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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.

McGraw Hill My Math Grade 4 Chapter 9 Lesson 8 Answer Key Model Fractions and Multiplication 1

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.

McGraw Hill My Math Grade 4 Chapter 9 Lesson 8 Answer Key Model Fractions and Multiplication 2

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 => \(\frac{42}{12}\)

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

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

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

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 × \(\frac{1}{6}\)

McGraw Hill My Math Grade 4 Chapter 9 Lesson 8 Answer Key Model Fractions and Multiplication 5

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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My Math 3rd Grade - Chapter 9 - 9.1 - Hands On: Take Apart to Multiply

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    Lesson 1 My Homework 65 . Find each sum. Identify the addition propetty. 4. 46 + O = Property Property Find each sum mentally. Problem Solving Mathematical ... 9. Commutative Property 10. parentheses 11. Identity Property 12. Associative Property symbols which show grouping (3 + 1) 3 (1 + 4) = 6+5=11 02+0=2

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    9 −−− × 6 Homework Helper Tyrone spent 8 minutes playing each level of a video game. The video game had 6 levels. How many minutes did he ... Lesson 1 My Homework 433 eHelp 00433_0434_Gr3_S_C08L1HW_115022.indd 433433_0434_Gr3_S_C08L1HW_115022.indd 433 110/17/11 12:37 PM0/17/11 12:37 PM.

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    of 9 follow a pattern. The tens digit in each product is 1 less than the factor that is not 9. The sum of the digits in the product is 9. So, there are 27 petals in all. 3 - 1 = 2 2 + 7 = 9 3 × 9 = 27 63 7 18 9 45 5 Program: GMH CCM Component: SE PDF Pass Vendor: Quad Graphics Grade: 3 Lesson 5 My Homework 459 eHelp Operations and Algebraic ...

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    Lesson 8 Multiply by 11 and 12 Practice Write an addition sentence and a multiplication sentence for each. 1. 5 rows of 11 counters + + + + = × = 2. 3 rows of 12 counters + + = × = Homework Helper Felisa can put 6 photos on each page of her scrapbook. How many photos can she place altogether on 11 pages? Find 6 × 11.