We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 8 Lesson 7 Multiply Fractions** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 8 Lesson 7 Answer Key Multiply Fractions

I Can solve problems involving the multiplication of a whole number or fraction by a fraction.

**Step it Out**

1. An annual fundraiser raised \(\frac{4}{5}\) of the amount of money in 2017 as it did in 2018. Five-thousand dollars was raised in 2018. How much money was raised in 2017?

A. In which year do you think more money was raised? Explain your reasoning.

Answer:

In the year 2018, more money was raised.

B. Write an equation to model the problem. Write the whole number factor as a fraction.

Answer:

The equation is \(\frac{4}{5}\) × 5,000 = 4,000.

Explanation:

The equation to the problem is \(\frac{4}{5}\) × 5,000 which is 4 × 1,000 = 4,000.

C. Solve the equation 4 × 5,000 ÷ 5 = r. How does this equation compare to your equation from Part B?

Answer:

r = 4,000.

Explanation:

The equation is 4 × 5,000 ÷ 5 = r. Where r is 4,000.

D. How much money was raised in 2017? Write your answer as a whole number. How does your answer compare to your answer from Part A?

Answer:

The money raised in 2017 was less. As the money raised was 4,000.

2. A soccer team is having a fundraiser. Of the items they are selling, \(\frac{3}{4}\) are gift cards. Two-thirds of the gift cards are restaurant gift cards.

A. What fraction of the items they are selling are restaurant gift cards? Write an equation to model the problem.

_____________________

Answer:

\(\frac{1}{2}\).

Explanation:

The equation will be \(\frac{2}{3}\) × \(\frac{3}{4}\) which is \(\frac{1}{2}\).

B. Describe how you could have used a visual model to find the answer.

_____________________

**Turn and Talk** How do you know your answer is reasonable?

**Check Understanding Math Board**

Question 1.

Of the movies in Mr. Jackson’s collection, \(\frac{7}{10}\) are on DVD. Of those,

\(\frac{1}{2}\) are science fiction movies. What fraction of Mr. Jackson’s movies are science fiction DVDs?

Answer:

The fraction of Mr. Jackson’s movies are science fiction DVDs is \(\frac{7}{20}\).

Explanation:

Given that Mr. Jackson’s collection, \(\frac{7}{10}\) are on DVD and \(\frac{7}{10}\) is on DVD. So the fraction of Mr. Jackson’s movies are science fiction DVDs is \(\frac{7}{10}\) × \(\frac{1}{2}\) which is \(\frac{7}{20}\).

**Find the product.**

Question 2.

\(\frac{3}{8}\) × 16

Answer:

\(\frac{3}{8}\) × 16 = 6.

Explanation:

Given that the equation is \(\frac{3}{8}\) × 16 which is 3× 2 = 6.

Question 3.

\(\frac{1}{2}\) × \(\frac{3}{5}\)

Answer:

\(\frac{1}{2}\) × \(\frac{3}{5}\) = \(\frac{3}{10}\).

Explanation:

Given that the equation is \(\frac{1}{2}\) × \(\frac{3}{5}\) which is \(\frac{3}{10}\).

Question 4.

\(\frac{1}{3}\) × 4

Answer:

\(\frac{1}{3}\) × 4 = 1\(\frac{1}{3}\).

Explanation:

Given that the equation is \(\frac{1}{3}\) × 4 which is \(\frac{4}{3}\) = 1\(\frac{1}{3}\).

**On Your Own**

Question 5.

**Use Structure** Does the order of the factors change the product? Explain.

18 × \(\frac{3}{8}\) = \(\frac{3}{8}\) × 18 =

Answer:

No

Explanation:

Given the equations are 18 × \(\frac{3}{8}\) which is \(\frac{54}{8}\) and \(\frac{3}{8}\) × 18 which is \(\frac{54}{8}\). Here, we can see that the product doesn’t change. As multiplication is commutative, so changing the order of the product of the factors will not be changed.

**Find the product.**

Question 6.

\(\frac{5}{9}\) × 18

Answer:

\(\frac{5}{9}\) × 18 = 10.

Explanation:

Given the equation is \(\frac{5}{9}\) × 18 which is 10.

Question 7.

32 × \(\frac{2}{3}\)

Answer:

32 × \(\frac{2}{3}\) = 21\(\frac{1}{3}\).

Explanation:

Given the equation is 32 × \(\frac{2}{3}\) which is \(\frac{64}{3}\) = 21\(\frac{1}{3}\).

Question 8.

\(\frac{7}{8}\) × \(\frac{9}{10}\)

Answer:

\(\frac{7}{8}\) × \(\frac{9}{10}\) = \(\frac{63}{80}\).

Explanation:

Given the equation is \(\frac{7}{8}\) × \(\frac{9}{10}\) which is \(\frac{63}{80}\).

Question 9.

Evaluate the numerical expression. \(\frac{5}{6}\) × (16 – 4)

- Which operation do you perform first? ____
- Write this answer as a fraction. _____
- What is the product of the numerators? _____
- What is the product of the denominators? ____
- What is the value of the numerical expression? ____

Answer:

\(\frac{5}{6}\) × (16 – 4) = 10.

Explanation:

Here, we perform bracket first which is 16 – 4 = 12.

This answer as a fraction is \(\frac{12}{1}\).

The product of the numerators is 5×12 = 60.

The product of the denominators is 6×1 = 6.

The value of the numerical expression is \(\frac{60}{6}\) = 10.

Question 10.

Explain how to find \(\frac{11}{12}\) of 4 by evaluating the numerical expression 11 × 4 ÷ 12.

Answer:

11 × 4 ÷ 12 = 3\(\frac{8}{12}\).

Explanation:

Given the expression is 11 × 4 ÷ 12, first we will multiply 11 × 4 which is 44 and then we will divide it by 12 which is 44÷12 which is 3\(\frac{8}{12}\).

Question 11.

**Reason** Sam is using craft felt to carpet two rooms in a dollhouse. Both rooms are \(\frac{5}{6}\) feet by \(\frac{7}{8}\) feet. How many square feet of craft felt does Sam need to carpet both rooms? Explain your reasoning.

Answer:

1\(\frac{22}{48}\) sqft.

Explanation:

Given that Both rooms are \(\frac{5}{6}\) feet by \(\frac{7}{8}\) feet. So the square feet of craft felt does Sam need to carpet both rooms is \(\frac{5}{6}\) × \(\frac{7}{8}\) which is \(\frac{35}{48}\). As for two rooms we will multiply with 2, so \(\frac{35}{48}\) × 2 which is 1\(\frac{22}{48}\) sqft.

Question 12.

**Model with Mathematics** The British Telecom Tower is about \(\frac{3}{7}\) the height of the Empire State Building. Write two different numerical expressions to model the height of the British Telecom Tower.

Answer:

The two expressions are \(\frac{3}{7}\)×443 and (3×443) ÷ 7.

Explanation:

Given that the British Telecom Tower is about \(\frac{3}{7}\) the height of the Empire State Building. So two different numerical expressions to model the height of the British Telecom Tower is \(\frac{3}{7}\)×443 and (3×443) ÷ 7.

Question 13.

**Use Structure** Kasim picks 8 pounds of strawberries. He uses \(\frac{5}{8}\) of the strawberries to make a fruit salad. Then he uses \(\frac{2}{3}\) of the remaining strawberries to make fruit smoothies. How many pounds of strawberries does Kasim have left after making fruit salad and smoothies? _______

Answer:

The number of pounds is 2.

Explanation:

Given that Kasim picks 8 pounds of strawberries and he uses \(\frac{5}{8}\) of the strawberries to make a fruit salad which is \(\frac{5}{8}\) × 8 = 5. Then he uses \(\frac{2}{3}\) of the remaining strawberries to make fruit smoothies which is \(\frac{2}{3}\) × 3 which is 2.

**Find the product.**

Question 14.

\(\frac{3}{5}\) × 7 = ____

Answer:

\(\frac{3}{5}\) × 7 = 4\(\frac{1}{5}\).

Explanation:

Given the equation is \(\frac{3}{5}\) × 7 which is \(\frac{21}{5}\) = 4\(\frac{1}{5}\).

Question 15.

\(\frac{1}{8}\) × \(\frac{2}{3}\) = ____

Answer:

\(\frac{1}{8}\) × \(\frac{2}{3}\) = \(\frac{1}{12}\).

Explanation:

Given the equation is \(\frac{1}{8}\) × \(\frac{2}{3}\) which is \(\frac{1}{12}\).

Question 16.

\(\frac{9}{11}\) ÷ (5 × 3) = ___

Answer:

\(\frac{9}{11}\) ÷ (5 × 3) = 12\(\frac{3}{11}\).

Explanation:

Given the equation is \(\frac{9}{11}\) ÷ (5 × 3). First we will solve the bracket which is 5 × 3 = 15 and \(\frac{9}{11}\) ÷ 15 which is \(\frac{135}{11}\) = 12\(\frac{3}{11}\).

Question 17.

\(\frac{17}{20}\) × (12 ÷ 2) = ___

Answer:

\(\frac{17}{20}\) × (12 ÷ 2) = 5\(\frac{1}{5}\).

Explanation:

Given the equation is \(\frac{17}{20}\) × (12 ÷ 2). First we will solve the bracket which is 12 ÷ 2 = 6 and \(\frac{17}{20}\) × 6 which is \(\frac{102}{20}\) = 5\(\frac{1}{5}\).

Question 18.

**Reason** Will the product be greater than, less than, or equal to 34? Explain your reasoning.

\(\frac{1}{3}\) × \(\frac{1}{3}\) × \(\frac{1}{3}\) × 34

Answer:

\(\frac{34}{27}\) which is less than 34.

Explanation:

Given the equation is \(\frac{1}{3}\) × \(\frac{1}{3}\) × \(\frac{1}{3}\) × 34 which is \(\frac{34}{27}\) which is less than 34.

Question 19.

**Construct Arguments** Jorge models the area of the rectangle with the equation \(\frac{2}{3}\) × 3 = m. Caleb models the area of the rectangle with the equation 2 × 3 ÷ 3 = p. Which equation is correct? Explain your reasoning.

Answer:

They both are correct.

Explanation:

Given that the equation Joorge is \(\frac{2}{3}\) × 3 = m where m is 2 sq ft and Caleb models the area of the rectangle with the equation (2 × 3) ÷ 3 = p where p is 6 ÷ 3 = p, p = 2 sq ft. So they both are correct.