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My Math 4 Volume 1 Common Core, Grade: 4 Publisher: McGraw-Hill

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McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 Answer Key Model Equivalent Fractions

All the solutions provided in  McGraw Hill My Math Grade 4 Answer Key PDF Chapter 8 Lesson 3 Model Equivalent Fractions will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 4 Answer Key Chapter 8 Lesson 3 Model Equivalent Fractions

The top number on a fraction is the numerator, The bottom number on a fraction is the denominator. Fractions that represent the same part of a number are equivalent fractions.

McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 Answer Key Model Equivalent Fractions 1

2. Find a fraction equivalent to \(\frac{1}{3}\). Place \(\frac{1}{6}\) – tiles below the \(\frac{1}{3}\) – tile to equal the length of the \(\frac{1}{3}\) – tile. How many \(\frac{1}{6}\) – tiles did you place? So, \(\frac{1}{3}\) and \(\frac{2}{6}\) are equivalent fractions.

McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 Answer Key Model Equivalent Fractions 2

Explanation: Fraction given: \(\frac{1}{3}\) \(\frac{1}{3}\) = \(\frac{1}{3}\) × \(\frac{4}{4}\) = \(\frac{4}{12}\). \(\frac{1}{3}\) = \(\frac{1}{3}\) × \(\frac{2}{2}\) = \(\frac{2}{6}\)

Try It Generate two fractions that are equivalent to \(\frac{1}{4}\). 1. The first number line is divided into fourths. Plot \(\frac{1}{4}\) on the number line.

McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 Answer Key Model Equivalent Fractions 4

Question 2. Mathematical PRACTICE Draw a Conclusion, determine whether \(\frac{1}{2}\) and \(\frac{3}{6}\) are equivalent fractions. Explain. Answer: Both fractions \(\frac{1}{2}\) and \(\frac{3}{6}\) are equivalent fractions.

Explanation: \(\frac{1}{2}\) = \(\frac{1}{2}\) \(\frac{3}{6}\) = \(\frac{3}{6}\) ÷ \(\frac{3}{3}\) = \(\frac{1}{2}\)

Practice It Recognize whether the fractions are equivalent. Write yes or no. Question 3. \(\frac{2}{4}\) and \(\frac{6}{12}\) Answer: Yes, \(\frac{2}{4}\) and \(\frac{6}{12}\) both are equivalent fractions.

Explanation: \(\frac{2}{4}\) = \(\frac{2}{4}\) ÷ \(\frac{2}{2}\) = \(\frac{1}{2}\) \(\frac{6}{12}\) = \(\frac{6{12}\) ÷ \(\frac{6}{6}\) = \(\frac{1}{2}\)

Question 4. \(\frac{6}{8}\) and \(\frac{5}{10}\) Answer: No, \(\frac{6}{8}\) and \(\frac{5}{10}\) both are not equivalent fractions.

Explanation: \(\frac{6}{8}\) = \(\frac{6}{8}\) ÷ \(\frac{2}{2}\) = \(\frac{3}{4}\) \(\frac{5}{10}\) = \(\frac{5}{10}\) ÷ \(\frac{5}{5}\) = \(\frac{1}{2}\)

Question 5. \(\frac{2}{3}\) and \(\frac{3}{5}\) Answer: No, \(\frac{2}{3}\) and \(\frac{3}{5}\) both are not equivalent fractions.

Explanation: \(\frac{2}{3}\) = \(\frac{2}{3}\) \(\frac{3}{5}\) = \(\frac{2}{3}\)

Question 6. \(\frac{9}{12}\) and \(\frac{3}{4}\) Answer: Yes, \(\frac{9}{12}\) and \(\frac{3}{4}\) both are equivalent fractions.

Explanation: \(\frac{9}{12}\) = \(\frac{9}{12}\) ÷ \(\frac{3}{3}\) = \(\frac{3}{4}\) \(\frac{3}{4}\) = \(\frac{3}{4}\)

Question 7. \(\frac{4}{6}\) and \(\frac{8}{12}\) Answer: Yes, \(\frac{4}{6}\) and \(\frac{8}{12}\) both are equivalent fractions.

Explanation: \(\frac{4}{6}\) = \(\frac{4}{6}\) ÷ \(\frac{2}{2}\)  = \(\frac{2}{3}\) \(\frac{8}{12}\) = \(\frac{8}{12}\) ÷ \(\frac{4}{4}\)  = \(\frac{2}{3}\)

Question 8. \(\frac{2}{3}\) and \(\frac{6}{10}\) Answer: No, \(\frac{2}{3}\) and \(\frac{6}{10}\) both are equivalent fractions.

Explanation: \(\frac{2}{3}\) = \(\frac{2}{3}\) \(\frac{6}{10}\) = \(\frac{6}{10}\)  ÷ \(\frac{2}{2}\)  = \(\frac{3}{5}\)

Generate two equivalent fractions for each fraction. Question 9. \(\frac{2}{4}\) Answer: Two equivalent fractions of \(\frac{2}{4}\) are \(\frac{4}{8}\) and \(\frac{12}{24}\)

Explanation: \(\frac{2}{4}\) = \(\frac{2}{4}\) × \(\frac{2}{2}\) = \(\frac{4}{8}\) \(\frac{2}{4}\) = \(\frac{2}{4}\) × \(\frac{6}{6}\) = \(\frac{12}{24}\)

Question 10. \(\frac{2}{6}\) Answer: Two equivalent fractions of \(\frac{2}{6}\) are \(\frac{4}{12}\) and \(\frac{12}{36}\)

Explanation: \(\frac{2}{6}\) = \(\frac{2}{6}\)× \(\frac{2}{2}\) = \(\frac{4}{12}\) \(\frac{2}{6}\) = \(\frac{2}{6}\) × \(\frac{6}{6}\) = \(\frac{12}{36}\)

Question 11. \(\frac{4}{8}\) Answer: Two equivalent fractions of \(\frac{4}{8}\) are \(\frac{16}{32}\) and \(\frac{32}{64}\)

Explanation: \(\frac{4}{8}\) = \(\frac{4}{8}\) × \(\frac{4}{4}\) = \(\frac{16}{32}\) \(\frac{4}{8}\) = \(\frac{4}{8}\)× \(\frac{8}{8}\) = \(\frac{32}{64}\)

Question 12. \(\frac{5}{10}\) Answer: Two equivalent fractions of \(\frac{5}{10}\) are \(\frac{10}{20}\) and \(\frac{55}{110}\)

Explanation: \(\frac{5}{10}\) = \(\frac{5}{10}\) × \(\frac{2}{2}\) = \(\frac{10}{20}\) \(\frac{5}{10}\) = \(\frac{5}{10}\) × \(\frac{11}{11}\) = \(\frac{55}{110}\)

Question 13. \(\frac{1}{3}\) Answer: Two equivalent fractions of \(\frac{1}{3}\) are \(\frac{5}{15}\) and \(\frac{3}{9}\)

Explanation: \(\frac{1}{3}\) = \(\frac{1}{3}\)× \(\frac{5}{5}\) = \(\frac{5}{15}\) \(\frac{1}{3}\) = \(\frac{1}{3}\)× \(\frac{3}{3}\) = \(\frac{3}{9}\)

Question 14. \(\frac{2}{3}\) Answer: Two equivalent fractions of \(\frac{2}{3}\) are \(\frac{14}{21}\) and \(\frac{12}{18}\)

Explanation: \(\frac{2}{3}\) = \(\frac{2}{3}\) × \(\frac{7}{7}\) = \(\frac{14}{21}\) \(\frac{2}{3}\) = \(\frac{2}{3}\) × \(\frac{6}{6}\) = \(\frac{12}{18}\)

Apply It Question 15. Mathematical PRACTICE Model Math There were 10 baked goods in a basket. Four of them were sold. Write a fraction to show the part of the baked goods that were not sold. Then write an equivalent fraction to this number. Answer: Fraction to show the part of the baked goods that were not sold = \(\frac{2}{5}\)

Explanation: Number of baked goods in a basket = 10. Number of baked goods in a basket sold = 4. Fraction to show the part of the baked goods that were not sold = Number of baked goods in a basket sold ÷ Number of baked goods in a basket = 4 ÷ 10 = 2 ÷ 5 or \(\frac{2}{5}\)

Question 16. Two-thirds of a jar of peanut butter has been used. Write an equivalent fraction. Answer: Equivalent fraction of \(\frac{2}{3}\) = \(\frac{10}{15}\)

Explanation: Two-thirds of a jar of peanut butter has been used. => \(\frac{2}{3}\) = \(\frac{2}{3}\) × \(\frac{5}{5}\) = \(\frac{10}{15}\)

McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 Answer Key Model Equivalent Fractions 7

Explanation: Fraction of the marbles are red = \(\frac{3}{10}\) Fraction of the marbles are blue = \(\frac{5}{10}\) Fraction of the marbles are green = \(\frac{2}{10}\) Simplest form: \(\frac{3}{10}\) = \(\frac{3}{10}\) \(\frac{5}{10}\) = \(\frac{5}{10}\) ÷ \(\frac{5}{5}\) = \(\frac{1}{2}\) \(\frac{2}{10}\) = \(\frac{2}{10}\) ÷ \(\frac{2}{2}\) = \(\frac{1}{5}\) \(\frac{4}{8}\) = \(\frac{4}{8}\) ÷ \(\frac{4}{4}\)  = \(\frac{1}{2}\)

Question 18. Mathematical PRACTICE Use Number Sense Daria used fraction tiles to show that \(\frac{3}{5}\) is equivalent to \(\frac{6}{10}\). Compare the number and size of fraction tiles needed to model each fraction. Answer: \(\frac{3}{5}\) is equivalent to \(\frac{6}{10}\) both are size are same.

Explanation: Given: \(\frac{3}{5}\) is equivalent to \(\frac{6}{10}\). \(\frac{3}{5}\) \(\frac{6}{10}\) = \(\frac{6}{10}\) ÷ \(\frac{2}{2}\) = \(\frac{3}{5}\)

McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 Answer Key Model Equivalent Fractions 8

Explanation: Equation: \(\frac{2}{??}\) × \(\frac{3}{3}\) = \(\frac{??}{6}\) => 6 × 2 = 12. \(\frac{2}{12}\) = \(\frac{1}{6}\)

Write About It Question 20. Write a real-world example of equivalent fractions. Answer: A real-world example of equivalent fractions is a piece of cake.

Explanation: I have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake. If I cut a cake into eight equal pieces and eat four of them, I will still have eaten half the cake. These are equivalent fractions.

McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 My Homework Answer Key

Practice Recognize whether the fractions are equivalent. Write yes or no. Question 1. \(\frac{3}{5}\) and \(\frac{6}{8}\) Answer: Yes, \(\frac{3}{5}\) and \(\frac{6}{8}\) both are equivalent fractions.

Explanation: \(\frac{3}{5}\) = \(\frac{3}{5}\) \(\frac{6}{8}\) = \(\frac{6}{8}\)  ÷ \(\frac{2}{2}\)  = \(\frac{3}{5}\)

Question 2. \(\frac{4}{5}\) and \(\frac{5}{6}\) Answer: No \(\frac{4}{5}\) and \(\frac{5}{6}\) both are not equivalent fractions.

Explanation: \(\frac{4}{5}\) = \(\frac{4}{5}\) \(\frac{5}{6}\) = \(\frac{5}{6}\)

Question 3. \(\frac{2}{4}\) and \(\frac{6}{12}\) Answer: Yes \(\frac{2}{4}\) and \(\frac{6}{12}\) both are equivalent fractions.

Explanation: \(\frac{2}{4}\) = \(\frac{2}{4}\) ÷ \(\frac{2}{2}\)  = \(\frac{1}{2}\) \(\frac{6}{12}\) = \(\frac{6}{12}\) ÷ \(\frac{6}{6}\)  = \(\frac{1}{2}\)

Question 4. \(\frac{2}{3}\) and \(\frac{4}{6}\) Answer: Yes \(\frac{2}{3}\) and \(\frac{4}{6}\) both are equivalent fractions.

Explanation: \(\frac{2}{3}\) = \(\frac{2}{3}\) \(\frac{4}{6}\) = \(\frac{4}{6}\) ÷ \(\frac{2}{2}\)  = \(\frac{2}{3}\)

Question 5. \(\frac{8}{12}\) and \(\frac{4}{6}\) Answer: Yes \(\frac{8}{12}\) and \(\frac{4}{6}\) both are equivalent fractions.

Explanation: \(\frac{8}{12}\) = \(\frac{8}{12}\) ÷ \(\frac{4}{4}\)  = \(\frac{2}{3}\) \(\frac{4}{6}\) = \(\frac{4}{6}\) ÷ \(\frac{2}{2}\)  = \(\frac{2}{3}\)

Question 6. \(\frac{5}{6}\) and \(\frac{9}{10}\) Answer: No \(\frac{5}{6}\) and \(\frac{9}{10}\) both are not equivalent fractions.

Explanation: \(\frac{5}{6}\) = \(\frac{5}{6}\) \(\frac{9}{10}\) = \(\frac{9}{10}\)

Generate two equivalent fractions for each fraction. Question 7. \(\frac{1}{3}\) Answer: Two equivalent fractions of \(\frac{1}{3}\) are \(\frac{7}{21}\) and \(\frac{3}{9}\)

Explanation: \(\frac{1}{3}\) = \(\frac{1}{3}\) × \(\frac{7}{7}\) = \(\frac{7}{21}\) \(\frac{1}{3}\) = \(\frac{1}{3}\) × \(\frac{3}{3}\) = \(\frac{3}{9}\)

Question 8. \(\frac{8}{12}\) Answer: Two equivalent fractions of \(\frac{8}{12}\) are \(\frac{16}{24}\) and \(\frac{24}{36}\)

Explanation: \(\frac{8}{12}\) = \(\frac{8}{12}\) × \(\frac{2}{2}\) = \(\frac{16}{24}\) \(\frac{8}{12}\) = \(\frac{8}{12}\) × \(\frac{3}{3}\) = \(\frac{24}{36}\)

Question 9. \(\frac{3}{4}\) Answer: Two equivalent fractions of \(\frac{3}{4}\) are \(\frac{15}{20}\) and \(\frac{6}{8}\)

Explanation: \(\frac{3}{4}\) = \(\frac{3}{4}\) × \(\frac{5}{5}\) = \(\frac{15}{20}\) \(\frac{3}{4}\) = \(\frac{3}{4}\) × \(\frac{2}{2}\) = \(\frac{6}{8}\)

Problem Solving Question 10. Mathematical PRACTICE Justify Conclusions Francie lives \(\frac{1}{5}\) mile from the school. Jake lives \(\frac{2}{10}\) mile from the school. Do they live the same distance from the school? Explain. Answer: Yes, they live the same distance from the school because \(\frac{1}{5}\)  is the simplest form of \(\frac{2}{10}\).

Explanation: Number of miles Francie lives from the school = \(\frac{1}{5}\) Number of miles Jake lives from the school = \(\frac{2}{10}\) Simplest  form: \(\frac{1}{5}\)  = \(\frac{1}{5}\) \(\frac{2}{10}\)  = \(\frac{2}{10}\) ÷ \(\frac{2}{2}\)  = \(\frac{1}{5}\)

McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 Answer Key Model Equivalent Fractions 9

Explanation: Numerator = the number above the line in a fraction showing how many of the parts indicated by the denominator are taken. The denominator = The numeric value below the line of a fraction is called the denominator. Equivalent fractions = They are fractions that represent the same value, even though they look different.

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lesson 4 my homework page 83

Find the perimeter of the rectangle or square.

P =     ft

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lesson 4 my homework page 83

P =     in.

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P =     cm

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P =     m

Lesson 13.2

Find the area of the rectangle or square.

lesson 4 my homework page 83

A =     square inches

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