## Math Expressions Common Core Grade 5 Unit 3 Lesson 2 Answer Key Multiplication with Non-Unit Fractions

**Math Expressions Grade 5 Unit 3 Lesson 2 Homework**

**Multiply.**

Question 1.

\(\frac{2}{3}\) . 15 = ____

Answer:

2/3 x 15 = 10.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{2}{3}\) . 15.

2/3 x 15.

5 x 2 = 10.

Question 2.

\(\frac{3}{4}\) . 8 = ____

Answer:

3/4 x 8 = 6.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{3}{4}\) . 8.

3/4 x 8.

3 x 2 = 6.

Question 3.

\(\frac{7}{8}\) . 32 = ____

Answer:

7/8 x 32 = 28.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{7}{8}\) . 32.

7/8 x 32.

7 x 4 = 28.

Question 4.

\(\frac{2}{9}\) . 27 = ____

Answer:

2/9 x 27 = 6.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{2}{9}\) . 27.

2/9 x 27.

2 x 3 = 6.

Question 5.

\(\frac{3}{8}\) . 56 = ____

Answer:

3/8 x 56 = 21.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{3}{8}\) . 56.

3/8 x 56.

7 x 3 = 21.

Question 6.

\(\frac{3}{4}\) . 16 = ____

Answer:

3/4 x 16 = 12.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{3}{4}\) . 16.

3/4 x 16.

3 x 4 = 12.

Question 7.

\(\frac{2}{3}\) . 21 = ____

Answer:

2/3 x 21 = 14.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{2}{3}\) . 21.

2/3 x 21.

7 x 2 = 14.

Question 8.

\(\frac{4}{5}\) . 35 = ____

Answer:

4/5 x 35 = 28.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{4}{5}\) . 35.

4/5 x 35.

4 x 7 = 28.

Question 9.

\(\frac{5}{7}\) . 28 = ____

Answer:

5/7 x 28 = 20.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{5}{7}\) . 28.

5/7 x 28.

5 x 4 = 20.

Question 10.

\(\frac{4}{9}\) . 45 = ____

Answer:

4/9 x 45 = 20.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{4}{9}\) . 45.

4/9 x 45.

4 x 5 = 20.

Question 11.

\(\frac{5}{12}\) . 24 = ____

Answer:

5/12 x 24 = 10.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{5}{12}\) . 24.

5/12 x 24.

5 x 2 = 10.

Question 12.

\(\frac{9}{12}\) . 70 = ____

Answer:

9/12 x 70 = 52.2.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{9}{12}\) . 70.

9/12 x 70.

9 x 5.8 = 52.2.

Question 13.

\(\frac{7}{9}\) . 18 = ____

Answer:

7/9 x 18 = 14.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{7}{9}\) . 18.

7/9 x 18.

7 x 2 = 14.

Question 14.

\(\frac{5}{8}\) . 80 = ____

Answer:

5/8 x 80 = 50.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{5}{8}\) . 80.

5/8 x 80.

5 x 10 = 50.

Question 15.

\(\frac{4}{15}\) . 45 = ____

Answer:

4/15 x 45 = 12.

Explanation:

In the above-given question,

given that,

multiply the fractions.

\(\frac{4}{15}\) . 45.

4/15 x 45.

4 x 3 = 12.

**Solve.**

Question 16.

Rebecca has 21 math problems to solve. She has solved \(\frac{2}{7}\) of them. How many problems has she solved?

Answer:

The number of problems she has solved = 6.

Explanation:

In the above-given question,

given that,

Rebecca has 21 math problems to solve.

She has solved \(\frac{2}{7}\) of them.

2/7 x 21.

2 x 3.

6.

so the number of problems she has solved = 6.

Question 17.

Tessa shot 36 free throws. She made 27 of them. What fraction of her free throws did Tessa make?

Answer:

The fraction of free throws did Tessa make = 9.

Explanation:

In the above-given question,

given that,

Tessa shot 36 free throws.

she made 27 of them.

36 – 27 = 9.

The fraction of free throws did Tessa make = 9.

Question 18.

A carousel has 56 horses. \(\frac{3}{8}\) of them are white. How many horses are not white?

Answer:

The number of horses is not white = 21.

Explanation:

In the above-given question,

given that,

A carousel has 56 horses.

\(\frac{3}{8}\) of them are white.

56 x 3/8.

7 x 3 = 21.

so the number of horses is not white = 21.

Question 19.

Nathan works at a hardware store. Today he sold 48 tools. \(\frac{5}{6}\) of the tools he sold were hammers. How many hammers did Nathan sell today?

Answer:

The number of hammers did Nathan sell today = 40.

Explanation:

In the above-given question,

given that,

Nathan works at a hardware store.

Today he sold 48 tools.

\(\frac{5}{6}\) of the tools he sold were hammering.

48 x 5/6.

8 x 5 = 40.

so the number of hammers did Nathan sell today = 40.

**Math Expressions Grade 5 Unit 3 Lesson 2 Remembering**

**Complete each exercise about the pairs of fraction bars.**

Question 1.

What equivalent fractions are shown? ____

Answer:

The equivalent fractions are 1/4 and 2/8.

Explanation:

In the above-given question,

given that,

the fractions are 2/8 and 1/4.

2/8 = 1/4.

2 x 1 = 2.

2 x 4 = 8.

so the equivalent fractions are 1/4 and 2/8.

Question 2.

Identify the multiplier. _____

Answer:

The equivalent fractions are 1/4 and 2/8.

Explanation:

In the above-given question,

given that,

the fractions are 2/8 and 1/4.

2/8 = 1/4.

2 x 1 = 2.

2 x 4 = 8.

so the equivalent fractions are 1/4 and 2/8.

Question 3.

What equivalent fractions are shown? _____

Answer:

The equivalent fractions are 2/4 and 4/8.

Explanation:

In the above-given question,

given that,

the fractions are 2/4 and 4/8.

2/4 = 1/2.

4/8 = 2/4.

2 x 2 = 4.

2 x 4 = 8.

so the equivalent fractions are 2/4 and 4/8.

Question 4.

Identify the divisor. ____

Answer:

**Write each amount as a decimal number.**

Question 5.

\(\frac{84}{1,000}\) = _____

Answer:

84/1000 = 0.084.

Explanation:

In the above-given question,

given that,

the fraction is 84/1000.

convert it to decimal number.

84/1000.

0.084.

Question 6.

\(\frac{31564}{1,000}\) = _____

Answer:

31564/1000 = 31.564.

Explanation:

In the above-given question,

given that,

the fraction is 31564/1000.

convert it to decimal number.

31564/1000.

31.564.

Question 7.

\(\frac{1176}{100}\) = _____

Answer:

1176/100 = 11.76.

Explanation:

In the above-given question,

given that,

the fraction is 1176/100.

convert it to decimal number.

1176/100.

11.76.

Question 8.

\(\frac{876}{1,000}\) = _____

Answer:

876/1000 = 0.876.

Explanation:

In the above-given question,

given that,

the fraction is 876/1000.

convert it to decimal number.

876/1000.

0.876.

**Solve. Write a multiplication equation for each problem.**

Jonas has 8 sponsors for the school walk-a-thon. Maura has 3 times as many sponsors as Jonas. Trenton has \(\frac{1}{4}\) as many sponsors as Jonas.

Question 9.

How many sponsors does Maura have? _____

Write the equation. _____

Answer:

The number of sponsors does Maura has = 24.

Explanation:

In the above-given question,

given that,

Jonas has 8 sponsors for the school walk-a-thon.

Maura has 3 times as many sponsors as Jonas.

Trenton has \(\frac{1}{4}\) as many sponsors as Jonas.

8 x 3 = 24.

so the number of sponsors does Maura has = 24.

Question 10.

How many sponsors does Trenton have? _____

Write the equation. _____

Answer:

The number of sponsors does Trenton has = 24.

Explanation:

In the above-given question,

given that,

Jonas has 8 sponsors for the school walk-a-thon.

Maura has 3 times as many sponsors as Jonas.

Trenton has \(\frac{1}{4}\) as many sponsors as Jonas.

8 x 1/4 = 2.

so the number of sponsors does Trenton has = 2.

Question 11.

**Stretch Your Thinking** Hannah and Jo are driving separately to a restaurant that is 60 miles away from their town. Hannah drives \(\frac{3}{5}\) of the distance and Jo drives \(\frac{5}{6}\) of the distance before stopping for gasoline. Who has driven farther? How many more miles does each driver need to drive to reach the restaurant?

Answer:

The number of miles does each driver needs to drive to reach the restaurant = 86.

Explanation:

In the above-given question,

given that,

Hannah and Jo are driving separately to a restaurant that is 60 miles away from their town.

Hannah drives \(\frac{3}{5}\) of the distance and Jo drives \(\frac{5}{6}\) of the distance before stopping for gasoline.

3/5 x 60 = 36.

5/6 x 60 = 50.

36 + 50 = 86.

so the number of miles does each driver needs to drive to reach the restaurant = 86.