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Grade 5 - Number and Operations - Fractions
Standard 5.NF.A.2 - Solve addition and subtraction word problems with mixed fractions.
Included Skills:
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
If you notice any problems, please let us know .
4.6 Add and Subtract Mixed Numbers
Learning objectives.
- Model addition of mixed numbers with a common denominator
- Add mixed numbers with a common denominator
- Model subtraction of mixed numbers
- Subtract mixed numbers with a common denominator
- Add and subtract mixed numbers with different denominators
Be Prepared 4.6
Before you get started, take this readiness quiz.
- Draw figure to model 7 3 . 7 3 . If you missed this problem, review Example 4.6 .
- Change 11 4 11 4 to a mixed number. If you missed this problem, review Example 4.9 .
- Change 3 1 2 3 1 2 to an improper fraction. If you missed this problem, review Example 4.11 .
Model Addition of Mixed Numbers with a Common Denominator
So far, we’ve added and subtracted proper and improper fractions, but not mixed numbers. Let’s begin by thinking about addition of mixed numbers using money.
If Ron has 1 1 dollar and 1 1 quarter, he has 1 1 4 1 1 4 dollars.
If Don has 2 2 dollars and 1 1 quarter, he has 2 1 4 2 1 4 dollars.
What if Ron and Don put their money together? They would have 3 3 dollars and 2 2 quarters. They add the dollars and add the quarters. This makes 3 2 4 3 2 4 dollars. Because two quarters is half a dollar, they would have 3 3 and a half dollars, or 3 1 2 3 1 2 dollars.
When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.
We can use fraction circles to model this same example:
Manipulative Mathematics
Example 4.81.
Model 2 1 3 + 1 2 3 2 1 3 + 1 2 3 and give the sum.
We will use fraction circles, whole circles for the whole numbers and 1 3 1 3 pieces for the fractions.
This is the same as 4 4 wholes. So, 2 1 3 + 1 2 3 = 4 . 2 1 3 + 1 2 3 = 4 .
Try It 4.161
Use a model to add the following. Draw a picture to illustrate your model.
1 2 5 + 3 3 5 1 2 5 + 3 3 5
Try It 4.162
2 1 6 + 2 5 6 2 1 6 + 2 5 6
Example 4.82
Model 1 3 5 + 2 3 5 1 3 5 + 2 3 5 and give the sum as a mixed number.
We will use fraction circles, whole circles for the whole numbers and 1 5 1 5 pieces for the fractions.
Adding the whole circles and fifth pieces, we got a sum of 3 6 5 . 3 6 5 . We can see that 6 5 6 5 is equivalent to 1 1 5 , 1 1 5 , so we add that to the 3 3 to get 4 1 5 . 4 1 5 .
Try It 4.163
Model, and give the sum as a mixed number. Draw a picture to illustrate your model.
2 5 6 + 1 5 6 2 5 6 + 1 5 6
Try It 4.164
1 5 8 + 1 7 8 1 5 8 + 1 7 8
Add Mixed Numbers
Modeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.
Add mixed numbers with a common denominator.
Step 1. Add the whole numbers.
Step 2. Add the fractions.
Step 3. Simplify, if possible.
Example 4.83
Add: 3 4 9 + 2 2 9 . 3 4 9 + 2 2 9 .
Try It 4.165
Find the sum: 4 4 7 + 1 2 7 . 4 4 7 + 1 2 7 .
Try It 4.166
Find the sum: 2 3 11 + 5 6 11 . 2 3 11 + 5 6 11 .
In Example 4.83 , the sum of the fractions was a proper fraction . Now we will work through an example where the sum is an improper fraction.
Example 4.84
Find the sum: 9 5 9 + 5 7 9 . 9 5 9 + 5 7 9 .
Try It 4.167
Find the sum: 8 7 8 + 7 5 8 . 8 7 8 + 7 5 8 .
Try It 4.168
Find the sum: 6 7 9 + 8 5 9 . 6 7 9 + 8 5 9 .
An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.
Example 4.85
Add by converting the mixed numbers to improper fractions: 3 7 8 + 4 3 8 . 3 7 8 + 4 3 8 .
Since the problem was given in mixed number form, we will write the sum as a mixed number.
Try It 4.169
Find the sum by converting the mixed numbers to improper fractions:
5 5 9 + 3 7 9 . 5 5 9 + 3 7 9 .
Try It 4.170
3 7 10 + 2 9 10 . 3 7 10 + 2 9 10 .
Table 4.2 compares the two methods of addition, using the expression 3 2 5 + 6 4 5 3 2 5 + 6 4 5 as an example. Which way do you prefer?
Model Subtraction of Mixed Numbers
Let’s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.
We will use fraction circles (pizzas!) to help us visualize the process.
Start with one whole.
Algebraically, you would write:
Example 4.86
Use a model to subtract: 1 − 1 3 . 1 − 1 3 .
Try It 4.171
Use a model to subtract: 1 − 1 4 . 1 − 1 4 .
Try It 4.172
Use a model to subtract: 1 − 1 5 . 1 − 1 5 .
What if we start with more than one whole? Let’s find out.
Example 4.87
Use a model to subtract: 2 − 3 4 . 2 − 3 4 .
Try It 4.173
Use a model to subtract: 2 − 1 5 . 2 − 1 5 .
Try It 4.174
Use a model to subtract: 2 − 1 3 . 2 − 1 3 .
In the next example, we’ll subtract more than one whole.
Example 4.88
Use a model to subtract: 2 − 1 2 5 . 2 − 1 2 5 .
Try It 4.175
Use a model to subtract: 2 − 1 1 3 . 2 − 1 1 3 .
Try It 4.176
Use a model to subtract: 2 − 1 1 4 . 2 − 1 1 4 .
What if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a $1 $1 bill and one quarter. What could you do? You could change the dollar bill into 4 4 quarters. The value of 4 4 quarters is the same as one dollar bill, but the 4 4 quarters are more useful for the parking meter. Now, instead of having a $1 $1 bill and one quarter, you have 5 5 quarters and can put 3 3 quarters in the meter.
This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.
We can also model this using fraction circles, much like we did for addition of mixed numbers.
Example 4.89
Use a model to subtract: 1 1 4 − 3 4 1 1 4 − 3 4
Try It 4.177
Use a model to subtract. Draw a picture to illustrate your model.
1 1 3 − 2 3 1 1 3 − 2 3
Try It 4.178
1 1 5 − 4 5 1 1 5 − 4 5
Subtract Mixed Numbers with a Common Denominator
Now we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.
- Step 1. Rewrite the problem in vertical form.
- If the top fraction is larger than the bottom fraction, go to Step 3.
- If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.
- Step 3. Subtract the fractions.
- Step 4. Subtract the whole numbers.
- Step 5. Simplify, if possible.
Example 4.90
Find the difference: 5 3 5 − 2 4 5 . 5 3 5 − 2 4 5 .
Since the problem was given with mixed numbers, we leave the result as mixed numbers.
Try It 4.179
Find the difference: 6 4 9 − 3 7 9 . 6 4 9 − 3 7 9 .
Try It 4.180
Find the difference: 4 4 7 − 2 6 7 . 4 4 7 − 2 6 7 .
Just as we did with addition, we could subtract mixed numbers by converting them first to improper fractions. We should write the answer in the form it was given, so if we are given mixed numbers to subtract we will write the answer as a mixed number .
Subtract mixed numbers with common denominators as improper fractions.
Step 1. Rewrite the mixed numbers as improper fractions.
Step 2. Subtract the numerators.
Step 3. Write the answer as a mixed number, simplifying the fraction part, if possible.
Example 4.91
Find the difference by converting to improper fractions:
9 6 11 − 7 10 11 . 9 6 11 − 7 10 11 .
Try It 4.181
Find the difference by converting the mixed numbers to improper fractions:
6 4 9 − 3 7 9 . 6 4 9 − 3 7 9 .
Try It 4.182
4 4 7 − 2 6 7 . 4 4 7 − 2 6 7 .
Add and Subtract Mixed Numbers with Different Denominators
To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we used above for adding or subtracting fractions with like denominators.
Example 4.92
Add: 2 1 2 + 5 2 3 . 2 1 2 + 5 2 3 .
Since the denominators are different, we rewrite the fractions as equivalent fractions with the LCD, 6 . 6 . Then we will add and simplify.
We write the answer as a mixed number because we were given mixed numbers in the problem.
Try It 4.183
Add: 1 5 6 + 4 3 4 . 1 5 6 + 4 3 4 .
Try It 4.184
Add: 3 4 5 + 8 1 2 . 3 4 5 + 8 1 2 .
Example 4.93
Subtract: 4 3 4 − 2 7 8 . 4 3 4 − 2 7 8 .
Since the denominators of the fractions are different, we will rewrite them as equivalent fractions with the LCD 8 . 8 . Once in that form, we will subtract. But we will need to borrow 1 1 first.
We were given mixed numbers, so we leave the answer as a mixed number.
Try It 4.185
Find the difference: 8 1 2 − 3 4 5 . 8 1 2 − 3 4 5 .
Try It 4.186
Find the difference: 4 3 4 − 1 5 6 . 4 3 4 − 1 5 6 .
Example 4.94
Subtract: 3 5 11 − 4 3 4 . 3 5 11 − 4 3 4 .
We can see the answer will be negative since we are subtracting 4 4 from 3 . 3 . Generally, when we know the answer will be negative it is easier to subtract with improper fractions rather than mixed numbers.
Try It 4.187
Subtract: 1 3 4 − 6 7 8 . 1 3 4 − 6 7 8 .
Try It 4.188
Subtract: 10 3 7 − 22 4 9 . 10 3 7 − 22 4 9 .
ACCESS ADDITIONAL ONLINE RESOURCES
- Adding Mixed Numbers
- Subtracting Mixed Numbers
Section 4.6 Exercises
Practice makes perfect.
Model Addition of Mixed Numbers
In the following exercises, use a model to find the sum. Draw a picture to illustrate your model.
1 1 5 + 3 1 5 1 1 5 + 3 1 5
2 1 3 + 1 1 3 2 1 3 + 1 1 3
1 3 8 + 1 7 8 1 3 8 + 1 7 8
1 5 6 + 1 5 6 1 5 6 + 1 5 6
Add Mixed Numbers with a Common Denominator
In the following exercises, add.
5 1 3 + 6 1 3 5 1 3 + 6 1 3
2 4 9 + 5 1 9 2 4 9 + 5 1 9
4 5 8 + 9 3 8 4 5 8 + 9 3 8
7 9 10 + 3 1 10 7 9 10 + 3 1 10
3 4 5 + 6 4 5 3 4 5 + 6 4 5
9 2 3 + 1 2 3 9 2 3 + 1 2 3
6 9 10 + 8 3 10 6 9 10 + 8 3 10
8 4 9 + 2 8 9 8 4 9 + 2 8 9
In the following exercises, use a model to find the difference. Draw a picture to illustrate your model.
1 1 6 − 5 6 1 1 6 − 5 6
1 1 8 − 5 8 1 1 8 − 5 8
In the following exercises, find the difference.
2 7 8 − 1 3 8 2 7 8 − 1 3 8
2 7 12 − 1 5 12 2 7 12 − 1 5 12
8 17 20 − 4 9 20 8 17 20 − 4 9 20
19 13 15 − 13 7 15 19 13 15 − 13 7 15
8 3 7 − 4 4 7 8 3 7 − 4 4 7
5 2 9 − 3 4 9 5 2 9 − 3 4 9
2 5 8 − 1 7 8 2 5 8 − 1 7 8
2 5 12 − 1 7 12 2 5 12 − 1 7 12
In the following exercises, write the sum or difference as a mixed number in simplified form.
3 1 4 + 6 1 3 3 1 4 + 6 1 3
2 1 6 + 5 3 4 2 1 6 + 5 3 4
1 5 8 + 4 1 2 1 5 8 + 4 1 2
7 2 3 + 8 1 2 7 2 3 + 8 1 2
9 7 10 − 2 1 3 9 7 10 − 2 1 3
6 4 5 − 1 1 4 6 4 5 − 1 1 4
2 2 3 − 3 1 2 2 2 3 − 3 1 2
2 7 8 − 4 1 3 2 7 8 − 4 1 3
Mixed Practice
In the following exercises, perform the indicated operation and write the result as a mixed number in simplified form.
2 5 8 · 1 3 4 2 5 8 · 1 3 4
1 2 3 · 4 1 6 1 2 3 · 4 1 6
2 7 + 4 7 2 7 + 4 7
2 9 + 5 9 2 9 + 5 9
1 5 12 ÷ 1 12 1 5 12 ÷ 1 12
2 3 10 ÷ 1 10 2 3 10 ÷ 1 10
13 5 12 − 9 7 12 13 5 12 − 9 7 12
15 5 8 − 6 7 8 15 5 8 − 6 7 8
5 9 − 4 9 5 9 − 4 9
11 15 − 7 15 11 15 − 7 15
4 − 3 4 4 − 3 4
6 − 2 5 6 − 2 5
9 20 ÷ 3 4 9 20 ÷ 3 4
7 24 ÷ 14 3 7 24 ÷ 14 3
9 6 11 + 7 10 11 9 6 11 + 7 10 11
8 5 13 + 4 9 13 8 5 13 + 4 9 13
3 2 5 + 5 3 4 3 2 5 + 5 3 4
2 5 6 + 4 1 5 2 5 6 + 4 1 5
8 15 · 10 19 8 15 · 10 19
5 12 · 8 9 5 12 · 8 9
6 7 8 − 2 1 3 6 7 8 − 2 1 3
6 5 9 − 4 2 5 6 5 9 − 4 2 5
5 2 9 − 4 4 5 5 2 9 − 4 4 5
4 3 8 − 3 2 3 4 3 8 − 3 2 3
Everyday Math
Sewing Renata is sewing matching shirts for her husband and son. According to the patterns she will use, she needs 2 3 8 2 3 8 yards of fabric for her husband’s shirt and 1 1 8 1 1 8 yards of fabric for her son’s shirt. How much fabric does she need to make both shirts?
Sewing Pauline has 3 1 4 3 1 4 yards of fabric to make a jacket. The jacket uses 2 2 3 2 2 3 yards. How much fabric will she have left after making the jacket?
Printing Nishant is printing invitations on his computer. The paper is 8 1 2 8 1 2 inches wide, and he sets the print area to have a 1 1 2 1 1 2 -inch border on each side. How wide is the print area on the sheet of paper?
Framing a picture Tessa bought a picture frame for her son’s graduation picture. The picture is 8 8 inches wide. The picture frame is 2 5 8 2 5 8 inches wide on each side. How wide will the framed picture be?
Writing Exercises
Draw a diagram and use it to explain how to add 1 5 8 + 2 7 8 . 1 5 8 + 2 7 8 .
Edgar will have to pay $3.75 $3.75 in tolls to drive to the city.
ⓐ Explain how he can make change from a $10 $10 bill before he leaves so that he has the exact amount he needs.
ⓑ How is Edgar’s situation similar to how you subtract 10 − 3 3 4 ? 10 − 3 3 4 ?
Add 4 5 12 + 3 7 8 4 5 12 + 3 7 8 twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?
Subtract 3 7 8 − 4 5 12 3 7 8 − 4 5 12 twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After reviewing this checklist, what will you do to become confident for all objectives?
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Add & subtract mixed numbers
Mixed numbers word problems.
These grade 5 word problems involve adding and subtracting mixed numbers with both like and unlike denominators and sometimes more than two terms . Some problems include superfluous data, forcing students to read and think about the questions, rather than simply recognizing a pattern to the solutions.
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Course: 5th grade > Unit 4
- Adding mixed numbers: 19 3/18 + 18 2/3
- Subtracting mixed numbers: 7 6/9 - 3 2/5
- Add and subtract mixed numbers with unlike denominators (no regrouping)
- Adding mixed numbers with regrouping
Subtracting mixed numbers with regrouping (unlike denominators)
- Add and subtract mixed numbers with unlike denominators (regrouping)
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Video transcript
Chapter 5, Lesson 5: Adding and Subtracting Mixed Numbers
- Extra Examples
- Group Activity Cards
- Personal Tutor
- Self-Check Quizzes
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IMAGES
VIDEO
COMMENTS
examples of adding and subtracting mixed numbers. Encourage adding color to the posters, arrows, and other helpful text to assist viewers in learning how to add/subtract mixed numbers. 5. Once completed, the students may share their posters with the class. 6. Distribute Practice page. Check and review the students' responses. 7.
Problem. Subtract. 5 2 5 − 3 4 5 =. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
Add and subtract mixed numbers (no regrouping) Google Classroom. Add. 7 1 12 + 4 9 12 =. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
Grade 5 - Number and Operations - Fractions. Standard 5.NF.A.2 - Solve addition and subtraction word problems with mixed fractions.. Included Skills: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem.
To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we used above for adding or subtracting fractions with like denominators. Example 4.92. Add: 212 + 523. 2 1 2 + 5 2 3.
Adding mixed numbers: 19 3/18 + 18 2/3. To add two mixed numbers, you can separate the whole number and fraction parts. Add the whole numbers together as you normally would, and then find a common denominator to add the fractions. Once you have your sum, you may need to simplify the fraction for your final answer.
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Group Activity Cards Personal Tutor Self-Check Quizzes ... Mathematics. Home > Chapter 5 > Lesson 5. Math Connects: Concepts, Skills, and Problem Solving, Course 1. Chapter 5, Lesson 5: Adding and Subtracting Mixed Numbers. Extra Examples; Group Activity Cards ...
Join Nagwa Classes. Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher! This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to add and subtract mixed numbers with like and unlike denominators.
Students work in pairs to practice solving mixed number addition and subtraction problems. While working, they are expected to show their thinking as they regroup whole numbers and fractions. For an optional extension, I provide a worksheet from the text book that has more complex problems.
Step 5: Thus, we have wholes. Case 4: Adding and Subtracting Mixed Numbers Method 2 In this second method, we will break the mixed number into wholes and parts. Step 1: Add or subtract the whole number part. Step 2: Check! Does the fraction part share a common denominator? If not, find one. Step 3: When necessary , create equivalent fractions.
These grade 5 word problems involve adding and subtracting mixed numbers with both like and unlike denominators and sometimes more than two terms. Some problems include superfluous data, forcing students to read and think about the questions, rather than simply recognizing a pattern to the solutions. Worksheet #1 Worksheet #2 Worksheet #3 ...
SmartScore. out of 100. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)!
Add and subtract mixed numbers with unlike denominators (no regrouping) Google Classroom. Add. 2 2 7 + 4 1 2 =. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone ...
20/24 + 18/24 = 38/24. This is an improper fraction. So now, you have to convert it to a mixed number. 24 goes into 38 one time with 14 left over. So we get: 1 14/24, or simplified, 1 7/12. Now we add the whole numbers: 5 + 5 = 10. Then, we add the mixed number to 10 which makes 11 7/12. Your final answer is 11 7/12.
Add and Subtract Mixed Numbers Find the sum or difference. Write your answer in simplest form. Lesson 6.6 COMMON CORE STANDARD CC.5.NF.1 Use equivalent fractions as a strategy to add and subtract fractions. 4. 12. + 61 35 5. 9. 13 20 12 24 2. 10. 12 17 18 69 28 3. 11. 14. 24 10 50 25 Problem Solving REAL WORLD 13. Jacobi bought 71 pounds of ...
Mixed numbers should first be converted to improper fractions. Then, with addition and subtraction, always find the least common denominator. Multiplication is simpler - just multiply the ...
Lesson 5 Activity 2: Adding Mixed Numbers Time: 15-20 Minutes Ask students what are some occasions when they might need to add fractions or mixed numbers, for example 1/3 and 2 ½. They might say when measuring in cooking, in construction, in figuring out medicine dosages. Solve the example: 1/3 + 2 ½ = 2/6 + 2 3/6 = 2 5/6.
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Group Activity Cards ... Home > Chapter 5 > Lesson 5. North Carolina Math Connects: Concepts, Skills, and Problem Solving, Course 1. Chapter 5, Lesson 5: Adding and Subtracting Mixed Numbers. Extra Examples; Group Activity Cards; Personal Tutor; Self-Check Quizzes; Log ...
Transcript. To subtract mixed numbers, first align the whole numbers and fractions so they can be subtracted separately. If the fractions have different denominators, find a common denominator and convert them accordingly. If the fraction on the bottom is larger, regroup by borrowing from the whole number on top.
That's a lot of meat. To add unlike fractions, you need to find the least common denominator. The denominator is the number on the bottom. The least common denominator is the smallest shared ...
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Group Activity Cards Personal Tutor ... Mathematics. Home > Chapter 5 > Lesson 5. New York Math Connects: Concepts, Skills, and Problem Solving, Course 1. Chapter 5, Lesson 5: Adding and Subtracting Mixed Numbers. Extra Examples; Group Activity Cards; Personal Tutor ...
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Group Activity Cards ... Mathematics. Home > Chapter 5 > Lesson 5. Oklahoma Math Connects Concepts, Skills, and Problem Solving Course 1. Chapter 5, Lesson 5: Adding and Subtracting Mixed Numbers. Extra Examples; Group Activity Cards; Personal Tutor; Self-Check Quizzes ...