Practice with the help of **Spectrum Math Grade 5 Answer Key Chapter 6 Lesson 6.7 Problem Solving **regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 6 Lesson 6.7 Problem Solving Answers Key

**Solve each problem. Write answers in simplest form. Show your work.**

Question 1.

Simon bought \(\frac{2}{3}\) pounds of cookies. He ate \(\frac{4}{5}\) of the cookies he bought. What was the weight of the cookies that Simon ate?

Simon ate _____________ pounds of cookies.

Answer:

Simon ate \(\frac{8}{15}\) pounds of cookies.

Explanation:

Given,

Simon bought \(\frac{2}{3}\) pounds of cookies.

He ate \(\frac{4}{5}\) of the cookies.

The weight of the cookies that Simon ate,

Multiply the fractions.

\(\frac{2\times 4}{3 \times 5}\) = \(\frac{8}{15}\)

Simon ate \(\frac{8}{15}\) pounds of cookies.

Question 2.

Students must take their tests home to be signed. Two-thirds of the class took home their tests. Only \(\frac{1}{8}\) of the students who took their tests home got them signed. What fraction of the entire class got their tests signed?

______________ of the class got their tests signed.

Answer:

\(\frac{1}{12}\) fraction of the entire class got their tests signed.

Explanation:

Given that,

Two-thirds of the class took home their tests.

Only \(\frac{1}{8}\) of the students who took their tests home got them signed. The fraction of the entire class got their tests signed,

\(\frac{2}{3}\) x \(\frac{1}{8}\) = \(\frac{2\times 1}{ 3\times 8}\)

= \(\frac{2}{24}\)

Reduce to the simplest form, \(\frac{1}{12}\)

So, \(\frac{1}{12}\) fraction of the entire class got their tests signed.

Question 3.

One serving of pancakes calls for \(\frac{1}{3}\) cups of milk. How many cups of milk are needed for 4 servings of pancakes?

______________ cups of milk are needed for four servings of pancakes.

Answer:

1\(\frac{1}{3}\) cups of milk are needed for four servings of pancakes.

Explanation:

Given that,

One serving of pancakes calls for \(\frac{1}{3}\) cups of milk.

Total cups of milk needed for 4 servings of pancakes = 4\(\frac{1}{3}\)

= \(\frac{4 × 1}{3}\)

Reduce to the simplest form, 1\(\frac{1}{3}\)

Therefore 1\(\frac{1}{3}\) cups of milk are needed for four servings of pancakes.

Question 4.

If Carlos works \(\frac{5}{12}\) of a day every day, how much will Carlos have worked after 5 days?

After five days, Carlos worked ____________ days.

Answer:

After five days, Carlos worked 2\(\frac{1}{12}\) days.

Explanation:

Given that,

If Carlos works \(\frac{5}{12}\) of a day every day,

Carlos have worked after 5 days = 5 x \(\frac{5}{12}\)

= \(\frac{5 × 5}{12}\) = \(\frac{25}{12}\)

Reduce to the simplest form, 2\(\frac{1}{12}\).

Question 5.

Tony had 1\(\frac{1}{2}\) gallons of orange juice. He drank \(\frac{2}{7}\) of the orange juice he had. How much orange juice did Tony drink?

Tony drank _______ gallons of orange juice.

Answer:

Tony drank \(\frac{3}{7}\) gallons of orange juice.

Explanation:

Given that,

Tony had 1\(\frac{1}{2}\) gallons of orange juice.

He drank \(\frac{2}{7}\) of the orange juice he had.

Total orange juice did Tony drink = 1\(\frac{1}{2}\) x \(\frac{2}{7}\)

= \(\frac{3}{2}\) x \(\frac{2}{7}\)

= \(\frac{3\times 2}{ 2\times 7}\)

= \(\frac{3}{7}\)

Question 6.

Miranda has 3 kites. Each kite needs 4\(\frac{2}{3}\) yards of string. How much string does Miranda need for all 3 kites?

Miranda needs ___________ yards of string.

Answer:

14 yards of string.

Explanation:

Given that,

Miranda has 3 kites.

Each kite needs 4\(\frac{2}{3}\) yards of string.

Total string does Miranda need for all 3 kites = 3 x 4\(\frac{2}{3}\)

= 3 x \(\frac{14}{3}\)

= \(\frac{3 × 14}{3}\)

= 14

Therefore, Miranda needs 14 yards of string.

**Solve each problem. Write answers in simplest form. Show your work.**

Question 1.

Howard read \(\frac{1}{16}\) of a book each day until he finished two books. How many days did it take Howard to read both books?

Howard read his books for _____________ days.

Answer:

32 days.

Explanation:

Given,

Howard read \(\frac{1}{16}\) of a book each day until he finished two books.

\(\frac{1}{16}\) of book in one day

to finish this book 16 days will take to finish one book

for 2 books

Number of days did it take Howard to read both books, 2 x 16 = 32 days.

\(\frac{1}{16}\) ÷ 2 = \(\frac{1}{16 \times 2}\) = \(\frac{1}{32}\)

Therefore, Howard read his books for 32 days.

Question 2.

The school day is 7 hours long. If recess lasts \(\frac{1}{4}\) hour, what fraction of the school day does recess make up?

Recess is _______________ of a school day.

Answer:

Recess is \(\frac{1}{28}\) of a school day.

Explanation:

Given,

The school day is 7 hours long.

If recess lasts \(\frac{1}{4}\) hour,

The fraction of the school day does recess make up,

\(\frac{1}{4}\) ÷ 7 = \(\frac{1}{4 \times 7}\) = \(\frac{1}{28}\)

Question 3.

Janet has 8 ounces of coffee beans. If each cup of coffee requires \(\frac{1}{9}\) ounce of coffee beans, how many cups of coffee can Janet make?

Janet can make ____________ cups of coffee.

Answer:

Janet can make 72 cups of coffee.

Explanation:

Given that,

Janet has 8 ounces of coffee beans.

If each cup of coffee requires \(\frac{1}{9}\) ounce of coffee beans,

Total cups of coffee can Janet make,

8 ÷ \(\frac{1}{9}\) = 8 x 9 = 72

Therefore, Janet can make 72 cups of coffee.

Question 4.

A recipe for one dozen cookies requires \(\frac{1}{2}\) cup of flour. How much flour is needed for each cookie?

Each cookie requires _____________ cup of flour.

Answer:

Each cookie requires \(\frac{1}{24}\) cup of flour.

Explanation:

Given that,

A recipe for one dozen cookies requires \(\frac{1}{2}\) cup of flour.

Total flour is needed for each cookie,

\(\frac{1}{2}\) ÷ 12 = \(\frac{1}{2 \times 12}\) = \(\frac{1}{24}\)

Question 5.

Keith has 7 yards of string. He needs \(\frac{1}{3}\) yard of string for each of his puppets. How many puppets can Keith make with his string?

Keith can make ____________ puppets.

Answer:

Keith can make 21 puppets.

Explanation:

Given that,

Keith has 7 yards of string.

He needs \(\frac{1}{3}\) yard of string for each of his puppets.

Number of puppets can Keith make with his string,

7 ÷ \(\frac{1}{3}\) = 7 x 3 = 21 puppets.

Question 6.

Mr. Garcia worked 4 hours on Wednesday. He took a quick break every \(\frac{1}{2}\) hour. How many breaks did Mr. Garcia take?

Mr. Garcia took ____________ breaks on Wednesday.

Answer:

Mr. Garcia took 8 breaks on Wednesday.

Explanation:

Given that,

Mr. Garcia worked 4 hours on Wednesday.

He took a quick break every \(\frac{1}{2}\) hour.

Number of breaks did Mr. Garcia take,

4 ÷ \(\frac{1}{2}\) = 4 x 2 = 8 breaks.