# Spectrum Math Grade 5 Chapter 6 Lesson 7 Answer Key Problem Solving

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

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.
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.
$$\frac{1}{12}$$ 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.
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.
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.
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.
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.

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.
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.
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.
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.
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.
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.
He took a quick break every $$\frac{1}{2}$$ hour.
4 ÷ $$\frac{1}{2}$$  = 4 x 2 = 8 breaks.