my homework lesson 2 add like fractions

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It is easy to add fractions that have the same kinds of parts.

1. Write an addition sentence.

2. Shade parts. Then write an addition sentence. Look at the example.

3. Shade parts. Then write an addition sentence.

4. Add the fractions and mixed numbers. You can shade parts in the pictures, if you need help.

5. Add. Shade parts with different colors. Give your answer as a mixed number.

6. Write each fraction as an addition in different ways. Think of breaking the fraction apart.

7. Add the mixed numbers. Shade parts to help.

8. Write each mixed number as an addition in different ways.

You will find free, printable worksheets for adding like fractions here .

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Lesson 1: Hands On: Use Models to Add Like Fractions

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My Math - 5th Grade - Chapter 9 - Add and Subtract Fractions

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McGraw Hill My Math Grade 4 Chapter 9 Lesson 8 Answer Key Model Fractions and Multiplication

All the solutions provided in  McGraw Hill My Math Grade 4 Answer Key PDF Chapter 9 Lesson 8 Model Fractions and Multiplication will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 4 Answer Key Chapter 9 Lesson 8 Model Fractions and Multiplication

You have learned to write a fraction as a sum of unit fractions. For example, \(\frac{4}{5}\) = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\). You can also write a fraction as a multiple of a unit fraction.

2. Use repeated addition: You know that \(\frac{4}{5}\) = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) => 4 times \(\frac{1}{5}\) is added to equal \(\frac{4}{5}\).

You know that 6 is a multiple of 2. Any multiples of 6, such as 12, 18, and 24, are also multiples of 2. The same is true for fractions. A multiple of a fraction can also be written as a multiple of a unit fraction.

2. Use repeated addition: 2 × \(\frac{4}{5}\) = \(\frac{4}{5}\) + \(\frac{4}{5}\). => \(\frac{4}{5}\) + \(\frac{4}{5}\) = \(\frac{8}{5}\) So, \(\frac{8}{5}\) is a multiple of \(\frac{4}{5}\). It is also a multiple of \(\frac{1}{5}\). \(\frac{8}{5}\) = 8 × \(\frac{1}{5}\)

Talk About It Question 1. Mathematical PRACTICE Identify Structure Write an equation showing how \(\frac{3}{8}\) is a multiple of \(\frac{1}{8}\). Answer: Equation showing \(\frac{3}{8}\) is a multiple of \(\frac{1}{8}\) is \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)

Explanation: \(\frac{3}{8}\) is a multiple of \(\frac{1}{8}\): => \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) => (1 + 1 + 1) ÷ 8 => \(\frac{3}{8}\)

Question 2. Write equations showing how \(\frac{6}{8}\) is a multiple of both \(\frac{3}{8}\) and \(\frac{1}{8}\). Answer: Equations showing \(\frac{6}{8}\) is a multiple of both \(\frac{3}{8}\) and \(\frac{1}{8}\) is 2 × \(\frac{3}{8}\) = 6 × \(\frac{1}{8}\)

Explanation: \(\frac{6}{8}\) is a multiple of both \(\frac{3}{8}\) and \(\frac{1}{8}\): 1. \(\frac{6}{8}\) is a multiple of both \(\frac{3}{8}\) => \(\frac{3}{8}\) + \(\frac{3}{8}\) => (3 + 3) ÷ 8 => \(\frac{6}{8}\) 2. \(\frac{6}{8}\) is a multiple of  \(\frac{1}{8}\): => \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)+ \(\frac{1}{8}\)+\(\frac{1}{8}\) + \(\frac{1}{8}\) => (1 + 1 + 1 + 1 + 1 + 1) ÷ 8 => \(\frac{6}{8}\)

Practice It Algebra Use an equation to write each fraction or product as a multiple of a unit fraction. Question 3. \(\frac{3}{4}\) ________________ Answer: Equation showing \(\frac{3}{4}\) as a multiple of a \(\frac{1}{4}\) unit fraction is \(\frac{1}{4}\) +  \(\frac{1}{4}\) +  \(\frac{1}{4}\)

Explanation: \(\frac{3}{4}\) as a multiple of a unit fraction: => \(\frac{1}{4}\) + \(\frac{1}{4}\)+ \(\frac{1}{4}\) => (1 + 1 +1) ÷ 4 => \(\frac{3}{4}\)

Question 4. \(\frac{7}{8}\) ________________ Answer: Equation showing \(\frac{7}{8}\) as a multiple of a \(\frac{1}{8}\) unit fraction is 7 × \(\frac{1}{8}\)

Explanation: \(\frac{7}{8}\) as a multiple of a unit fraction: => \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\)+ \(\frac{1}{8}\)+ \(\frac{1}{8}\)+ \(\frac{1}{8}\)+ \(\frac{1}{8}\) => (1 + 1 + 1 + 1 + 1 + 1 + 1) ÷ 8 => \(\frac{7}{8}\)

Question 5. \(\frac{5}{12}\) ________________ Answer: Equation showing \(\frac{5}{12}\) as a multiple of a \(\frac{1}{12}\) unit fraction is 5 × \(\frac{1}{12}\)

Explanation: \(\frac{5}{12}\) as a multiple of a unit fraction: => \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\)+ \(\frac{1}{12}\)+ \(\frac{1}{12}\) => (1 + 1 + 1 + 1 + 1) ÷ 12 => \(\frac{5}{12}\)

Question 6. \(\frac{5}{6}\) ________________ Answer: Equation showing \(\frac{5}{6}\) as a multiple of a \(\frac{1}{6}\) unit fraction is 5 × \(\frac{1}{6}\)

Explanation: Equation showing \(\frac{5}{6}\) as a multiple of a unit fraction: => \(\frac{1}{6}\) + \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+\(\frac{1}{6}\) => (1 + 1 + 1 + 1 + 1) ÷ 6 => \(\frac{5}{6}\)

Question 7. 2 × \(\frac{2}{3}\) ________________ Answer: Equation showing 2 × \(\frac{2}{3}\) as a multiple of a \(\frac{1}{3}\) and \(\frac{2}{3}\) unit fraction is 4 × \(\frac{1}{3}\) = 2 × \(\frac{2}{3}\)

Explanation: 2 × \(\frac{2}{3}\) as a multiple of a unit fraction: => \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) => 4 × \(\frac{1}{3}\) or 2 × \(\frac{2}{3}\)

Question 8. 2 × \(\frac{5}{6}\) ________________ Answer: Equation showing 2 × \(\frac{5}{6}\) as a multiple of a \(\frac{5}{6}\) and \(\frac{1}{6}\) is \(\frac{5}{6}\) + \(\frac{5}{6}\) = 10 × \(\frac{1}{6}\)

Explanation: 2 × \(\frac{5}{6}\) as a multiple of a unit fraction: => \(\frac{5}{6}\)+ \(\frac{5}{6}\) => \(\frac{10}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\)+\(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\) + \(\frac{1}{6}\) => 10 × \(\frac{1}{6}\) => 10\(\frac{1}{6}\)

Question 9. 4 × \(\frac{3}{4}\) ________________ Answer: Equation showing 4 × \(\frac{3}{4}\) as a multiple of a \(\frac{3}{4}\) unit fraction is \(\frac{3}{4}\) + \(\frac{3}{4}\)+ \(\frac{3}{4}\)+\(\frac{3}{4}\)

Explanation: 4 × \(\frac{3}{4}\) as a multiple of a unit fraction: =>\(\frac{3}{4}\) + \(\frac{3}{4}\)+ \(\frac{3}{4}\)+\(\frac{3}{4}\) => (3 + 3 + 3 + 3) ÷ 4 => 12 ÷ 4 or \(\frac{12}{4}\)

Question 10. 3 × \(\frac{7}{8}\) ________________ Answer: Equation showing 3 × \(\frac{7}{8}\) as a multiple of a \(\frac{7}{8}\) unit fraction is \(\frac{7}{8}\) + \(\frac{7}{8}\) + \(\frac{7}{8}\)

Explanation: 3 × \(\frac{7}{8}\) as a multiple of a unit fraction: => \(\frac{7}{8}\) + \(\frac{7}{8}\) + \(\frac{7}{8}\) => (7 + 7 + 7) ÷ 8 => 21 ÷ 8 or \(\frac{21}{8}\)

Question 11. 5 × \(\frac{3}{5}\) ________________ Answer: Equation showing 5 × \(\frac{3}{5}\) as a multiple of a \(\frac{3}{5}\) unit fraction is \(\frac{3}{5}\) + \(\frac{3}{5}\) + \(\frac{3}{5}\)+ \(\frac{3}{5}\)+ \(\frac{3}{5}\)

Explanation: 5 × \(\frac{3}{5}\) as a multiple of a unit fraction: => \(\frac{3}{5}\) + \(\frac{3}{5}\) + \(\frac{3}{5}\)+ \(\frac{3}{5}\)+ \(\frac{3}{5}\) => (3 + 3 + 3 + 3 + 3) ÷ 5 =\(\frac{15}{5}\)

Question 12. 6 × \(\frac{7}{12}\) ________________ Answer: Equation showing 6 × \(\frac{7}{12}\) as a multiple of a \(\frac{7}{12}\) unit fraction is \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) +\(\frac{7}{12}\) + \(\frac{7}{12}\)

Explanation: 6 × \(\frac{7}{12}\) as a multiple of a unit fraction: => \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) +\(\frac{7}{12}\) + \(\frac{7}{12}\) => (7 + 7 + 7 + 7 + 7 + 7) ÷ 12 => \(\frac{42}{12}\)

Explanation: Number of pound of blackberries Gracie and Jackson each bought = \(\frac{2}{3}\) . 2 × \(\frac{2}{3}\) as a multiple of a unit fraction = ?? => \(\frac{2}{3}\) + \(\frac{2}{3}\) => (2 + 2) ÷ 3 => \(\frac{4}{3}\) => \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\)  +\(\frac{1}{3}\) => 4 × \(\frac{1}{3}\)

Question 15. Mathematical PRACTICE Use Algebra Find the unknown in the equation m × \(\frac{1}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\). Answer: Unknown in the equation m × \(\frac{1}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) is 5.

Explanation: Equation given: m × \(\frac{1}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\). => m = ?? => m × \(\frac{1}{6}\) = \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) => m × \(\frac{1}{6}\) = (1 + 1 + 1 + 1 + 1) ÷ 6 => m × \(\frac{1}{6}\) = 5 × \(\frac{1}{6}\) => m = {5 × \(\frac{1}{6}\)} ÷ 5 × \(\frac{1}{6}\) => m = 5.

Write About It Question 16. How can any fraction \(\frac{a}{b}\) be written as a multiple of a unit fraction? Answer: Any fraction \(\frac{a}{b}\) be written as a multiple of a unit fraction by using the number of times the unit fraction holds to express the given fraction.

McGraw Hill My Math Grade 4 Chapter 9 Lesson 8 My Homework Answer Key

Explanation: Equation showing to the above fraction tiles: \(\frac{1}{6}\) + \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\)+ \(\frac{1}{6}\) => (1 + 1 + 1 + 1 + 1) ÷ 6 => 5 × \(\frac{1}{6}\)

Explanation: Equation showing to the above fraction tiles: \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) => (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 ) ÷ 10 => 8 × \(\frac{1}{10}\)

Algebra Use an equation to write each fraction or product as a multiple of a unit fraction. Question 3. \(\frac{3}{8}\) ___________________ Answer: Equation showing \(\frac{3}{8}\) as a multiple of a \(\frac{1}{8}\) unit fraction is 3 × \(\frac{1}{8}\)

Explanation: \(\frac{3}{8}\) = \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = 3 × \(\frac{1}{8}\)

Question 4. \(\frac{7}{12}\) ___________________ Answer: Equation showing \(\frac{7}{12}\) as a multiple of a \(\frac{1}{12}\) unit fraction is 7 × \(\frac{1}{12}\)

Explanation: \(\frac{7}{12}\) = \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) = (1 + 1 + 1 + 1 + 1 + 1 + 1) ÷ 12 = 7 × \(\frac{1}{12}\)

Question 5. \(\frac{6}{10}\) ___________________ Answer: Equation showing \(\frac{6}{10}\) as a multiple of a \(\frac{1}{10}\) unit fraction is 6 × \(\frac{1}{10}\)

Explanation: \(\frac{6}{10}\) = \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) = (1 + 1 + 1 + 1 + 1 + 1) ÷ 10 = 6 × \(\frac{1}{10}\)

Question 6. \(\frac{4}{5}\) ___________________ Answer: Equation showing \(\frac{4}{5}\) as a multiple of a \(\frac{1}{5}\) unit fraction is 4 × \(\frac{1}{5}\)

Explanation: \(\frac{4}{5}\) = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) = (1 + 1 + 1 + 1) ÷ 5 = 4 × \(\frac{1}{5}\)

Question 7. 3 × \(\frac{4}{5}\) ___________________ Answer: Equation showing 3 × \(\frac{4}{5}\) as a multiple of a \(\frac{1}{5}\) unit fraction is 12 × \(\frac{1}{5}\)

Explanation: 3 × \(\frac{4}{5}\) = \(\frac{12}{5}\) = \(\frac{1}{5}\)  + \(\frac{1}{5}\) + \(\frac{1}{5}\)  + \(\frac{1}{5}\)  + \(\frac{1}{5}\)  + \(\frac{1}{5}\) + \(\frac{1}{5}\)  + \(\frac{1}{5}\) + \(\frac{1}{5}\)  + \(\frac{1}{5}\) + \(\frac{1}{5}\)  + \(\frac{1}{5}\) = 12 × \(\frac{1}{5}\)

Question 8. 5 × \(\frac{2}{5}\) ___________________ Answer: Equation showing 5 × \(\frac{2}{5}\) as a multiple of a \(\frac{1}{5}\) unit fraction is 10 × \(\frac{1}{5}\)

Explanation: 5 × \(\frac{2}{5}\) = \(\frac{10}{5}\) = \(\frac{1}{5}\)  + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)  + \(\frac{1}{5}\) + \(\frac{1}{5}\)  + \(\frac{1}{5}\) + \(\frac{1}{5}\)  + \(\frac{1}{5}\) = 10 × \(\frac{1}{5}\)

Question 9. 8 × \(\frac{6}{10}\) ___________________ Answer: Equation showing 8 × \(\frac{6}{10}\) as a multiple of a \(\frac{8}{10}\) unit fraction is 6 × \(\frac{8}{10}\)

Explanation: 8 × \(\frac{6}{10}\) = \(\frac{48}{10}\) = \(\frac{8}{10}\) + \(\frac{8}{10}\) + \(\frac{8}{10}\)+ \(\frac{8}{10}\) + \(\frac{8}{10}\)+ \(\frac{8}{10}\) = 6 × \(\frac{8}{10}\)

Question 10. 7 × \(\frac{8}{12}\) ___________________ Answer: Equation showing 7 × \(\frac{8}{12}\) as a multiple of a \(\frac{7}{12}\) unit fraction is 8 × \(\frac{7}{12}\)

Explanation: 7 × \(\frac{8}{12}\) = \(\frac{56}{12}\) = \(\frac{7}{12}\) + \(\frac{7}{12}\)  + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\) + \(\frac{7}{12}\)  + \(\frac{7}{12}\) + \(\frac{7}{12}\) = 8 × \(\frac{7}{12}\)

Problem Solving Question 11. Mathematical PRACTICE Model Math Marcia has one cup of tea each day for 7 days. She puts \(\frac{2}{3}\) tablespoons of honey in each cup of tea. Write an equation that represents 7 × \(\frac{2}{3}\) as a multiple of a unit fraction. Answer: Equation that represents 7 × \(\frac{2}{3}\) as a multiple of a \(\frac{1}{3}\) unit fraction is 14 × \(\frac{1}{3}\)

Explanation: Number of days Marcia has one cup of tea = 7. Number of cups of tea he has each day = 1. Number of tablespoons of honey in each cup of tea she puts = \(\frac{2}{3}\). Total number of tea with tablespoons of honey he has = Number of days Marcia has one cup of tea × Number of cups of tea he has each day × Number of tablespoons of honey in each cup of tea she puts = 7 × 1 × \(\frac{2}{3}\) = \(\frac{14}{3}\) = \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\)+ \(\frac{1}{3}\)+ \(\frac{1}{3}\)+ \(\frac{1}{3}\)+ \(\frac{1}{3}\)+\(\frac{1}{3}\)+ \(\frac{1}{3}\)+\(\frac{1}{3}\)+\(\frac{1}{3}\) + \(\frac{1}{3}\) = 14 × \(\frac{1}{3}\)

Question 12. Sam buys 4 tropical fish. Each fish is \(\frac{5}{8}\) of an inch long. Write an equation that represents 4 × \(\frac{5}{8}\) as a multiple of a unit fraction. Answer: Equation that represents 4 × \(\frac{5}{8}\) as a multiple of a \(\frac{5}{8}\) unit fraction is \(\frac{5}{8}\) + \(\frac{5}{8}\)+ \(\frac{5}{8}\)+ \(\frac{5}{8}\)

Explanation: Number of tropical fish Sam buys = 4. Number of inches each fish = \(\frac{5}{8}\) Total number of inches all fishes = Number of tropical fish Sam buys × Number of inches each fish = 4 × \(\frac{5}{8}\) => \(\frac{20}{8}\)

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