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.