## Math Expressions Common Core Grade 5 Unit 3 Lesson 13 Answer Key Review Operations with Fractions

**Math Expressions Grade 5 Unit 3 Lesson 13 Homework**

Question 1.

Dan’s Ice Cream comes in cartons of two sizes. The large carton holds 4\(\frac{1}{2}\) pounds. The small carton holds 1\(\frac{3}{4}\) pounds less. How much ice cream does the small carton hold?

Answer:

The small carton holds 2.25 pounds ice cream.

Explanation:

In the above-given question,

given that,

Dan’s Ice Cream comes in cartons of two sizes.

The large carton holds 4\(\frac{1}{2}\) pounds.

The small carton holds 1\(\frac{3}{4}\) pounds less.

4(1/2) – 1(3/4).

9/2 – 7/4.

9/2 = 4.5.

7/4 = 1.75.

4.5 – 1.75 = 2.25.

so the small carton holds 2.25 pounds of ice cream.

Question 2.

Mac picked four baskets of blueberries. The weights of the berries in pounds are given below. Order the weights from lightest to heaviest.

\(\frac{5}{4}\) \(\frac{9}{10}\) \(\frac{4}{5}\) \(\frac{13}{20}\)

Answer:

The weights from lightest to heaviest = 13/20, 4/5, 9/10, and 5/4.

Explanation:

In the above-given question,

given that,

Mac picked four baskets of blueberries.

Order the weights from lightest to heaviest.

5/4 = 1.25.

9/10 = 0.9.

4/5 = 0.8.

13/20 = 0.65.

so the weights from lightest to heaviest = 13/20, 4/5, 9/10, and 5/4.

Question 3.

Four cones of Dan’s Ice Cream hold \(\frac{1}{2}\) pound. How much ice cream does each cone hold?

Answer:

The ice cream does each cone holds = 3.5 pounds.

Explanation:

In the above-given question,

given that,

Four cones of Dan’s Ice Cream hold \(\frac{1}{2}\) pound.

1/2 = 0.5.

4 – 0.5 = 3.5.

so the ice cream does each cone holds = 3.5 pounds.

Question 4.

If a dish of ice cream holds \(\frac{1}{4}\) pound, how many dishes can you get from a 4\(\frac{1}{2}\)-pound carton of Dan’s Ice Cream?

Answer:

Dan’s carton of Ice cream = 4.25.

Explanation:

In the above-given question,

given that,

If a dish of ice cream holds \(\frac{1}{4}\) pound.

4(1/2) = 9/2.

9/2 = 4.5.

1/4 = 0.25.

4.5 – 0.25 = 4.25.

**Solve. Give your answer in simplest form.**

Question 5.

3 ÷ \(\frac{1}{5}\) = ___

Answer:

3 ÷ 0.2 = 15.

Explanation:

In the above-given question,

given that,

the fractions are 3 and 1/5.

divide the fractions.

3 ÷ 1/5.

1/5 = 0.2.

3 ÷ 0.2 = 15.

Question 6.

1\(\frac{3}{4}\) + \(\frac{11}{16}\) = ___

Answer:

1(3/4) + 11/16 = 2.58.

Explanation:

In the above-given question,

given that,

the fractions are 7/4 and 11/6.

add the fractions.

7/4 = 1.75.

11/6 = 1.83.

1.75 + 1.83 = 2.58.

Question 7.

\(\frac{9}{14}\) . 2\(\frac{1}{3}\) = ___

Answer:

9/14 . 2(1/3) = 1.472.

Explanation:

In the above-given question,

given that,

the fractions are 9/14 and 2(1/3).

multiply the fractions.

7/3 = 2.3.

9/14 = 0.64.

2.3 x 0.64 = 1.472.

Question 8.

2\(\frac{2}{3}\) . 6 = ___

Answer:

2(2/3) . 6 = 15.6.

Explanation:

In the above-given question,

given that,

the fractions are 2(2/3) and 6.

multiply the fractions.

2(2/3) = 8/3.

8/3 = 2.6.

2.6 . 6 = 15.6.

Question 9.

\(\frac{1}{3}\) + \(\frac{2}{5}\) = ___

Answer:

1/3 + 2/5 = 0.7.

Explanation:

In the above-given question,

given that,

the fractions are 1/3 and 2/5.

add the fractions.

1/3 = 0.3.

2/5 = 0.4.

0.3 + 0.4 = 0.7.

Question 10.

\(\frac{5}{6}\) + \(\frac{8}{9}\) = ___

Answer:

5/6 + 8/9 = 1.71.

Explanation:

In the above-given question,

given that,

the fractions are 5/6 and 8/9.

add the fractions.

5/6 = 0.83.

8/9 = 0.88.

0.83 + 0.88 = 1.71.

Question 11.

\(\frac{1}{8}\) ÷ 4 = ___

Answer:

1/8 / 4 = 0.075.

Explanation:

In the above-given question,

given that,

the fractions are 1/8 and 4.

divide the fractions.

1/8 = 0.3.

0.3 / 4 = 0.075.

Question 12.

\(\frac{2}{5}\) – \(\frac{1}{10}\) = ___

Answer:

2/5 – 1/10 = 0.3.

Explanation:

In the above-given question,

given that,

the fractions are 2/5 and 1/10.

subtract the fractions.

1/10 = 0.1.

2/5 = 0.4.

0.4 – 0.1 = 0.3.

Question 13.

3\(\frac{5}{7}\) – 1\(\frac{1}{2}\) = ____

Answer:

3(5/7) – 1(1/2) = 2.2.

Explanation:

In the above-given question,

given that,

the fractions are 3(5/7) and 1(1/2).

subtract the fractions.

26/7 = 3.7.

3/2 = 1.5.

3.7 – 1.5 = 2.2.

Question 14.

\(\frac{7}{8}\) ∙ \(\frac{2}{7}\) = ___

Answer:

7/8 . 2/7 = 0.245.

Explanation:

In the above-given question,

given that,

the fractions are 7/8 and 2/7.

multiply the fractions.

7/8 = 0.875.

2/7 = 0.28.

0.875 . 0.28 = 0.245.

**Math Expressions Grade 5 Unit 3 Lesson 13 Remembering**

**Use benchmarks of 0, \(\frac{1}{2}\), and 1 to estimate the sum or difference. Then find the actual sum or difference.**

Question 1.

\(\frac{5}{10}\) + \(\frac{4}{9}\)

Estimate: ____

Sum: ____

Answer:

5/10 + 4/9 = 0.9.

Explanation:

In the above-given question,

given that,

the fractions are 5/10 and 4/9.

add the fractions.

5/10 = 0.5.

4/9 = 0.4.

0.5 + 0.4 = 0.9.

Question 2.

\(\frac{13}{14}\) – \(\frac{3}{7}\)

Estimate: ____

Difference: ____

Answer:

13/14 – 3/7 = 0.5.

Explanation:

In the above-given question,

given that,

the fractions are 13/14 and 3/7.

subtract the fractions.

13/14 = 0.92.

3/7 = 0.42.

0.92 – 0.42 = 0.5.

Question 3.

\(\frac{8}{9}\) – \(\frac{7}{8}\)

Estimate: ____

Difference: ____

Answer:

8/9 – 7/8 = 0.01.

Explanation:

In the above-given question,

given that,

the fractions are 8/9 and 7/8.

subtract the fractions.

8/9 = 0.88.

7/8 = 0.87.

0.88 – 0.87 = 0.01.

Question 4.

\(\frac{13}{14}\) + \(\frac{3}{4}\)

Estimate: ____

Sum: ____

Answer:

13/14 + 3/4 = 1.67.

Explanation:

In the above-given question,

given that,

the fractions are 13/14 and 3/4.

add the fractions.

13/14 = 0.92.

3/4 = 0.75.

0.92 + 0.75 = 1.67.

**Write an equation. Then solve. Show your Work.**

Question 5.

A rectangle has an area of 20 square feet and a length of 6 feet. What is its width?

Answer:

The width of the rectangle = 3.3 feet.

Explanation:

In the above-given question,

given that,

A rectangle has an area of 20 square feet and a length of 6 feet.

area of the rectangle = l x b.

20 = 6 x w.

20/6 = w.

w = 3.3 feet.

Question 6.

Bailey attends gymnastics practice for 8 hours each week. This is \(\frac{1}{4}\) the number of hours that the gym is open for practice. How many hours is the gym open for practice?

Answer:

The number of hours is the gym open for practice = 2.

Explanation:

In the above-given question,

given that,

Bailey attends gymnastics practice for 8 hours each week.

This is \(\frac{1}{4}\) the number of hours that the gym is open for practice.

8 x 1/4.

2 x 1 = 2.

so the number of hours is the gym open for practice = 2.

**Solve.**

Question 7.

\(\frac{1}{4}\) ÷ 3 = ___

Answer:

1/4 ÷ 3 = 0.08.

Explanation:

In the above-given question,

given that,

the fractions are 1/4 and 3.

divide the fractions.

1/4 = 0.25.

0.25 / 3 = 0.08.

Question 8.

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

Answer:

1/4 . 3 = 0.75.

Explanation:

In the above-given question,

given that,

the fractions are 1/4 and 3.

multiply the fractions.

1/4 = 0.25.

0.25 . 3 = 0.75.

Question 9.

14 . \(\frac{1}{6}\) = ___

Answer:

14 . 1/6 = 0.75.

Explanation:

In the above-given question,

given that,

the fractions are 14 and 1/6.

multiply the fractions.

1/6 = 0.25.

0.25 . 3 = 0.75.

Question 10.

**Stretch Your Thinking** How is solving \(\frac{1}{8}\) ÷ 5 different from solving \(\frac{1}{8}\) . 5?

Answer:

Yes, both of them are different.

Explanation:

In the above-given question,

given that,

the fractions are 1/8 and 5.

multiply and divide the fractions.

1/8 = 0.125.

0.125 x 5 = 0.625.

0.125 / 5 = 0.025.

so both of them are different.