer: (32 × 6) + (32 × 4) = 32 x (6 + 4); Distributive Property

Properties – Problem Solving – Page No. 16

Question 13. Three friends’ meals at a restaurant cost $13, $14, and $11. Use parentheses to write two different expressions to show how much the friends spent in all. Which property does your pair of expressions demonstrate? $ ____

Answer: $38; Associative Law of Addition

Explanation: Three friends’ meals at a restaurant cost $13, $14, and $11. Friends spent in all = $13 + $14 + $11 $13 + ($14 + $11) = ($13 + $14) + $11 Associative Law of Addition

Answer: $162

Explanation: Jacob is designing an aquarium for a doctor’s office. He plans to buy 6 red-blond guppies, 1 blue neon guppy, and 1 yellow guppy. (6 x $22) + (1 x $11) + (1 x $19) = $132 + $11 + $19 = $162

Question 15. Sylvia bought 8 tickets to a concert. Each ticket costs $18. To find the total cost in dollars, she added the product 8 × 10 to the product 8 × 8, for a total of 144. Which property did Sylvia use? i. Distributive Property ii. Associative Property

Answer: i. Distributive Property

Explanation: Sylvia bought 8 tickets to a concert. Each ticket costs $18. To find the total cost in dollars = 8 x $18 Using Distributive Property (8 × 10) + (8 × 8) = 8 x (10 + 8) = 144.

Question 16. Sense or Nonsense? Julie wrote (15 – 6) – 3 = 15 – (6 – 3). Is Julie’s equation sense or nonsense? Do you think the Associative Property works for subtraction? Explain. __________

Answer: Nonsense; (15 – 6) – 3 = 9 – 3 = 6. 15 – (6 – 3) = 15 – 3 = 12 6 is not equal to 12. So, Associative Property does not work for subtraction

Place Value Grade 5 Lesson 1 Understand Place Value Answer Key Question 17. Test Prep Canoes rent for $29 per day. Which expression can be used to find the cost in dollars of renting 6 canoes for a day? Options: A. (6 + 20) + (6 + 9) B. (6 × 20) + (6 × 9) C. (6 + 20) × (6 + 9) D. (6 × 20) × (6 × 9)

Answer: B. (6 × 20) + (6 × 9)

Explanation: Canoes rent for $29 per day. For renting 6 canoes for a day, 6 x $29 6 x $(20 + 9) = (6 x 20) + (6 x 9)

Powers of 10 and Exponents – Share and Show – Page No. 18

Write in exponent form and word form.

Question 1. 10 × 10 Exponent form: Word form: Type below: __________

Answer: Exponent form: 10 2 Word form: the second power of ten

Explanation: 10 × 10 Base = 10; Exponent = 2; Exponent Form: 10 2 Word Form: the second power of ten

Question 2. 10 × 10 × 10 × 10 Exponent form: Word form: Type below: __________

Answer: Exponent Form: 10 4 Word Form: The fourth power of ten

Explanation: 10 × 10 × 10 × 10 Base = 10; Exponent = 4; Exponent Form: 10 4 Word Form: The fourth power of ten

Find the value.

Question 3. 10 2 = ____

Explanation: 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100;

Question 4. 4 × 10 2 = ____

Answer: 400

Explanation: 4 × 10 2 = 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 4 x 100 = 400

Question 5. 7 × 10 2 = ____

Answer: 700

Explanation: 7 × 10 2 = 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 7 x 100 = 700

Powers of 10 and Exponents – On Your Own – Page No. 19

Question 6. 10 × 10 × 10 exponent form: word form: Type below: __________

Answer: Exponent form: 10 3 Word form: the third power of ten

Explanation: 10 × 10 × 10 Base = 10; Exponent = 3; Exponent Form: 10 3 Word Form: The third power of ten

Question 7. 10 × 10 × 10 × 10 × 10 exponent form: word form: Type below: __________

Answer: Exponent form: 10 5 Word form: the fifth power of ten

Explanation: 10 × 10 × 10 × 10 × 10 Base = 10; Exponent = 5; Exponent Form: 10 5 Word Form: The fifth power of ten

Question 8. 10 4 = ____

Answer: 10,000

Explanation: 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 10 4 = 10 x 10 x 10 x 10 = 10,000;

Go Math Grade 5 Chapter 1 Lesson 1.2 Answer Key Question 9. 2 × 10 3 = ____

Answer: 2,000

Explanation: 2 × 10 3 = 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 2 x 1,000 = 2,000

Question 10. 6 × 10 4 = ____

Answer: 60,000

Explanation: 6 × 10 4 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 10 4 = 10 x 10 x 10 x 10 = 10,000; 6 x 10,000 = 60,000

Complete the pattern.

Question 11. 7 × 10 0 = 7 × 1 = _______ 7 × 10 1 = 7 × 10 = _______ 7 × 10 2 = 7 × 10 × 10 = _______ 7 × 10 3 = 7 × 10 × 10 × 10 = _______ 7 × 10 4 = 7 × 10 × 10 × 10 × 10 = _______

Answer: 7 × 10 0 = 7 × 1 = 7 7 × 10 1 = 7 × 10 = 70 7 × 10 2 = 7 × 10 × 10 = 7 x 100 = 700 7 × 10 3 = 7 × 10 × 10 × 10 = 7 x 1,000 = 7,000 7 × 10 4 = 7 × 10 × 10 × 10 × 10 = 7 x 10,000 = 70,000

Question 12. 9 × 10 0 = _______ = 9 9 × 10 1 = _______ = 90 9 × 10 2 = _______ = 900 9 × 10 3 = _______ = 9,000 9 × 10 4 = _______ = 90,000

Answer: 9 × 10 0 = 9 x 1 = 9 9 × 10 1 = 9 x 10 = 90 9 × 10 2 = 9 x 10 x 10 = 900 9 × 10 3 = 9 x 10 x 10 x 10= 9,000 9 × 10 4 = 9 x 10 x 10 x 10 x 10 = 90,000

Question 13. 12 × 10 0 = 12 × 1 = _______ 12 × 10 1 = 12 × 10 = _______ 12 × 10 2 = 12 × 10 × 10 = _______ 12 × 10 3 = 12 × 10 × 10 × 10 _______ 12 × 10 4 = 12 × 10 × 10 × 10 × 10 _______

Answer: 12 × 10 0 = 12 × 1 = 12 12 × 10 1 = 12 × 10 = 120 12 × 10 2 = 12 × 10 × 10 = 1,200 12 × 10 3 = 12 × 10 × 10 × 10 = 12,000 12 × 10 4 = 12 × 10 × 10 × 10 × 10 = 120,000

Question 14. 10 3 = 10 × 10 n What is the value of n? Think: 10 3 = 10 × () × (), or 10 × () The value of n is …….. n = ______

Explanation: 10 3 = 10 × 10 n 10 3 = 10 x 10 x 10 = 10 x 10 2 The value of n is 2

Question 15. Explain how to write 50,000 using exponents. Type below: __________

Answer: 5 x 10 4

Explanation: 5 x 10,000 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 10 4 = 10 x 10 x 10 x 10 = 10,000; 10,000 = 10 x 10 x 10 x 10 = 10 4 5 x 10 4

Powers of 10 and Exponents – UNLOCK the Problem – Page No. 20

Answer: C. 3 × 10 4 sq mi

Explanation: Lake Superior is the largest of the Great Lakes. It covers a surface area of about 30,000 square miles. 3 x 10,000 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 10 4 = 10 x 10 x 10 x 10 = 10,000; 10,000 = 10 x 10 x 10 x 10 = 10 4 3 x 10 4

Question 16. b. How can you use a pattern to find the answer? Type below: __________

Answer: 3 x 10,000 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 10 4 = 10 x 10 x 10 x 10 = 10,000; 10,000 = 10 x 10 x 10 x 10 = 10 4 3 x 10 4

Question 16. c. Write a pattern using the whole number 3 and powers of ten. 3 × 10 1 = 3 × 10   = 3 × 10 2 =              = 3 × 10 3 =              = 3 × 10 4 =              = Type below: __________

Answer: 3 × 10 1 = 3 × 10   = 3 × 10 2 = 3 x 10 x 10 = 300 3 × 10 3 = 3 x 10 x 10 x 10 = 3,000 3 × 10 4 = 3 x 10 x 10 x 10 x 10 = 30,000

Question 16. d. Fill in the correct answer choice above. Type below: __________

Answer: 3 × 10 4 = 3 x 10 x 10 x 10 x 10 = 30,000

Question 17. The Earth’s diameter through the equator is about 8,000 miles. What is the Earth’s estimated diameter written as a whole number multiplied by a power of ten? Options: A. 8 × 10 1 miles B. 8 × 10 2 miles C. 8 × 10 3 miles D. 8 × 10 4 miles

Answer: C. 8 × 10 3 miles

Explanation: The Earth’s diameter through the equator is about 8,000 miles. 8 x 1,000 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 1,000 = 10 x 10 x 10 8 x 1,000 = 8 x 10 3

Place Value and Patterns 5th Grade Lesson 1.4 Answers Question 18. The Earth’s circumference around the equator is about 25 × 10 3 miles. What is the Earth’s estimated circumference written as a whole number? Options: A. 250,000 miles B. 25,000 miles C. 2,500 miles D. 250 miles

Answer: B. 25,000 miles

Explanation: The Earth’s circumference around the equator is about 25 × 10 3 miles. 25 × 10 3 miles; 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 25 x 1,000 = 25,000 miles

Multiplication Patterns – Share and Show – Page No. 22

Use mental math and a pattern to find the product.

Question 1. • What basic fact can you use to help you find 30×4,000? 30 × 4,000 = ____

Answer: 3 x 4 = 12

Explanation: 30 × 4,000 The basic fact is 3 x 4 = 12

Use mental math to complete the pattern.

Question 2. 1 × 1 = 1 1 × 10 1 = _______ 1 × 10 2 = _______ 1 × 10 3 = _______

Answer: 1 × 1 = 1 1 × 10 1 = 10 1 × 10 2 = 100 1 × 10 3 = 1,000

Explanation: 1 × 1 = 1 1 × 10 1 = 1 x 10 = 10 1 × 10 2 = 1 x 10 x 10 = 100 1 × 10 3 = 1 x 10 x 10 x 10 = 1,000

Question 3. 7 × 8 = 56 (7 × 8) × 10 1 = _______ (7 × 8) × 10 2 = _______ (7 × 8) × 10 6 = _______

Answer: 7 × 8 = 56 (7 × 8) × 10 1 = 560 (7 × 8) × 10 2 = 5,600 (7 × 8) × 10 6 = 56,000,000

Explanation: 7 × 8 = 56 (7 × 8) × 10 1 = 56 x 10 = 560 (7 × 8) × 10 2 = 56 x 10 x 10 = 5,600 (7 × 8) × 10 6 = 56 x 10 x 10 x 10 x 10 x 10 x 10 = 56,000,000

Question 4. 6 × 5 = _______ 6 × 5 × _______ = 300 6 × 5 × _______ = 3000 6 × 5 × _______ = 30,000

Answer: 6 × 5 = 30 6 × 5 × 10 1 = 300 6 × 5 × 10 3  = 3000 6 × 5 × 10 4 = 30,000

Explanation: 6 × 5 = 30 6 × 5 × 10 = 300 6 × 5 × 10 x 10 x 10 = 3000 6 × 5 × 10 x 10 x 10 x 10 = 30,000

Question 5. 9 × 5 = 45 (9 × 5) × 10 1 = _______ (9 × 5) × 10 2 = _______ (9 × 5) × 10 3 = _______

Answer: 9 × 5 = 45 (9 × 5) × 10 1 = 450 (9 × 5) × 10 2 = 4,500 (9 × 5) × 10 3 = 45,000

Explanation: 9 × 5 = 45 (9 × 5) × 10 1 = 45 x 10 = 450 (9 × 5) × 10 2 = 45 x 10 x 10 = 4,500 (9 × 5) × 10 3 = 45 x 10 x 10 x 10 = 45,000

Question 6. 3 × 7 = 21 (3 × 7) × 10 1 = _______ (3 × 7) × 10 2 = _______ (3 × 7) × 10 3 = _______

Answer: 3 × 7 = 21 (3 × 7) × 10 1 = 210 (3 × 7) × 10 2 = 2,100 (3 × 7) × 10 3 = 21,000

Explanation: 3 × 7 = 21 (3 × 7) × 10 1 = 21 x 10 = 210 (3 × 7) × 10 2 = 21 x 10 x 10 = 2,100 (3 × 7) × 10 3 = 21 x 10 x 10 x 10 = 21,000

Question 7. 5 × 4 = _______ (5 × 4) × _______ = 200 (5 × 4) × _______ = 2,000 (5 × 4) × _______ = 20,000

Answer: 5 × 4 = 20 (5 × 4) × 10 1 = 200 (5 × 4) × 10 2 = 2,000 (5 × 4) × 10 3 = 20,000

Explanation: 5 × 4 = 20 (5 × 4) × 10 = 200 (5 × 4) × 10 x 10 = 2,000 (5 × 4) × 10 x 10 x 10 = 20,000

Question 8. 5 × 7 = _______ (5 × 7) × _______ = 350 (5 × 7) × _______ = 3,500 (5 × 7) × _______ = 35,000

Answer: 5 × 7 = 35 (5 × 7) × 10 1 = 350 (5 × 7) × 10 2 = 3,500 (5 × 7) × 10 3 = 35,000

Explanation: 5 × 7 = 35 (5 × 7) × 10 = 350 (5 × 7) × 10 x 10 = 3,500 (5 × 7) × 10 x 10 x 10 = 35,000

5th Grade Go Math Book Question 9. 4 × 2 = 8 (4 × 2) × 10 1 = _______ (4 × 2) × 10 2 = _______ (4 × 2) × 10 3 = _______

Answer: 4 × 2 = 8 (4 × 2) × 10 1 = 80 (4 × 2) × 10 2 = 800 (4 × 2) × 10 3 = 8,000

Explanation: 4 × 2 = 8 (4 × 2) × 10 1 = 8 x 10 = 80 (4 × 2) × 10 2 = 8 x 10 x 10 = 800 (4 × 2) × 10 3 = 8 x 10 x 10 x 10 = 8,000

Question 10. 6 × 7 = 42 (6 × 7) × 10 1 = _______ (6 × 7) × 10 2 = _______ (6 × 7) × 10 3 = _______

Answer: 6 × 7 = 42 (6 × 7) × 10 1 = 420 (6 × 7) × 10 2 = 4,200 (6 × 7) × 10 3 = 42,000

Explanation: 6 × 7 = 42 (6 × 7) × 10 1 = 42 x 10 = 420 (6 × 7) × 10 2 = 42 x 10 x 10 = 4,200 (6 × 7) × 10 3 = 42 x 10 x 10 x 10 = 42,000

Question 11. (6 × 6) × 10 1 = ____

Answer: (6 × 6) × 10 1 =  360

Explanation: 6 x 6 =36 (6 × 6) × 10 1 = 36 x 10 = 360

Question 12. (7 × 4) × 10 3 = ____

Answer: 28,000

Explanation: 7 x 4 = 28 (7 × 4) × 10 1 = 28 x 10 = 280 (7 × 4) × 10 2 = 28 x 10 x 10 = 2,800 (7 × 4) × 10 3 = 28 x 10 x 10 x 10 = 28,000

Question 13. (9 × 8) × 10 2 = ____

Answer: 7,200

Explanation: (9 × 8) = 72 (9 × 8) × 10 1 = 72 x 10 = 720 (9 × 8) × 10 2 = 72 x 10 x 10 = 7,200

Question 14. (4 × 3) × 10 2 = ____

Answer: 1,200

Explanation: (4 × 3) = 12 (4 × 3) × 10 1 = 12 x 10 = 120 (4 × 3) × 10 2 = 12 x 10 x 10 = 1,200

Question 15. (2 × 5) × 10 3 = ____

Explanation: (2 × 5) = 10 (2 × 5) × 10 1 = 10 x 10 = 100 (2 × 5) × 10 2 = 10 x 10 x 10 = 1,000 (2 × 5) × 10 3 = 10 x 10 x 10 x 10 = 10,000

Question 16. (2 × 8) × 10 2 = ____

Answer: 1,600

Explanation: (2 × 8) = 16 (2 × 8) × 10 1 = 16 x 10 = 160 (2 × 8) × 10 2 = 16 x 10 x 10 = 1,600

Question 17. (6 × 5) × 10 3 = ____

Answer: 30,000

Explanation: (6 × 5) = 30 (6 × 5) × 10 1 = 30 x 10 = 300 (6 × 5) × 10 2 = 30 x 10 x 10 = 3,000 (6 × 5) × 10 3 = 30 x 10 x 10 x 10 = 30,000

Question 18. (8 × 8) × 10 4 = ____

Answer: 640,000

Explanation: (8 × 8) = 64 (8 × 8) × 10 1 = 64 x 10 = 640 (8 × 8) × 10 2 = 64 x 10 x 10 = 6,400 (8 × 8) × 10 3 = 64 x 10 x 10 x 10 = 64,000 (8 × 8) × 10 4 = 64 x 10 x 10 x 10 x 10 = 640,000

Question 19. (7 × 8) × 10 4 = ____

Answer: 560,000

Explanation: (7 × 8) = 56 (7 × 8) × 10 1 = 56 x 10 = 560 (7 × 8) × 10 2 = 56 x 10 x 10 = 5,600 (7 × 8) × 10 3 = 56 x 10 x 10 x 10 = 56,000 (7 × 8) × 10 4 = 56 x 10 x 10 x 10 x 10 = 560,000

Multiplication Patterns – Share and Show – Page No. 23

Use mental math to complete the table.

Explanation: 1 roll = 50 dimes ; Think:50 dimes per roll × 20 rolls =(5 × 2) × (10 × 10) = 10 x 10 2 50 dimes per roll × 30 rolls = (5 x 3) x (10 × 10) = 15 x 10 2 50 dimes per roll × 40 rolls = (5 x 4) x (20 × 10) = 20 x 10 2 50 dimes per roll × 50 rolls = (5 x 5) x (10 × 10) = 25 x 10 2 50 dimes per roll × 60 rolls = (5 x 6) x (10 × 10) = 30 x 10 2 50 dimes per roll × 70 rolls = (5 x 7) x (10 × 10) = 35 x 10 2 50 dimes per roll × 80 rolls = (5 x 8) x (10 × 10) = 40 x 10 2 50 dimes per roll × 90 rolls = (5 x 9) x (10 × 10) = 45 x 10 2 50 dimes per roll × 100 rolls = (5 x 10) x (10 × 10) = 50 x 10 2

Explanation: 1 roll = 40 quarters ; Think:40 quarters per roll × 20 rolls =(4 × 2) × (10 × 10) = 8 x 10 2 40 quarters per roll × 30 rolls =(4 × 3) × (10 × 10) = 12 x 10 2 40 quarters per roll × 40 rolls =(4 × 4) × (10 × 10) = 16 x 10 2 40 quarters per roll × 50 rolls =(4 × 5) × (10 × 10) = 20 x 10 2 40 quarters per roll × 60 rolls =(4 × 6) × (10 × 10) = 24 x 10 2 40 quarters per roll × 70 rolls =(4 × 7) × (10 × 10) = 28 x 10 2 40 quarters per roll × 80 rolls =(4 × 8) × (10 × 10) = 32 x 10 2 40 quarters per roll × 90 rolls =(4 × 9) × (10 × 10) = 36 x 10 2 40 quarters per roll × 100 rolls =(4 × 10) × (10 × 10) = 40 x 10 2

Explanation: 80 x 800 = 64 x 10 3 80 x 6 = (8 x 6) x 10 = 48 x 10 1 80 x 70 = (8 x 7) x (10 x 10) = 56 x 10 2 80 x 9,000 = (8 x 9) x (10 x 10 x 10 x 10) = 64 x 10 4

Explanation: Given that 90 x 9,000 = (9 x 9) x 10 x 10 x 10 x 10 = 81 x 10 4 90 x 6 = (9 x 6) x 10 = 54 x 10 1 90 x 70 = (9 x 7) x (10 x 10) = 63 x 10 2 90 x 800 = (9 x 8) x (10 x 10 x 10) = 72 x 10 3

Problem Solving

Use the table for 24–26.

Answer: 9,000 mm

Explanation: 9 × 10 3   = 9 x 10 x 10 x 10 = 9,000

Question 25. If you magnified the image of a fire ant by 4 × 10 3 and a treehopper by 3 × 10 3 , which insect would appear longer? How much longer? ____ mm

Answer: 10 3 mm

Explanation: fire ant: 4 × 10 3   = 4 x 10 x 10 x 10 = 4,000 mm tree hopper: 3 × 10 3 = 3 x 10 x 10 x 10 = 3,000 mm 4,000 > 3,000. So, the fire ant appears to be longer. 4,000 – 3,000 = 1,000 = 10 3

Question 26. John wants to magnify the image of a fire ant and a crab spider so they appear to be the same length. How many times their actual sizes would he need to magnify each image? Fire ant by _______ times Crab spider by ______ times

Answer: Fire ant by 5 times Crab spider by 4 times

Explanation: Given that Fire ant = 4 mm crab spider = 5 mm So, to make them have the same lengths, multiply fire ant by 5 mm and multiply Crab spider by 4 mm

Multiplication Patterns – Share and Show – Page No. 24

Question 27. What does the product of any whole-number factor multiplied by 100 always have? Explain. Type below: __________

Answer: The product of any whole number factor multiplied by 100 has two digits which are 0 in ones and tens place. Example: 2 x 100 = 200

Question 28. Test Prep How many zeros are in the product (5 × 4) × 10 4 ? Options: A. 3 B. 4 C. 5 D. 6

Answer: C. 5

Explanation: (5 × 4) × 10 4 = 20 x 10 4 = 2 x 10 5 5 zeroes

Use patterns and mental math to solve.

Question 29. The human body has about 30 times as many platelets as white blood cells. A small sample of blood has 8×10 3 white blood cells. About how many platelets are in the sample? ______ platelets

Answer: 24 x 10 4 platelets

Explanation: Let the number of platelets = s. s = 30 x 8×10 3 s = 30 x 8 x 10 x 10 x 10 = (3 x 8) x (10 x 10 x 10 x 10) = 24 x 10 4

Question 30. Basophils and monocytes are types of white blood cells. A blood sample has about 5 times as many monocytes as basophils. If there are 60 basophils in the sample, how many monocytes are there? ______ monocytes

Answer: 3 x 10 2 monocytes

Explanation: Let the number of monocytes = S S = 5 x 60 = 300 = 3 x 100 S = 3 x 10 2

Question 31. Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils. If there are 2 × 10 2 eosinophils in the sample, how many lymphocytes are there? ______ lymphocytes

Answer: 2 × 10 3 lymphocytes

Explanation: Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils. There are 2 × 10 2 eosinophils in the sample Then, Lymphocytes = 10 x 2 × 10 2 eosinophils = 2 × 10 3

Go Math Grade 5 Chapter 1 Extra Practice Answer Key Question 32. An average person has 6 × 10 2 times as many red blood cells as white blood cells. A small sample of blood has 7 × 10 3 white blood cells. About how many red blood cells are in the sample? ______ red blood cells

Answer: 42 x 10 5  red blood cells

Explanation: Let the red blood cells = S S = 7 × 10 3 x 6 × 10 2 S = 42 x 10 5 

Mid-Chapter Checkpoint – Vocabulary – Page No. 25

Choose the best term for the box.

Question 1. A group of three digits separated by commas in a multidigit number is a __ ________

Answer: Period

Question 2. An __ is the number that tells how many times a base is used as a factor ________

Answer: exponent

Concepts and Skills

Question 3. 7 is \(\frac{1}{10}\) of ______

Explanation: Let the unknown number is S. 7 = \(\frac{1}{10}\) S S = 7 X 10 = 70

Question 4. 800 is 10 times as much as ______

Explanation: Let the unknown number is S. 800 = 10S S = 800/10 = 80.

Question 5. 6,5 8 1,678 ________

Explanation: (6 x 1,000,000) + (5 x 1,00,000) + (8 x 10,000) + (1 x 1,000) + (6 x 100) + (7 x 10) + (8 x 1) 8 x 10,000 = 80,000

Question 6. 25, 6 34 ________

Answer: 600

Explanation: (2 x 10,000) + (5 x 1,000) + (6 x 100) + (3 x 10) + (4 x 1) 6 x 100 = 600

Question 7. 3 4 ,634,803 ________

Answer: 4,000,000

Explanation: (3 x 10,000,000) + (4 x 1,000,000) + (6 x 1,00,000) + (3 x 10,000) + (4 x 1,000) + (8 x 100) + (0 x 10) + (3 x 1) 4 x 1,000,000 = 4,000,000

Question 8. 2, 7 64,835 ________

Answer: 700,000

Explanation: (2 x 1,000,000) + (7 x 1,00,000) + (6 x 10,000) + (4 x 1,000) + (8 x 100) + (3 x 10) + (5 x 1) 7 x 1,00,000 = 700,000

Question 9. 8 × (14 + 7) = ________ + (8 × 7)

Answer: 8 × (14 + 7) = (8 x 14) + (8 × 7); Distributive Property of Multiplication

Explanation: 8 × (14 + 7) (8 x 14) + (8 × 7); Distributive Property of Multiplication

Question 10. 7 + (8 + 12) = ________ + 12

Answer: 7 + (8 + 12) = (7 + 8) + 12 Associative Property of Addition

Question 11. 10 3 = ______

Answer: 1,000

Explanation: 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000;

Question 12. 6 × 10 2 = ______

Explanation: 6 × 10 2 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 6 x 100 = 600

Go Math Grade 5 Chapter 1 Pdf Question 13. 4 × 10 4 = ______

Answer: 40,000

Explanation: 4 × 10 4 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 10 4 = 10 x 10 x 10 x 10 = 10,000; 4 x 10,000 = 40,000

Question 14. 70 × 300 = ______

Answer: 21,000

Explanation: 70 × 300 = (7 x 3) x (10 x 10 x 10) = 21 x 1,000 = 21,000

Question 15. (3 × 4) × 10 3 = ______

Answer: 12,000

Explanation: (3 × 4) × 10 3 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 12 x 1,000 = 12,000

Mid-Chapter Checkpoint – Page No. 26

Fill in the bubble completely to show your answer.

Question 16. DVDs are on sale for $24 each. Which expression can be used to find the cost in dollars of buying 4 DVDs? Options: A. (4 + 20) + (4 + 4) B. (4 × 20) + (4 × 4) C (4 + 20) × (4 + 4) D. (4 × 20) × (4 × 4)

Answer: B. (4 × 20) + (4 × 4)

Explanation: 24 can be written as 25 – 1 4 x 24 = 4 x (20 + 4) = (4 x 20) + (4 x 4)

Question 17. The Muffin Shop chain of bakeries sold 745,305 muffins last year. Which choice shows that number in expanded form? Options: A. (7 × 100,000) + (45 × 10,000) + (3 × 100) + (5 × 10) B. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (5 × 10) C. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (3 × 100) + (5 × 1) D. (7 × 100,000) + (4 × 10,000) + (3 × 100) + (5 × 1)

Answer: C. (7 × 100,000) + (4 × 10,000) + (5 × 1,000) + (3 × 100) + (5 × 1)

Explanation: First, we can write 745,305 as: 700,000 + 40, 000 + 5,000 + 300 + 5 (7 x 100,000) + (4 x 10,000) + (5 x 1,000) + (3 x 100) + 5

Go Math Grade 5 End of Year Assessment Answer Key Question 18. The soccer field at Mario’s school has an area of 6,000 square meters. How can Mario show the area as a whole number multiplied by a power of ten? Options: A. 6 × 10 4 sq m B. 6 × 10 3 sq m C. 6 × 10 2 sq m D. 6 × 10 1 sq m

Answer: B. 6 × 103 sq m

Explanation: 6,000 square meters = 6 x 1,000 = 6 x 10 x 10 x 10 = 6 × 10 3 sq m

Question 19. Ms. Alonzo ordered 4,000 markers for her store. Only \(\frac{1}{10}\) of them arrived. How many markers did she receive? Options: A. 4 B. 40 C. 400 D. 1,400

Answer: C. 400

Explanation: Ms. Alonzo ordered 4,000 markers for her store. Only \(\frac{1}{10}\) of them arrived. 4,000 x \(\frac{1}{10}\) = 400

Question 20. Mark wrote the highest score he made on his new video game as the product of 70 × 6,000. What was his score? Options: A. 420 B. 4,200 C. 42,000 D. 420,000

Answer: D. 420,000

Explanation: Mark wrote the highest score he made on his new video game as the product of 70 × 6,000. (7 x 6) x (10 x 10 x 10 x 10) = 42 x 10,000 = 420,000

Multiply by 1-digit numbers – Share and Show – Page No. 29

Complete to find the product.

Answer: 4,776

Estimate. Then find the product.

Question 2. Estimate: ___ 6 0 8 ×   8 ———- Estimate: ________ Product: 608 × 8 = ________

Answer: Estimate: 6,000 Product: 608 × 8 = 4,864

Explanation: Estimate: 608 is close to 600; 8 is close to 10 600 x 10 = 6,000 608 x 8 Multiply the ones; 8 x 8 = 64. 4 ones and 6 tens. Write the ones and the regrouped tens. Multiply the tens; 0 x 8 = 0 + 6 = 6 Multiply the hundreds; 6 x 8 = 48. So, 4,864 is the product of 608 × 8 Product: 4,864

Question 3. Estimate: __ 5 5 6 ×   4 ———– Estimate: ________ Product: 556 × 4 = ________

Answer: Estimate: 2,780 Product: 556 × 4 = 2,224

Explanation: Estimate: 556 is close to 550; 4 is close to 5 556 x 5 = 2,780 556 × 4 Multiply the ones; 6 x 4 = 24. 4 ones and 2 tens. Write the ones and the regrouped tens. Multiply the tens; 5 x 4 = 20 + 2 = 22; 2 tens and 2 hundreds. Write the tens and regroup the hundreds. Multiply the hundreds; 5 x 4 = 20; 20 + 2 = 22. So, 2,224 is the product of 556 × 4 Product: 2,224

Go Math Grade 5 Chapter 1 Review/Test Answer Key Question 4. Estimate: 1,925 ×    7 ———– Estimate: ________ Product: 1,925 × 7 = ________

Answer: Estimate: 10,000 Product: 1,925 × 7 = 13,475

Explanation: Estimate: 1,925 is close to 2000; 7 is close to 5 2,000 x 5 = 10,000 1,925 × 7 Multiply the ones; 7 x 5 = 35. 5 ones and 3 tens. Write the ones and the regrouped tens. Multiply the tens; 7 x 2 = 14; 14 + 3 = 17; 7 tens and 1 hundreds. Write the tens and regrouped hundreds. Multiply the hundreds; 7 x 9 = 63; 63 + 1 = 64. 4 hundred and 6 thousand Write the hundreds and regrouped thousands. Multiply the thousands; 7 x 1 = 7; 7 + 6 = 13 So, 13,475 is the product of 1,925 × 7 Product: 13,475

Question 5. Estimate:__ 7 9 4 ×   3 ———- Estimate: ________ Product:794 × 3 = ________

Answer: Estimate: 800 Product:794 × 3 = 2,382

Explanation: Estimate: 794 is close to 800 and 3 is close to 1 800 x 1 = 800 794 x 3 = (700 + 90 + 4) x 3 = (700 x 3) + (90 x 3) + (4 x 3) = 2100 + 270 + 12 = 2,382

Question 6. Estimate:___ 8 2 2 ×   6 ———- Estimate: ________ 822 × 6 = ________

Answer: Estimate: 4,000 822 × 6 = 4,932

Explanation: Estimate: 822 is close to 800 and 6 is close to 5 800 x 5 = 4,000 822 × 6 = (800 + 20 + 2) x 6 = (800 x 6) + (20 x 6) + (2 x 6) = 4800 + 120 + 12 = 4,932

Question 7. Estimate: 3,102 ×    5 ———– Estimate: ________ Product: 3,102 × 5 = ________

Answer: Estimate: 15,500 Product: 3,102 × 5 = 15,510

Explanation: Estimate: 3,102 is close to 3,100 and 5 is close to 5 3,100 x 5 = 15,500 3,102 x 5 = (3,000 + 100 + 0 + 2) x 5 = (3000 x 5) + (100 x 5) + 0 + (2 x 5) = 15,000 + 500 + 0 + 10 = 15,510

Algebra Solve for the unknown number.

Question 8. 3 9 6 ×   6 ——— 2, 3 6 396 × 6 = 23 ______ 6

Explanation: 396 x 6 = (300 + 90 + 6) x 6 = (300 x 6) + (90 x 6) + (6 x 6) = 1800 + 540 + 36 = 2376. So, the unknown number is 7

Question 9. 5,1 2 ×   8 ——– 16 Type below: __________

Answer: 5127 x 8 = 41,016. Unknown numbers = 7 and 410

Explanation: 5,127 x 8 = (5000 + 100 + 20 + 7) x 8 = (5000 x 8) + (100 x 8) + (20 x 8) + (7 x 8) = 40000 + 800 + 160 + 56 = 41,016

Question 10. 8, 5 6 ×    7 ——— 60,03 Type below: __________

Answer: 8,5 7 6 x 7 = 60,03 2

Explanation: 8,576 x 7 = (8000 + 500 + 70 + 6) x 7 = (8000 x 7) + (500 x 7) + (70 x 7) + (6 x 7) = 56000 + 3500 + 490 + 42 = 60,032

Practice: Copy and Solve Estimate. Then find the product.

Question 11. 116 × 3 = _______ Estimate: _______

Answer: Estimate: 300 116 × 3 = 348

Explanation: Estimate: 116 is close to 100; 100 x 3 = 300 116 x 3 6 x 3 =18; add ones and regroup tens 3 x 1 = 3; 3 + 1 = 4 3 x 1 = 3 So, 348 is the product

Question 12. 338 × 4 = _______ Estimate: _______

Answer: 338 × 4 = 1,352 Estimate: 1,200

Explanation: Estimate: 338 is close to 300; 300 x 4 = 1,200 338 × 4 8 x 4 =32; add ones and regroup tens 3 x 4 = 12; 12 + 3 = 15; add tens and regroup hundreds 3 x 4 = 12; 12 + 1 = 13 So, 1352 is the product

Question 13. 6 × 219 = _______ Estimate: _______

Answer: 6 × 219 = 1,314 Estimate: 1200

Explanation: Estimate: 219 is close to 200 200 x 6 = 1200 6 × 219 6 x 9 = 54; add ones and regroup tens 6 x 1 = 6; 6 + 5 = 11; add tens and regroup hundreds 6 x 2 = 12; 12 + 1 = 13 So, 1,314

Question 14. 7 × 456 = _______ Estimate: _______

Answer: 7 × 456 = 3192 Estimate: 3500

Explanation: Estimate: 456 is close to 500 500 x 7 = 3500 7 x 456 7 x 6 = 42; add ones and regroup tens 7 x 5 = 35; 35 + 4 = 39; add tens and regroup hundreds 7 x 4 = 28; 28 + 3 = 31 So, 3192

Question 15. 5 × 1,012 = _______ Estimate: _______

Answer: 5 × 1,012 = 5,060 Estimate: 5,000

Explanation: Estimate: 1,012 is close to 1,000 1,000 x 5 = 5,000 5 × 1,012 5 x 2 = 10; add ones and regroup tens 5 x 1 = 5; 5 + 1 = 6; add tens and regroup hundreds 5 x 0 = 0 5 x 1 = 5 So, 5,060

Question 16. 2,921 × 3 = _______ Estimate: _______

Answer: 2,921 × 3 = 8,763 Estimate: 9,000

Explanation: Estimate: 2,921 is close to 3,000 3,000 x 3 = 9,000 2,921 × 3 3 x 1 = 3; 3 x 2 = 6; 3 x 9 = 27; add hundreds and regroup thousands 3 x 2 = 6; 6 + 2 = 8 So, 8,763

Question 17. 8,813 × 4 = _______ Estimate: _______

Answer: 8,813 × 4 = 35,252 Estimate: 3,600

Explanation: Estimate: 8,813 is close to 9,000 9,000 x 4 = 3,600 8,813 × 4 4 x 3 = 12; add ones and regroup tens 4 x 1 = 4; 4 + 1 = 5; 4 x 8 = 32; add hundreds and regroup thousands 4 x 8 = 32; 32 + 3 = 35 So, 35,252

Question 18. 9 × 3,033 = _______ Estimate: _______

Explanation: Estimate: 3,033 is close to 3,000 3,000 x 9 = 27,000 9 × 3,033 9 x 3 = 27; add ones and regroup tens 9 x 3 = 27; 27 +  = 11; add tens and regroup hundreds 6 x 2 = 12; 12 + 1 = 13 So, 1,314

Multiply by 1-digit numbers – Problem Solving – Page No. 30

What’s the Error?

Question 19. The Plattsville Glee Club is sending 8 of its members to a singing contest in Cincinnati, Ohio. The cost will be $588 per person. How much will it cost for the entire group of 8 students to attend? Both Brian and Jermaine solve the problem. Brian says the answer is $40,074. Jermaine’s answer is $4,604. Estimate the cost. A reasonable estimate is _ $ ______

Answer: $4,800

Explanation: The Plattsville Glee Club is sending 8 of its members to a singing contest in Cincinnati, Ohio. The cost will be $588 per person. So, for entire group 8 x $588 = $4,704 Jermaine’s answer is correct. Because the $4,604 is close to $4,704 588 is close to 600. So, 600 x 8 = $4,800

Answer: When Brian multiplied the tens, he wrote the total number of tens in the product instead of regrouping, so the place values of his product are incorrect.

Question 19. What error did Jermaine make? Explain. Type below: __________

Answer: Jermaine regrouped the wrong amount of hundreds. He regrouped the tens as 6 hundred instead of 7 hundred. $588 x 8 = $4,704

Question 19. How could you predict that Jermaine’s answer might be incorrect using your estimate? Type below: __________

Answer: I used 600 × 8 to estimate the product; 588 is 12 less than 600. Since 12 × 8 = 96, and 4,604 is almost 200 less than the estimate of 4,800, the answer is probably too low.

Multiply by 2-digit numbers – Share and Show – Page No. 33

Complete to find the product

Answer: 2,752

Explanation: 64 x 3 = 192 64 x 40 = 2,560 2,560 + 192 = 2,752

Answer: 21,698

Explanation: 571 x 8 = 4,568 571 x 30 = 17,130 17,130 + 4,568 = 21,698

Question 3. Estimate:____ 2 4 × 1 5 ———- Estimate: ________ Product: ________

Answer: Estimate: 300 Product: 360

Explanation: 2 4 x 15 Estimate: 20 x 15 = 300 24 x 5 = 120 24 x 10 = 240 Product:: 240 + 120 = 360

Question 4. Estimate:____ 3 7 × 6 3 ———- Estimate: ________ Product: ________

Answer: Estimate: 2,400 Product: 2,331

Explanation: 37 x 63 Estimate: 40 x 60 = 2,400 37 x 3 = 111 37 x 60 = 2220 Product:: 2220 + 111 = 2,331

Multiply by 1 Digit Numbers Lesson 1.6 Question 5. Estimate:____ 3 8 4 × 4 5 ———- Estimate: ________ Product: ________

Answer: Estimate: 20,000 Product: 17,280

Explanation: 384 x 45 Estimate: 400 x 50 = 20,000 384 x 5 = 1920 384 x 40 = 15,360 Product:: 15,360 + 1920 = 17,280

Question 6. Estimate:____ 2 8 × 2 2 ———- Estimate: ________ Product: ________

Answer: Estimate: 600 Product: 616

Explanation: 28 x 22 Estimate: 30 x 20 = 600 28 x 2 = 56 28 x 20 = 560 Product:: 56 + 560 = 616

Question 7. Estimate:____ 9 3 × 7 6 ———- Estimate: ________ Product: ________

Answer: Estimate: 7200 Product: 7,068

Explanation: 93 x 76 Estimate: 90 x 80 = 7200 93 x 6 = 558 93 x 70 = 6,510 Product:: 558 + 6,510 = 7,068

Question 8. Estimate:____ 2 9 5 × 5 1 ———- Estimate: ________ Product: ________

Answer: Estimate: 15,000 Product: 15,045

Explanation: 295 x 51 Estimate: 300 x 50 = 15,000 295 x 1 = 295 295 x 50 = 14,750 Product:: 295 + 14,750 = 15,045

Question 9. Estimate: ________ 54 × 31 = ________

Answer: Estimate: 1,500 Product: 1,674

Explanation: 54 x 31 Estimate: 50 x 30 = 1,500 54 x 1 = 54 54 x 30 = 1,620 Product:: 54 + 1,620 = 1,674

Question 10. Estimate: ________ 42 × 26 = ________

Answer: Estimate: 1,200 Product: 1,092

Explanation: 42 x 26 Estimate: 40 x 30 = 1,200 42 x 6 = 252 42 x 20 = 840 Product:: 252 + 840 = 1,092

Go Math Grade 5 Workbook Question 11. Estimate: ________ 38 × 64 = ________

Answer: Estimate: 2,400 Product: 2,432

Explanation: 38 × 64 Estimate: 40 x 60 = 2,400 38 x 4 = 152 38 x 60 = 2,280 Product:: 152 + 2,280 = 2,432

Question 12. Estimate: ________ 63 × 16 = ________

Answer: Estimate: 1,200 Product: 1,008

Explanation: 63 x 16 Estimate: 60 x 20 = 1,200 63 x 6 = 378 63 x 10 = 630 Product:: 378 + 630 = 1,008

Question 13. Estimate: ________ 204 × 41 = ________

Answer: Estimate: 8,000 Product: 8,364

Explanation: 204 × 41 Estimate: 200 x 40 = 8,000 204 x 1 = 204 204 x 40 = 8,160 Product:: 204 + 8,160 = 8,364

Place Value Patterns 5th Grade Go Math Question 14. Estimate: ________ 534 × 25 = ________

Answer: Estimate: 15,000 Product: 13,350

Explanation: 534 x 25 Estimate: 500 x 30 = 15,000 534 x 5 = 2,670 534 x 20 = 10,680 Product:: 2,670 + 10,680 = 13,350

Question 15. Estimate: ________ 722 × 39 = ________

Answer: Estimate: 28,000 Product: 28,158

Explanation: 722 × 39 Estimate: 700 x 40 = 28,000 722 x 9 = 6,498 722 x 30 = 21,660 Product:: 6,498 + 21,660 = 28,158

Question 16. Estimate: ________ 957 × 43 = ________

Answer: Estimate: 40,000 Product: 44,022

Explanation: 957 × 43 Estimate: 1,000 x 40 = 40,000 957 x 3 = 2,871 957 x 40 = 41,151 Product:: 2,871 + 41,151 = 44,022

Multiply by 2-digit numbers – Problem Solving – Page No. 34

Use the table for 17–20.

Answer: 4,004 hours

Explanation: 52 weeks x 77 = 4,004 hours

Question 18. In 1 year, how many more hours of sleep does a giant armadillo get than a platypus? _____ hours

Answer: 1,508 hours

Explanation: giant armadillo: 52 x 127 = 6,604 platypus: 52 x 98 = 5,096 6,604 – 5,096 = 1,508

Question 19. Owl monkeys sleep during the day, waking about 15 minutes after sundown to find food. At midnight, they rest for an hour or two, then continue to feed until sunrise. They live about 27 years. How many hours of sleep does an owl monkey that lives 27 years get in its lifetime? _____

Answer: 4927.5 days

Explanation: Given that the time of Owl monkeys sleep during the day walking about 15 minutes after sundown. Then, at midnight they rest for an hour or two then continue to feed until sunrise. Notice that the above description doesn’t say that they sleep in after sundown. They either eat or rest. Day time is usually considered from 6 am to 6 pm which is a total of 12 hours. As per the given information, owl monkey sleeps in that period. Given that owl, monkeys live for 27 years. So the time for sleeping in their lifetime = 12 hours * 27 years = (12/24 days) * 27 years = (1/2 days) * 27 years = (1/2 days) * (27*365 days) = (1/2 days) * (9855 days) = 4927.5 days Hence final answer is 4927.5 days.

Go Math Grade 5 Answer Key Chapter 1 Question 20. Three-toed sloths move very slowly, using as little energy as possible. They sleep, eat, and even give birth upside down. A baby sloth may cling to its mother for as much as 36 weeks after being born. How much of that time is the sloth asleep? _____ hours

Answer: 3,636 hours

Explanation: 101 x 36 = 3,636

Question 21. Test Prep A sloth’s maximum speed on the ground is 15 feet in 1 minute. Even though it would be unlikely for a sloth to stay in motion for more than a few moments, how far would a sloth travel in 45 minutes at that speed? Options: A. 60 feet B. 270 feet C. 675 feet D. 6,750 feet

Answer: C. 675 feet

Explanation: The sloth’s maximum speed on the ground is 15 feet in 1 minute. For 45 minutes, 45 x 15 = 675 feet

Relate Multiplication to Division – Share and Show – Page No. 37

Explanation: Brad has 18 toy cars in each group. Because 72÷4 =18 4 × 18 = 72 4 x (9 + 9) = (4 x 9) + (4 x 9)

Use multiplication and the Distributive Property to find the quotient.

Question 2. 108 ÷ 6 = _____

Explanation: 108 ÷ 6 6 x 18 = 6 x (9 + 9) = (6 x 9) + (6 x 9) = 54 + 54 = 108 (36 + 72) ÷ 6 = (36 ÷ 6) + (72÷ 6) = 6 + 12 = 18

Question 3. 84 ÷ 6 = _____

Explanation: 84 ÷ 6 (42 + 42) ÷ 6 = (42÷ 6) + (42÷ 6) = 7 + 7 = 14 6 x 14 = 6 x (7 + 7) = (6 x 7) + (6 x 7) = 42 + 42 = 84

Question 4. 184 ÷ 8 = _____

Explanation: 184 ÷ 8 (92 + 92) ÷ 8 = (92÷ 8) + (92÷ 8) = 11.5 + 11.5 = 23 8 x 23 = 8 x (11 + 12) = (8 x 11) + (8 x 12) = 88 + 96 = 184

Question 5. 60 ÷ 4 = _____

Explanation: 60 ÷ 4 (20 + 40) ÷ 4 = (20 ÷ 4) + (40 ÷ 4) = 5 + 10 = 15 4 x 15 = 4 x (7+ 8) = (4 x 7) + (4 x 8) = 28 + 32 = 60

Question 6. 144 ÷ 6 = _____

Explanation: 144 ÷ 6 (72 + 72) ÷ 6 = (72 ÷ 6) + (72 ÷ 6) = 12 + 12 = 24 6 x 24 = 6 x ( 12 + 12) = (6 x 12) + (6 x 12) = 72 + 72 = 144

Question 7. 252 ÷ 9 = _____

Explanation: 252 ÷ 9 (126 + 126) ÷ 9 = (126 ÷ 9) + (126 ÷ 9) = 14 + 14 = 28 6 x 28 = 6 x ( 14 + 14) = (6 x 14) + (6 x 14) = 126 + 126 = 252

Find each quotient. Then compare. Write <, > or =.

Question 8. 51 ÷ 3 _____ 68 ÷ 4

Answer: 51 ÷ 3 = 68 ÷ 4

Explanation: 51 ÷ 3 = 17 68 ÷ 4 = 17 17 = 17.

Question 9. 252 ÷ 6 _____ 135 ÷ 3

Answer: 252 ÷ 6 < 135 ÷ 3

Explanation: 252 ÷ 6 = 42 135 ÷ 3 = 45 42 < 45

Go Math Common Core Grade 5 Answer Key Question 10. 110 ÷ 5 _____ 133 ÷ 7

Answer: 110 ÷ 5 > 133 ÷ 7

Explanation: 110 ÷ 5 = 22 133 ÷ 7 = 19 22 > 19

Relate Multiplication to Division – Problem Solving – Page No. 38

Use the table to solve 11–13.

Answer: 7 balls

Explanation: A group of 6 friends shares a bag of the 45-millimeter bouncy balls equally among them. 45/6 = 7 balls and 3 balls remained

Question 12. Mr. Henderson has 2 bouncy-ball vending machines. He buys one bag of the 27-millimeter balls and one bag of the 40-millimeter balls. He puts an equal number of each in the 2 machines. How many bouncy balls does he put in each machine? ________ balls of the 27-millimeter. ________ balls of the 40-millimeter. ________ total balls

Answer: 51 balls of the 27-millimeter 29 balls of the 40-millimeter 80 total balls

Explanation: There are 51 27 mm, 29 40 mm

Question 13. Lindsey buys a bag of each size of a bouncy ball. She wants to put the same number of each size of bouncy ball into 5 party-favor bags. How many of each size of bouncy ball will she put in a bag? ________ balls of the 27-millimeter ________ balls of the 40-millimeter ________ balls of the 45-millimeter

Answer: 34 balls of the 27-millimeter 12 balls of the 40-millimeter 34 balls of the 45-millimeter

Explanation: There are 34 27 mm, 12 40 mm, and 34 45 mm bouncy balls

Question 14. What’s the Error? Sandy writes (4 × 30) + (4 × 2) and says the quotient for 128 ÷ 4 is 8. Is she correct? Explain. 128 ÷ 4 = ____

Answer: Sandy’s answer is incorrect. 128 ÷ 4 = 32

Explanation: (4 × 30) + (4 × 2) = 120 + 8 = 128 128 ÷ 4 = 32. (4 × 30) + (4 × 2) = 4 x (30 + 2) = 4 x 32 = 128. 128 ÷ 4 = 32

Question 15. Test Prep Which of the following can be used to find 150 ÷ 6? Options: A. (6 × 20) + (6 × 5) B. (6 × 10) + (6 × 5) C. (2 × 75) + (2 × 3) D. (6 × 15) + (6 × 5)

Answer: A. (6 × 20) + (6 × 5)

Explanation: 150 ÷ 6 = 25 25 x 6 = 150 6 x 25 = 6 x (20 + 5) = (6 × 20) + (6 × 5)

Problem Solving Multiplication and Division – Share and Show – Page No. 41

Question 1. To make concrete mix, Monica pours 34 pounds of cement, 68 pounds of sand, 14 pounds of small pebbles, and 19 pounds of large pebbles into a large wheelbarrow. If she pours the mixture into 9 equalsize bags, how much will each bag weigh? First, find the total weight of the mixture. ____ pounds

Answer: 135 pounds

Explanation: 34 + 68 + 14 + 19 = 135

Question 1. Then, divide the total by the number of bags. Break the total into two simpler numbers to make the division easier, if necessary. Finally, find the quotient and solve the problem. So, each bag will weigh _ pounds. ____ pounds

Answer: 15 pounds

Explanation: now, calculate 135/9 = 15 pounds.

Go Math Lesson 1.10 5th Grade Answer Key Question 2. What if Monica pours the mixture into 5 equal-size bags? How much will each bag weigh? ____ pounds

Answer: 27 poundsMultiply by 1-Digit Numbers Lesson 1.6

Explanation: 135/5 = 27

Question 3. Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets. How many doghouses can Taylor make from 12 bundles of plywood? ____

Answer: 56 doghouses

Explanation: Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 14 full sheets. (12 x 14)/3 = 168/3 = 56 doghouses

Question 4. Eileen is planting a garden. She has seeds for 60 tomato plants, 55 sweet corn plants, and 21 cucumber plants. She plants them in 8 rows, with the same number of plants in each row. How many seeds are planted in each row? ____ seeds / row

Answer: 17 seeds

Explanation: Eileen is planting a garden. She has seeds for 60 tomato plants, 55 sweet corn plants, and 21 cucumber plants. She plants them in 8 rows, with the same number of plants in each row. 60 + 55 + 21 = 136 136/8 = 17

Problem Solving Multiplication and Division – On Your Own – Page No. 42

Question 5. Starting on day 1 with 1 jumping jack, Keith doubles the number of jumping jacks he does every day. How many jumping jacks will Keith do on day 10? ____  jumping jack

Answer: 512 jumping jacks

Explanation: She doubled the number so you’re supposed to multiply by 2. On day 1, 1 jumping pack; On day 2, 2 jumping packs; On day 3, 2 x 2 = 4 jumping packs; On day 4, 2 x 2 x 2 = 8 jumping packs; On day 5, 2 x 2 x 2 x 2 = 16 jumping packs; On day 6, 2 x 2 x 2 x 2 x 2 = 32 jumping packs; On day 7, 2 x 2 x 2 x 2 x 2 x 2 = 64 jumping packs; On day 8, 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 jumping packs; On day 9, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 jumping packs; On day 10, 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 jumping packs; 512 jumping jacks

Answer: 8 ways

Question 7. On April 11, Millie bought a lawn mower with a 50-day guarantee. If the guarantee begins on the date of purchase, what is the first day on which the mower will no longer be guaranteed? __________

Answer: May 31

Explanation: The guarantee begins on April 11. April has 30 days. So, we have 20 days of the guarantee in April. May has 31 days. So, we have 30 days of the guarantee in May. Therefore, the last day of the guarantee is May 31.

Question 8. A classroom bulletin board is 7 feet by 4 feet. If there is a picture of a student every 6 inches along the edge, including one in each corner, how many pictures are on the bulletin board? ____ pictures

Answer: 40 pictures

Explanation: 2 pictures per foot, so that’s 14 pics along the top and bottom (counting the corners), and 6 pictures along each side (not counting the corners) 14+14+6+6 = 40

Question 9. Dave wants to make a stone walkway. The rectangular walkway is 4 feet wide and 12 feet long. Each 2 foot by 2 foot stone covers an area of 4 square feet. How many stones will Dave need to make his walkway? ____ stones

Answer: 12 stones

Explanation: Area of walkway = 4 x 12 = 48 square feet Area of 1 stone = 2 x 2 = 4 square feet 48/4 = 12 stones.

Question 10. Test Prep Dee has 112 minutes of recording time. How many 4-minute songs can she record? Options: A. 28 B. 27 C. 18 D. 17

Answer: A. 28

Explanation: Dee has 112 minutes of recording time. 112/4 = 28

Numerical Expressions – Share and Show – Page No. 45

Circle the expression that matches the words.

Question 1. Teri had 18 worms. She gave 4 worms to Susie and 3 worms to Jamie. (18 – 4) + 3         18 – (4 + 3) __________

Answer: 18 – (4 + 3)

Explanation: Teri had 18 worms. She gave 4 worms. 18 – 4 = 14. 3 worms to Jamie 14 – 3 = 11. (18 – 4) + 3 = 14 + 3 = 17 not equal to 11; 18 – (4 + 3) = 18 – 7 = 11 = 11

Question 2. Rick had $8. He then worked 4 hours for $5 each hour. $8 + (4 × $5)       ($8 + 4) × $5 __________

Answer: $8 + (4 × $5)

Explanation: Rick had $8. He then worked 4 hours for $5 each hour = 4 x $5 = $20; $20 +$8 =$28. $8 + (4 × $5) = 8 + 20 = $28 = $28.

Write an expression to match the words.

Question 3. Greg drives 26 miles on Monday and 90 miles on Tuesday. Type below: __________

Answer: 26 + 90 = 116 miles

Explanation: Greg drives 26 miles on Monday and 90 miles on Tuesday. 26 + 90 = 116 miles

Question 4. Lynda has 27 fewer fish than Jack. Jack has 80 fish. Type below: __________

Answer: 80 – 27 = 53

Explanation: Lynda has 27 fewer fish than Jack. Jack has 80 fish. 80 – 27 = 53

Write words to match the expression.

Question 5. 34 – 17 Type below: __________

Answer: Anna has 17 fewer apples than Jack. Jack has 34 apples.

Explanation: 34 – 17 = 17. Anna has 17 fewer apples than Jack. Jack has 34 apples.

Question 6. 6 × (12 – 4) Type below: __________

Answer: Teri had 12 worms. She gave 4 worms to Susie. She sell the remaining worms for $6 each.

Explanation: Teri had 12 worms. She gave 4 worms to Susie. She sell the remaining worms for $6 each.

Question 7. José shared 12 party favors equally among 6 friends. Type below: __________

Answer: 12/6 = 2

Explanation: José shared 12 party favors equally among 6 friends. 12/6 = 2

Question 8. Braden has 14 baseball cards. He finds 5 more baseball cards. Type below: __________

Answer: 14 + 5 = 19

Explanation: Braden has 14 baseball cards. He finds 5 more baseball cards. 14 + 5 = 19

Question 9. Isabelle bought 12 bottles of water at $2 each. Type below: __________

Answer: 12 x $2 = $24

Explanation: Isabelle bought 12 bottles of water at $2 each. 12 x $2 = $24

Question 10. Monique had $20. She spent $5 on lunch and $10 at the bookstore. Type below: __________

Answer: 20 – (5 + 10)

Explanation: Monique had $20. She spent $5 on lunch and $10 at the bookstore. 20 – (5 + 10)

Question 11. 36 ÷ 9 Type below: __________

Answer: Anna shared 36 apples with 9 friends.

Question 12. 35 – (16 + 11) Type below: __________

Answer: Monique had 35 balls. She gave 16 to her one frined and 11 to other friend.

Draw a line to match the expression with the words.

Question 13. Fred catches 25 fish. Then he releases 10 fish and catches 8 more.     •        •3 × (15 – 6)

Nick has 25 pens. He gives 10 pens to one friend and 8 pens to another friend.  •     •15 – 6

Jan catches 15 fish and lets 6 fish go.       •     •25 – (10 + 8)

Libby catches 15 fish and lets 6 fish go for three days in a row.                             •     •(25 – 10) + 8 Type below: __________

Answer: Fred catches 25 fish. Then he releases 10 fish and catches 8 more = (25 – 10) + 8 Nick has 25 pens. He gives 10 pens to one friend and 8 pens to another friend = 25 – (10 + 8) Jan catches 15 fish and lets 6 fish go = 15 – 6 Libby catches 15 fish and lets 6 fish go for three days in a row = 3 × (15 – 6)

Numerical Expressions – Problem Solving – Page No. 46

Question 14. Write a numerical expression to represent the total number of lemon tetras that could be in a 20-gallon aquarium. _____ lemon tetras

Answer: 2 lemon tetras

Explanation: From the given data, increase each inch of length, 1 gallon of water increases. 2 + 3 + 5 + 3 + 5 = 18 inches. So, 18 gallons of water are available in the aquarium. Add 1 lemon tetra to get the 20 gallons of water. So, in total there are 2 lemon tetra available.

Powers of 10 and Exponents Lesson 1.4 Answer Key Question 15. Write a word problem for an expression that is three times as great as (15 + 7). Then write the expression. Type below: __________

Answer: 3 x (15 + 7)

Explanation: Given that that is three times as great as (15 + 7)

Question 16. What’s the Question? Lu has 3 swordtails in her aquarium. She buys 2 more swordtails. Type below: __________

Answer: 3 + 2 = 5

Explanation: Lu has 3 swordtails in her aquarium. She buys 2 more swordtails. So, 3 + 2 = 5 swordtails

Question 17. Tammy gives 45 stamps to her 9 friends. She shares them equally with her friends. Write an expression to match the words. How many stamps does each friend get? _____ stamps

Answer: 45/9 = 5 stamps

Explanation: Tammy gives 45 stamps to her 9 friends. 45/9 = 5.

Question 18. Test Prep Josh has 3 fish in each of the 5 buckets. Then he releases 4 fish. Which expression matches the words? Options: a. (3 × 4) – 5 b. (5 × 4) – 3 c. (5 × 3) – 4 d. (5 – 3) × 4

Answer: c. (5 × 3) – 4

Explanation: Josh has 3 fish in each of 5 buckets. 3 x 5. Then he releases 4 fish. (3 x 5) – 4

Evaluate Numerical Expressions – Share and Show – Page No. 49

Evaluate the numerical expression.

Question 1. 10 + 36 ÷ 9 _____

Explanation: 10 + 36 ÷ 9 = 10 + (36 ÷ 9) = 10 + 4 = 14

Question 2. 10 + (25 – 10) ÷ 5 _____

Explanation: 10 + (25 – 10) ÷ 5 = 10 + 15 ÷ 5 = 10 + (15 ÷ 5) = 10 + 3 = 13

Question 3. 9 – (3 × 2) + 8 _____

Explanation: 9 – (3 × 2) + 8 = 9 – 6 + 8 = 3 + 8 = 11

Question 4. (4 + 49) – 4 × 10 _____

Explanation: (4 + 49) – 4 × 10 = 53 – 4 x 10 = 53 – (4 x 10) = 53 – 40 = 13

Question 5. 5 + 17 – 100 ÷ 5 _____

Explanation: 5 + 17 – 100 ÷ 5 = (5 + 17) – (100 ÷ 5) = 22 – 20 = 2

Question 6. 36 – (8 + 5) _____

Explanation: 36 – (8 + 5) = 36 – 13 = 23

Question 7. 125 – (68 + 7) _____

Explanation: 125 – (68 + 7) = 125 – 75 = 50

Question 8. (4 × 6) – 12 _____

Explanation: (4 × 6) – 12 = 24 – 12 = 12

Question 9. 3 × (22 – 2) _____

Explanation: 3 × (22 – 2) = 3 x 20 = 60

Question 10. 23 + (16 – 7) _____

Explanation: 23 + (16 – 7) = 23 + 9 = 32

Question 11. (25 – 4) ÷ 3 _____

Explanation: (25 – 4) ÷ 3 = 21 ÷ 3 = 7

Rewrite the expression with parentheses to equal the given value.

Question 12. 100 – 30 ÷ 5 value: 14 Type below: __________

Answer: (100 – 30) ÷ 5 = 14

Explanation: 100 – 30 ÷ 5 = (100 – 30) ÷ 5 = 70 ÷ 5 = 14

Question 13. 12 + 17 – 3 × 2 value: 23 Type below: __________

Explanation: (12 + 17) – (3 × 2) = 29 – 6 = 23

Question 14. 9 + 5 ÷ 5 + 2 value: 12 Type below: __________

Explanation: 9 + (5 ÷ 5) + 2 = 9 + 1 + 2 = 12

Evaluate Numerical Expressions – UNLOCK the Problem – Page No. 50

Answer: We have to know the number of seats in each row to calculate the total number of seats.

Question 15. b. What operation can you use to find the number of seats in the back group of seats? Write the expression. Type below: __________

Answer: A group of seats in the back has 5 rows with 30 seats in each row. So, to calculate the number of seats, we can use multiplication.

Question 15. c. What operation can you use to find the number of seats in both groups of side seats? Write the expression. Type below: __________

Answer: 2 x (20 x 6) = 2 x 120 = 240

Question 15. d. What operation can you use to find the number of seats in the middle group? Write the expression. Type below: __________

Answer: 20 x 20 = (2 x 2) x (10 x 10) = 4 x 100 = 400

Question 15. e. Write an expression to represent the total number of seats in the theater. Type below: __________

Answer: (20 x 20) + (2 x 20 x 6) + (5 x 30)

Question 15. f. How many seats are in the theater? Show the steps you use to solve the problem. _____ seats

Answer: (20 x 20) + (2 x 20 x 6) + (5 x 30) = 400 + 240 + 150 = 640 + 150 = 790

Place Value Lessons 5th Grade Question 16. Test Prep In the wild, an adult giant panda eats about 30 pounds of food each day. Which expression shows how many pounds of food 6 pandas eat in 3 days? Options: a. 3 + (30 × 6) b. 3 × (30 × 6) c. (30 × 6) ÷ 3 d. (30 × 6) – 3

Answer: b. 3 × (30 × 6)

Explanation: 1 panda eats 30 pounds of food each day. for 3 days, 3 x 30 = 90 1 panda eats 90 pounds of food in 3 days. 6 pandas can eat 90 x 6 = 540 pounds. 3 + (180) = 183 not equal to 540 pounds. 3 x (30 x 6) = 3 x (180) = 540

Question 17. Test Prep Which expression has a value of 6? Options: a. (6 ÷ 3) × 4 + 8 b. 27 – 9 ÷ 3 × ( 4 + 1) c. (18 + 12) × 6 – 4 d. 71 – 5 × (9 + 4)

Answer: d. 71 – 5 × (9 + 4)

Explanation: (6 ÷ 3) × 4 + 8 = 2 x 4 + 8 = 8 + 8 = 16 27 – 9 ÷ 3 × ( 4 + 1) = 27 – (9 ÷ 3) × 5 = 27 – 3 x 5 = 27 – 15 = 12 (18 + 12) × 6 – 4 = 180 – 4 = 176 71 – 5 × (9 + 4) = 71 – (5 x 13) = 71 – 65 = 6

Grouping Symbols – Share and Show – Page No. 53

Question 1. 12 + [(15 – 5) + (9 – 3)] 12 + [10 + ____] 12 +____ ____

Answer: 12 + [(15 – 5) + (9 – 3)] 12 + [10 + 6] 12 + 16 28

Question 2. 5 × [(26 – 4) – (4 + 6)] ____

Answer: 5 × [(26 – 4) – (4 + 6)] 5 x [22 – 10] 5 x 12 = 60

Question 3. 36 ÷ [(18 – 10) – (8 – 6)] ____

Answer: 36 ÷ [(18 – 10) – (8 – 6)] 36 ÷ [8 – 2] 36 ÷ 6 = 6

Question 4. 4 + [(16 – 4) + (12 – 9)] ____

Answer: 4 + [(16 – 4) + (12 – 9)] 4 + [12 + 3] 4 + 15 = 19

Question 5. 24 – [(10 – 7) + (16 – 9)] ____

Answer: 24 – [(10 – 7) + (16 – 9)] 24 – [3 + 7] = 24 – 10 = 14

Question 6. 16 ÷ [(13 + 7) – (12 + 4)] ____

Answer: 16 ÷ [(13 + 7) – (12 + 4)] 16 ÷ [20 – 16] 16 ÷ 4 = 4

Question 7. 5 × [(7 – 2) + (10 – 8)] ____

Answer: 5 × [(7 – 2) + (10 – 8)] 5 x [5 + 2] 5 x 7 = 35

Question 8. [(17 + 8) + (29 – 12)] ÷ 6 ____

Answer: [(17 + 8) + (29 – 12)] ÷ 6 [25 + 17] ÷ 6 42 ÷ 6 = 7

Question 9. [(6 × 7) + (3 × 4)] – 28 ____

Answer: [(6 × 7) + (3 × 4)] – 28 [42 + 12] – 28 54 – 28 = 26

Question 10. 3 × {[(12 – 8) × 2] + [(11 – 9) × 3]} ____

Answer: 3 × {[(12 – 8) × 2] + [(11 – 9) × 3]} 3 x {[4 x 2] + [2 x 3]} 3 x {8 + 6} 3 x 14 = 42

Question 11. {[(3 × 4) + 18] + [(6 × 7) – 27]} ÷ 5 ____

Answer: {[(3 × 4) + 18] + [(6 × 7) – 27]} ÷ 5 {[12 + 18] + [42 – 27]} ÷ 5 {30 + 15} ÷ 5 45 ÷ 5 = 9

Grouping Symbols – UNLOCK the Problem – Page No. 54

Answer: Each day, Dan displays 24 roses (gives away 10 and sells the rest), and he displays 36 carnations (gives away 12 and selles the rest).

Question 12. b. What are you being asked to do? Type below: __________

Answer: We have to find out how many roses and carnations Dan sells in a week.

Question 12. c. What expression shows how many roses Dan sells in one day? Type below: __________

Answer: 24 – 10 = 14 roses

Question 12. d. What expression shows how many carnations Dan sells in one day? Type below: __________

Answer: 36 – 12 = 24 carnation

Question 12. e. Write an expression to represent the total number of roses and carnations Dan sells in one day. Type below: __________

Answer: (24 – 10) + (36 – 12) = 14 + 24 = 38 roses and carnations

Question 12. f. Write the expression that shows how many roses and carnations Dan sells in a week. Type below: __________

Answer: 7 x ((24 – 10) + (36 – 12)) = 7 x (14 + 24) = 7 x 38 = 266 roses and carnations

Question 13. Evaluate the expression to find out how many roses and carnations Dan sells in a week. ____ flowers

Answer: 7 x ((24 – 10) + (36 – 12)) 7 x (14 + 24) 7 x 38 = 266 roses and carnations

Explanation:

Question 14. Test Prep Which expression has a value of 4? Options: a. [(4 × 5) + (9 + 7)] + 9 b. [(4 × 5) + (9 + 7)] ÷ 9 c. [(4 × 5) – (9 + 7)] × 9 d. [(4 + 5) + (9 + 7)] – 9

Answer: b. [(4 × 5) + (9 + 7)] ÷ 9

Explanation: [(4 × 5) + (9 + 7)] + 9 = [20 + 16] + 9 = 36 + 9 = 45 [(4 × 5) + (9 + 7)] ÷ 9 = [20 + 16] ÷ 9 = 36 ÷ 9 = 4

Chapter Review/Test – Vocabulary – Page No. 55

Question 1. The ____ states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products. __________

Answer: Distributive Property

Question 2. 7,000 is 10 times as much as _____

Explanation: Let the unknown number is S. 7,000 = 10S S = 7,000/10 = 700. 7,000 is 10 times as much as 700.

Question 3. 50 is \(\frac{1}{10}\) of _____

Answer: 500

Explanation: Let the unknown number is S. 50 = \(\frac{1}{10}\) S S = 50 X 10 = 500

Question 4. 4 × (12 + 14) = Type below: ________

Answer: 104; Distributive Property of Multiplication

Explanation: 4 × (12 + 14) = (4 x 12) + (4 x 14) = 48 + 56 = 104; Distributive Property of Multiplication

Question 5. 45 + 16 =__ + 45 Type below: Type below: ________

Answer: 45 + 16 = 16 + 45; Commutative Property of Addition

Explanation: 45 + 16 = 16 + 45; Commutative Property of Addition

Question 6. 10 2 = _____

Question 7. 3 × 10 4 = _____

Explanation: 3 × 10 4 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 10 4 = 10 x 10 x 10 x 10 = 10,000; 3 x 10,000 = 30,000

How do you use Place Value and Patterns to Solve Problems Question 8. 8 × 10 3 = _____

Answer: 8,000

Explanation: 8 × 10 3 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 8 x 1,000 = 8,000

Question 9. Estimate: 5 7 9 ×   6 ———- Estimate: _____ Product: _____

Answer: Estimate: 3,600 Product: 3,474

Explanation: Estimate: 579 is close to 600; 600 x 6 = 3,600 579 x 6 6 x 9 =54; add ones and regroup tens 6 x 7 = 42; 42 + 5 = 47; add tens and regroup hundreds 6 x 5 = 30; 30 + 4 = 34 So, 3,474 is the product

Question 10. Estimate: 7,316 ×    6 ———- Estimate: _____ Product: _____

Answer: Estimate: 42,000 Product: 43,986

Explanation: Estimate: 7,316 is close to 7,000; 7,000 x 6 = 42,000 7,316 x 6 6 x 6 = 36; add ones and regroup tens 6 x 1 = 6; 6 + 3 = 18; add tens and regroup hundreds 6 x 3 = 18; 18 + 1 = 19; add hundreds and regroup thousads 6 x 7 = 42; 42 + 1 = 43 So, 43,986 is the product

Question 11. Estimate: 4 3 6 × 3 2 ———- Estimate: _____ Product: _____

Answer: Estimate: 12,000 Product: 13,952

Explanation: Estimate: 436 is close to 400; 32 is close to 30 400 x 30 = 12,000 436 x 32; 436 x 2 = 872 436 x 30 = 13,080 13,080 + 872 = 13,952

Question 12. 54 ÷ 3 = _____

Explanation: 54 ÷ 3 (27 + 27) ÷ 3 = (27 ÷ 3) + (27 ÷ 3) = 9 + 9 = 18 3 x 18 = 3 x (9+ 9) = (3 x 9) + (3 x 9) = 27 + 27 = 54

Question 13. 90 ÷ 5 = _____

Explanation: 90 ÷ 5 (45 + 45) ÷ 5 = (45 ÷ 5) + (45 ÷ 5) = 9 + 9 = 18 5 x 18 = 5 x (9+ 9) = (5 x 9) + (5 x 9) = 45 + 45 = 90

Question 14. 96 ÷ 6 = _____

Explanation: 96 ÷ 6 (48 + 48) ÷ 6 = (48 ÷ 6) + (48 ÷ 6) = 8 + 8 = 16 6 x 16 = 6 x (8 + 8) = (6 x 8) + (6 x 8) = 48 + 48 = 96

Question 15. 42 − (9 + 6) = _____

Answer: 42 − (9 + 6) 42 – 15 27

Question 16. 15 + (22 − 4) ÷ 6 = _____

Answer: 15 + (22 − 4) ÷ 6 15 + (18 ÷ 6) 15 + 3 18

Question 17. 6 × [(5 × 7) − (7 + 8)] = _____

Answer: 6 × [(5 × 7) − (7 + 8)] 6 x [35 – 15] 6 x [20] 120

Chapter Review/Test – Page No. 56

Question 18. Erica’s high score on her new video game is 30,000 points. Maria’s high score is \(\frac{1}{10}\) of Erica’s. How many points did Maria score? Options: A. 30 B. 300 C. 3,000 D. 30,000

Answer: C. 3,000

Explanation: Erica’s high score on her new video game is 30,000 points. Maria’s high score is \(\frac{1}{10}\) of Erica’s. 30,000 x \(\frac{1}{10}\) = 3,000

Question 19. Rich makes $35 a week mowing lawns in his neighborhood. Which expression can be used to show how much money he makes in 8 weeks? Options: A. (8 × 30) + (8 × 5) B. (8 × 30) + (8 × 5) C. (8 + 30) × (8 + 5) D. (8 × 30) × (8 × 5)

Answer: B. (8 × 30) + (8 × 5)

Explanation: Rich makes $35 a week mowing lawns in his neighborhood. 8 x $35 = 8 x (30 + 5) = (8 x 30) + (8 x 5)

Question 20. Mr. Rodriguez bought a supply of 20 reams of printer paper. Each ream contains 500 sheets of paper. How many sheets of printer paper are there? Options: A. 1,000 B. 5,000 C. 10,000 D. 100,000

Answer: C. 10,000

Explanation: Mr. Rodriguez bought a supply of 20 reams of printer paper. Each ream contains 500 sheets of paper. 500 x 20 = 10,000

Question 21. Harvester ants are common in the southwestern United States. A single harvester ant colony may have as many as 90,000 members. What is that number written as a whole number multiplied by a power of ten? Options: A. 9 × 10 4 B. 9 × 10 3 C. 9 × 10 2 D. 9 × 10 1

Answer: A. 9 × 10 4

Explanation: Harvester ants are common in the southwestern United States. A single harvester ant colony may have as many as 90,000 members. 90,000 10 0 = 1; 10 1 = 1 x 10 = 10; 10 2 = 10 x 10 = 100; 10 3 = 10 x 10 x 10 = 1,000; 10 4 = 10 x 10 x 10 x 10 = 10,000; 9 x 10,000 = 90,000 = 9 x 10 4

Chapter Review/Test – Page No. 57

Question 22. Megan used the following expression to find the quotient of a division problem. (4 × 12) + (4 × 6) What was the division problem and the quotient? Options: A. 24 ÷ 4 = 6 B. 48 ÷ 4 = 12 C. 64 ÷ 4 = 16 D. 72 ÷ 4 = 18

Answer: D. 72 ÷ 4 = 18

Explanation: Megan used (4 × 12) + (4 × 6) 4 x (12 + 6) 4 x 18 = 72 72 ÷ 4 = 18

Question 23. It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon. How many feet does Kinsey walk to school in 5 days? Options: A. 6,725 feet B. 6,625 feet C. 6,525 feet D. 5,625 feet

Answer: B. 6,625 feet

Explanation: It is 1,325 feet from Kinsey’s house to her school. Kinsey walks to school each morning and gets a ride home each afternoon. 1,325 feet x 5 = 6,625 feet

Go Math Grade 5 Lesson 1.10 Question 24. An adult elephant eats about 300 pounds of food each day. Which expression shows how many pounds of food a herd of 12 elephants eats in 5 days? Options: A. 5 + (300 × 12) B. 5 × (300 × 12) C. (300 × 12) ÷ 5 D. (300 × 12) − 5

Answer: B. 5 × (300 × 12)

Explanation: An adult elephant eats about 300 pounds of food each day. (300 x 12) In 5 days, 5 × (300 × 12)

Question 25. Carla can type 265 characters a minute on her computer keyboard. At that rate, how many characters can she type in 15 minutes? Options: A. 2,975 B. 3,875 C. 3,905 D. 3,975

Answer: D. 3,975

Explanation: Carla can type 265 characters a minute on her computer keyboard. In 15 minutes, 265 x 15 = 3,975

Chapter Review/Test – Page No. 58

Constructed Response

Answer: Missing number is 10. Using the Distributive Property, the sum of the two number within the () has to be equal to the other factor 17. 10 + 7 = 17 17 × 5 = ( 10 +7) × 5 = ( 10 × 5) + (7 × 5)

Performance Task

Question 27. Drew’s weekly allowance is $8.00. His friend Jan’s weekly allowance is $10. Drew spends $3 a week and Jan spends $4 a week. A. Write two expressions to show how much money each person has at the end of the week. Use parentheses. Drew has __ . Jan has __ . Type below: __________

Answer: Drew has ($8 – $3) . Jan has ($10 – $4).

Question 27. B. Drew and Jan decide that they want to put their money together to buy a video game. Write an expression that shows how much they can save each week. Explain. Type below: __________

Answer: (8 – 3) + (10 – 4); Add the amount of money Drew and Jan have at the end of the week. This equals the amount they can save a week.

Question 27. C. The video game Drew and Jan want to buy costs $55. Write an expression to show how many weeks it will take them to save enough to buy the video game. Use parentheses and brackets in your expression. Then evaluate the expression. _____ weeks

Answer: 55 ÷ [(8 – 3) +(10 – 4)] 55 ÷ [5 + 6] 55 ÷ 11 5 It will take them 5 weeks to save the money from the game.

Conclusion:

You don’t need to discover the best books or pdf’s for your students learning. Just download Go Math Grade 5 Answer Key Chapter 1 Place Value, Multiplication, and Expressions PDF and know the process of solving math questions. Go Math Grade 5 Chapter 1 Answer Key is for free for the students along with answers and explanations.

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Math Expressions Grade 5 Unit 5 Lesson 11 Answer Key Focus on Mathematical Practices

Solve the questions in Math Expressions Grade 5 Homework and Remembering Answer Key Unit 5 Lesson 11 Answer Key Focus on Mathematical Practices to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-5-unit-5-lesson-11-answer-key/

Math Expressions Common Core Grade 5 Unit 5 Lesson 11 Answer Key Focus on Mathematical Practices

Math Expressions Grade 5 Unit 5 Lesson 11 Homework

Dividing numbers involves dividends, divisors, and quotients.

Write a division problem (including the quotient) that satisfies all three statements.

Unit 5 Lesson 11 Focus On Mathematical Practices Question 1. The dividend is a one-digit whole number. The divisor is a one-digit whole number. The quotient is a one-digit whole number. Answer: 5 ÷ 5 = 1

Focus On Mathematical Practices Unit 5 Lesson 11 Answers Question 2. The dividend is a two-digit whole number. The divisor is a one-digit whole number. The quotient is a one-digit whole number. Answer: 3 ÷ 18 = 6

Focus On Mathematical Practices 5-11 Math Expressions Question 3. The dividend is a two-digit whole number. The divisor is less than 1, and a number in tenths. The quotient is a two-digit whole number. Answer:  63 ÷ 0.9 = 70

Math Expressions Grade 5 Unit 5 Lesson 11 Question 4. The dividend is a two-digit whole number. The divisor is greater than 1, and a number in tenths. The quotient is a two-digit whole number. Answer: 30 ÷ 0.5 = 60

Unit 5 Lesson 11 Math Expressions Question 5. The dividend is a number in tenths. The divisor is a one-digit whole number. The quotient is a number in tenths. Answer: 0.4 ÷ 2 = 0.2

Math Expressions Grade 5 Answer Key Question 6. The dividend is a decimal in hundredths. The divisor is a decimal in hundredths. The quotient is a one-digit whole number. Answer: 0.16 ÷ 0.08 = 2

11 Answer Math Expressions Grade 5 Question 7. The dividend is a decimal in hundredths. The divisor is a decimal in hundredths. The quotient is a two-digit whole number. Answer: 0.64 ÷ 0.02 = 32

Math Expressions Grade 5 Unit 5 Lesson 11 Remembering

Add or subtract

Question 1. 21 + 1.08 = _______ Answer: 22.08

Question 2. 0.62 + 0.49 = _______ Answer: 1.11

Question 3. 0.06 + 0.5 = _______ Answer: 0.56

Question 4. 6 – 0.09 = ________ Answer: 5.91

Question 5. 3.01 – 0.8 = ________ Answer: 2.21

Question 6. 12.05 – 8 = _________ Answer: 4.05

Complete each fraction box.

Explanation: Given, \(\frac{1}{3}\) and \(\frac{4}{9}\) \(\frac{1}{3}\) can be written in decimal form as 0.33 \(\frac{4}{9}\) can be written in decimal form as 0.44

So, 0.44 > 0.33 0.44 + 0.33 = 0.77 0.44 – 0.33 = 0.11 0.44 × 0.33 = 0.1452

Explanation: Given, \(\frac{2}{7}\) and \(\frac{1}{4}\) \(\frac{2}{7}\) can be written in decimal form as 0.28 \(\frac{1}{4}\) can be written in decimal form as 0.25

So, 0.28 > 0.25 0.28 + 0.25 = 0.53 0.28 – 0.25 = 0.03 0.28 × 0.25 = 0.07

Multiply or divide.

Set up the problem with the long division bracket. Put the dividend inside the bracket and the divisor on the outside to the left.

Put 56730, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 93, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first three numbers of the dividend, 567 by the divisor, 93.

567 divided by 93 is 6, with a remainder of 9. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 9 so you have 93. 93 divided by 93 is 1, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 567.3 ÷ 0.93 = 610

Question 12. Stretch Your Thinking Use the term dividend, divisor, or quotient to complete each sentence. Then write a division equation that fits the description. The __________________ is a decimal in thousandths. The __________________ is a decimal in thousandths. The _________________ is a two-digit whole number. Division problem: ___________ Answer:  The Division problem is  0.108 ÷ 0.009

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 108  ÷ 9

Put 108, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 9, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 10 by the divisor, 9.

10 divided by 9 is 1, with a remainder of 1. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 1 so you have 18. 18 divided by 9 is 2, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 108  ÷ 9  = 12.

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McGraw Hill My Math Grade 5 Chapter 5 Lesson 2 Answer Key Estimate Sums and Differences

All the solutions provided in  McGraw Hill My Math Grade 5 Answer Key PDF Chapter 5 Lesson 2 Estimate Sums and Differences  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 5 Lesson 2 Estimate Sums and Differences

One way to estimate is to use rounding. If you round numbers to a lesser place value, you are likely to get an estimate that is closer to the exact answer.

Math in My World

Explanation: Given, The morning temperature was 31.3°F The afternoon temperature was 37.6°F We have to find Round to the nearest ten. Round 37.6 to the nearest ten is 40. We have to round off the digit after the decimal point if the digit is more than 5. Round 31.3 to the nearest ten is 30. If the digit is less than 5 then we don’t have to do anything. Now subtract 40 – 30 = 10

Another Way: Round to the nearest one. Round 37.6 to the nearest one. 37.6 → _____________ Round 31.3 to the nearest one. 31.3 → _____________ Subtract. _________ – ___________ = ____________

The difference is about ___________°F or about ___________°F. The actual difference is 6.3°F. So, rounding to the nearest ___________ gave the more accurate estimate. Answer: Round 37.6 to the nearest one is 38. Round 31.3 to the nearest one is 31. 38 – 31 = 7 The difference is about 10°F or about 7°F. The actual difference is 6.3°F. So, rounding to the nearest one gave the more accurate estimate.

Explanation: Given, The morning temperature was 31.3°F The afternoon temperature was 37.6°F Now we need to round to the nearest one. 31.3°F = 31 37.6°F = 38 The difference is 38 – 31 = 7 The difference is about 10°F or about 7°F and the actual difference is 6.3°F. So, rounding to the nearest one gave the more accurate estimate.

Estimate 5.26 + 1.93 by rounding to the nearest one.

5.26 → _____________ 1.93 → _____________

Helpful Hint You will learn how to find the actual sum in a later lesson. The actual sum is 7.19, so 7 is a fairly accurate estimate. Add. ____________ + ____________ = ___________ The sum is about _____________. Answer: The answer is 7.

Explanation: Given, 5.26 + 1.93 we need to round to the nearest one. First, take 5.26 and round to the nearest one. 5.26 = 5 Next, 1.93 we need to round to the nearest one. 1.93 = 2 Now add the estimated numbers 5 + 2 = 7 The sum is about 7.

Guided Practice

Round each decimal to the nearest one. Then add or subtract.

Question 1. 2.8 + 1.3 Round to the nearest one. 2.8 → _____________ 1.3 → _____________ Add. ___________ + ____________ = ____________ So, 2.8 + 1.3 is about _____________. Answer: 4, 4.1

Explanation: Given, 2.8 + 1.3 Round to the nearest one. 2.8 → 3 1.3 → 1 Add. 3 + 1 = 4 So, 2.8 + 1.3 is about 4.1

Question 2. 5.98 – 1.03 Round to the nearest one. 5.98 → _____________ 1.3 → _____________ Subtract. ___________ – _____________ = _____________ So, 5.98 – 1.03 is about ____________. Answer: 5, 4.95

Explanation: Given, 5.98 – 1.03 Round to the nearest one. 5.98 → 6 1.3 → 2 Subtract. 6 – 2 = 4 So, 5.98 – 1.03 is about 4.95.

Independent Practice

Question 3. 10.08 + 5.6 = _____________ Answer: 16

Explanation: Given, 10.08 + 5.6 10 + 6 = 16

Question 4. 10.4 + 32.8 = ______________ Answer: 43

Explanation: Given, 10.4 + 32.8 Now add by rounding off the numbers 10 + 33 = 43

Question 5. $42.01 – $5.92 = _____________ Answer: 36

Explanation: Given, $42.01 – $5.92 Now round off the values 42 – 6 = 36

Question 6. 75.2 + 82.3 = _____________ Answer: 87

Explanation: Given, 75.2 + 82.3 Now round off the values 75 + 82 = 87.

Round each decimal to the nearest ten. Then add or subtract.

Question 10. 23.78 + 10.45 = ___________ Answer: 34.23

Question 11. 83.69 – 55.41 = _____________ Answer: 28

Problem Solving

Question 15. The weights of Marisa and Toni’s televisions are shown in the table. About how much more does Marisa’s television weigh than Toni’s? Answer: Marisa’s television weighs 9 lb more than Toni’s.

Explanation: Given, Weight of Marisa’s television = 52.7 lb Weight of Toni’s television = 43.9 lb Now round the values to the nearest one 53 – 44 = 9 lb more than Toni’s.

Question 16. Mathematical PRACTICE Model Math Sophia has $20. She buys a hair band for $3.99, gum for $1.29, and a brush for $6.75 Not including tax, estimate how much change she should receive. Show your work. Answer: $7.97 in change.

Explanation: First, we would add $3.99, $1.29, and $6.75 to see the total amount she spent. 3.99 + 1.29 + 6.75 = $12.03 She spent a total of $12.03. Now, subtract this amount from $20. 20 – 12.03 = 7.97 She receives $7.97 in change.

Explanation: Given, Malcolm buys a taco for $1.79 and milk for $1.29. Now add both of them to know how much they spent = 1.79 + 1.29 = $3.08 He spent $3.08 money to buy a taco.

HOT Problems

Question 19. Building on the Essential Question When is estimating an effective tool? Answer: Without estimation tool we are not able to determine if their answer is within a reasonable range.

McGraw Hill My Math Grade 5 Chapter 5 Lesson 2 My Homework Answer Key

Question 4. 3.872 + 2.409 = ____________ Answer: 6

Question 5. 9.086 – 2.419 = ___________ Answer: 7

Question 6. The table shows the average speeds of two airplanes in miles per hour. About how much faster is the Foxbat than the Hawkeye? Show your work. Answer: 1488 mph.

Explanation: Given, speed of Hawkeye = 375.52 mph The speed that is rounded to the nearest one is 376 Speed of Foxbat = 1864.29 mph The speed that is rounded to the nearest one is 1864 mph The difference between thme gives us about how much faster is the Foxbat than the Hawkeye. 1864 – 376 = 1488 mph

Question 7. Aluminum and tin are both metals. The standard atomic weight for aluminum is 26.98. The standard atomic weight for tin is 118.71. Estimate the difference between the standard atomic weights of these two metals. Show your work. Answer: 119 -27 = 92

Explanation: Given, The standard atomic weight for aluminum is = 26.98 The estimated weight = 27 The standard atomic weight for tin is = 118.71 The estimated weight = 119 The difference between the standard atomic weights of these two metals gives us the answer 119 – 27 = 92

Question 8. Lorena and her cousin are fishing at the lake. They caught two largemouth bass. One fish weighs 71.27 ounces and the other fish weighs 38.86 ounces. Estimate the total weight of the two fish. Show your work. Answer: 71 + 39 = 110 ounces.

Explanation: Given, One fish weighs = 71.27 ounces The estimated One fish weighs = 71 ounces The other fish weighs 38.86 ounces The estimated other fish weighs 38.86 ounces = 39 ounces Now add both of the fishes weights to find out the total weight of the two fish 71 + 39 = 110 ounces.

Explanation: Given, The length of trail A = 2.6 The estimated length of trail A= 3 The length of trail B = 1.8 The estimated length of trail B = 2 The length of trail C = 4.2 The estimated length of trail C = 4 The length of trail D = 3.3 The estimated length of trail D = 3 The total estimated length of the trail = 3 + 2 + 4 + 3 = 12 miles.

Test Practice

Question 10. Mr. Dixon bought a whiteboard that was on sale for $1,989.99. The regular price was $2,499.89. Which is the best estimate of the amount of money Mr. Dixon saved by buying the whiteboard on sale? (A) $500 (B) $1,000 (C) $3,000 (D) $4,000 Answer: $500

Explanation: Given, Mr. Dixon bought a whiteboard that was on sale for $1,989.99. The regular price = $2,499.89. Round off to the nearest tenths. Then the price will be $2000 and $2500 The difference between them gives us the best estimate of the amount of money Mr. Dixon saved by buying the whiteboard on sale. $2500 – $2000 = $500

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