Go through the Spectrum Math Grade 6 Answer Key Chapter 2 Lesson 2.5 Problem Solving and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 2 Lesson 2.5 Problem Solving Answers Key
Solve each problem. Write answers in simplest form.
Question 1.
Sam and José mowed \(\frac{2}{3}\) of the yard. José mowed \(\frac{3}{4}\) of that amount. What part of the yard did José mow?
José mowed ________________ of the yard.
Answer:
Part of the yard José mowed now = \(\frac{8}{9}\).
José mowed \(\frac{8}{9}\) of the yard.
Explanation:
Part of the yard Sam and José mowed = \(\frac{2}{3}\).
Part of Jose mowed = \(\frac{3}{4}\).
Part of the yard José mowed now = Part of the yard Sam and José mowed ÷ Part of Jose mowed
= \(\frac{2}{3}\) ÷ \(\frac{3}{4}\)
= \(\frac{2}{3}\) × \(\frac{4}{3}\)
= \(\frac{8}{9}\)
Question 2.
Maria practices the piano \(\frac{5}{6}\) of an hour every day. How many hours does she practice in 14 days?
Maria practices ___________________ hours.
Answer:
Number of hours she practices in 14 days = \(\frac{35}{3}\) or 11\(\frac{2}{3}\).
Maria practices \(\frac{35}{3}\) or 11\(\frac{2}{3}\) hours.
Explanation:
Number of hours ever day Maria practices the piano = \(\frac{5}{6}\).
Number of days she practices = 14.
Number of hours she practices in 14 days = Number of hours ever day Maria practices the piano × Number of days she practices
= \(\frac{5}{6}\) × 14
= \(\frac{5}{3}\) × 7
= \(\frac{35}{3}\) or 11\(\frac{2}{3}\)
Question 3.
It takes 6 hours to clean the Smith’s house. How long does it take to clean \(\frac{5}{8}\) of the house?
It takes ________ hours.
Answer:
Number of hours it takes to clean \(\frac{5}{8}\) = \(\frac{48}{5}\) or 9\(\frac{3}{5}\).
It takes \(\frac{48}{5}\) or 9\(\frac{3}{5}\) hours.
Explanation:
Number of hours it takes to clean the Smith’s house = 6.
Length of the part of the house to clean = \(\frac{5}{8}\)
Number of hours it takes to clean \(\frac{5}{8}\) = Number of hours it takes to clean the Smith’s house ÷ Length of the part of the house to clean
= 6 ÷ \(\frac{5}{8}\)
= 6 × \(\frac{8}{5}\)
= \(\frac{48}{5}\) or 9\(\frac{3}{5}\)
Question 4.
A container holding 6\(\frac{2}{3}\) pints of juice will be divided equally among 5 people. How much juice will each person get?
Each person will get ____ pints.
Answer:
Number of pints of juice each person gets = \(\frac{2}{15}\).
Each person will get \(\frac{2}{15}\) pints.
Explanation:
Total number of pints of juice a container holds = 6\(\frac{2}{3}\).
Number of people the juice is equally divided = 5.
Number of pints of juice each person gets = Total number of pints of juice a container holds ÷ Number of people the juice is equally divided
= 6\(\frac{2}{3}\) ÷ 5
= {[(6 × 3) + 2] ÷ 3} ÷ 5
= [(18 + 2) ÷ 3] ÷ 5
= \(\frac{2}{3}\) ÷ 5
= \(\frac{2}{3}\) × \(\frac{1}{5}\)
= \(\frac{2}{15}\)
Question 5.
A 7-hour class will be divided into equal sessions of 1\(\frac{2}{5}\) hours. How many sessions will be needed?
_________________ sessions will be needed.
Answer:
Number of sessions will be needed = 5.
5 sessions will be needed.
Explanation:
Number of hours of class will be divided into equal sessions = 7.
Number of hours each session = 1\(\frac{2}{5}\).
Number of sessions will be needed = Number of hours of class will be divided into equal sessions ÷ Number of hours each session
= 7 ÷ 1\(\frac{2}{5}\)
= 7 ÷ {[(1 × 5) + 2] ÷ 5}
= 7 ÷ [(5 + 2) ÷ 5]
= 7 ÷ \(\frac{7}{5}\)
= 7 × \(\frac{5}{7}\)
= 1 × \(\frac{5}{1}\)
= \(\frac{5}{1}\)
= 5.
Question 6.
Jamie divided 6\(\frac{2}{5}\) ounces of candy into equal amounts. He put the candy into containers that hold 2\(\frac{2}{3}\) ounces each. How many containers will be completely filled?
___________________ containers will be filled.
Answer:
Number of containers will be completely filled = \(\frac{12}{5}\) or 2\(\frac{2}{5}\).
\(\frac{12}{5}\) or 2\(\frac{2}{5}\) containers will be filled.
Explanation:
Number of ounces of candy Jamie divided into equal amounts = 6\(\frac{2}{5}\).
Number of ounches each container holds = 2\(\frac{2}{3}\).
Number of containers will be completely filled = Number of ounces of candy Jamie divided into equal amounts ÷ Number of ounches each container holds
= 6\(\frac{2}{5}\) ÷ 2\(\frac{2}{3}\)
= {[(6 × 5) + 2] ÷ 5} ÷ {[(2 × 3) + 2] ÷ 3}
= [(30 + 2) ÷ 5] ÷ [(6 + 2) ÷ 3]
= \(\frac{32}{5}\) ÷ \(\frac{8}{3}\)
= \(\frac{32}{5}\) × \(\frac{3}{8}\)
= \(\frac{4}{5}\) × \(\frac{3}{1}\)
= \(\frac{12}{5}\) or 2\(\frac{2}{5}\)
Question 7.
Dawson baked one pie in \(\frac{7}{12}\) of an hour. How long will it take Dawson to bake 9 pies?
Dawson will bake 9 pies in ___________________ hours
Answer:
Number of hours Dawson to bake = \(\frac{21}{4}\) or 5\(\frac{1}{4}\).
Dawson will bake 9 pies in \(\frac{21}{4}\) or 5\(\frac{1}{4}\) hours.
Explanation:
Number of hours Dawson baked one pie = \(\frac{7}{12}\)
Number of pies Dawson to bake = 9.
Number of hours Dawson to bake = Number of hours Dawson baked one pie × Number of pies Dawson to bake
= \(\frac{7}{12}\) × 9
= \(\frac{7}{4}\) × 3
= \(\frac{21}{4}\) or 5\(\frac{1}{4}\)
Solve each problem. Write answers in simplest form.
Question 1.
How many pieces of string that are \(\frac{2}{7}\) of an inch long can be cut from a piece of string that is \(\frac{7}{8}\) of an inch long?
______ pieces of string can be cut.
Answer:
Number of pieces of string = \(\frac{49}{16}\) or 3\(\frac{1}{16}\).
\(\frac{49}{16}\) or 3\(\frac{1}{16}\) pieces of string can be cut.
Explanation:
Number of inches each string = \(\frac{2}{7}\).
Number of inches the string = \(\frac{7}{8}\).
Number of pieces of string = Number of inches the string ÷ Number of inches each string
= \(\frac{7}{8}\) ÷ \(\frac{2}{7}\)
= \(\frac{7}{8}\) × \(\frac{7}{2}\)
= \(\frac{49}{16}\) or 3\(\frac{1}{16}\)
Question 2.
Five pounds of walnuts will be divided equally into containers which will hold \(\frac{5}{8}\) of a pound each. How many containers will be filled?
___________________ containers will be filled.
Answer:
Number of containers = 8.
8 containers will be filled.
Explanation:
Number of pounds of walnuts will be divided equally into containers = 5.
Number of pounds each container holds = \(\frac{5}{8}\).
Number of containers = Number of pounds of walnuts will be divided equally into containers ÷ Number of pounds each container holds
= 5 ÷ \(\frac{5}{8}\)
= 5 × \(\frac{8}{5}\)
= 1 × \(\frac{8}{1}\)
= \(\frac{8}{1}\)
= 8.
Question 3.
A ribbon is \(\frac{7}{9}\) of a yard long. It will be divided equally among 3 people. What is the length of ribbon that each person will get?
Each person will get _________________ of a yard.
Answer:
Number of yards of ribbon each person gets = \(\frac{7}{27}\)
Each person will get \(\frac{7}{27}\) of a yard.
Explanation:
Number of yards a ribbon = \(\frac{7}{9}\).
Number of peoples it is divided = 3.
Number of yards of ribbon each person gets = Number of yards a ribbon ÷ Number of peoples it is divided
= \(\frac{7}{9}\) ÷ 3
= \(\frac{7}{9}\) × \(\frac{1}{3}\)
= \(\frac{7}{27}\)
Question 4.
Raul can ride his bike 7\(\frac{1}{2}\) miles in one hour. How far can he ride in 2\(\frac{1}{3}\) hours?
Raul can ride ___________________ miles.
Answer:
Number of miles he can ride = 3.
Raul can ride 3 miles.
Explanation:
Number of miles Raul can ride his bike in one hour = 7\(\frac{1}{2}\).
Number of hours = 2\(\frac{1}{3}\)
Number of miles he can ride = Number of hours × Number of miles Raul can ride his bike in one hour
= 2\(\frac{1}{3}\) × 7\(\frac{1}{2}\)
= {[(2 × 3) + 1] ÷ 3} × {[(7 × 2) + 1] ÷ 7}
= [(6 + 1) ÷ 3] × [(14 + 1) ÷ 7]
= \(\frac{7}{3}\) × \(\frac{15}{7}\)
= \(\frac{1}{3}\) × \(\frac{15}{1}\)
= \(\frac{1}{1}\) × \(\frac{3}{1}\)
= \(\frac{3}{1}\)
= 3.
Question 5.
If 8 boards are stacked on top of each other and each board is 2\(\frac{1}{4}\)– inches thick, how high is the stack?
The stack is ___________________ inches high.
Answer:
Number of inches is the stack = 18.
The stack is 18 inches high.
Explanation:
Number of boards are stacked on top of each other = 8.
Number of inches of each board = 2\(\frac{1}{4}\).
Number of inches is the stack = Number of boards are stacked on top of each other × Number of inches of each board
= 8 × 2\(\frac{1}{4}\)
= 8 × {[(2 × 4) + 1] ÷ 4}
= 8 × [(8 + 1) ÷ 4]
= 8 × \(\frac{9}{4}\)
= 2 × \(\frac{9}{1}\)
= \(\frac{18}{1}\)
= 18.
Question 6.
A bag of potatoes weighs 2\(\frac{1}{2}\) pounds. How much would 3\(\frac{1}{3}\) bags weigh?
The bags would weigh ________________ pounds.
Answer:
Number of pounds the bags weighs = \(\frac{4}{3}\) or 1\(\frac{1}{3}\).
The bags would weigh \(\frac{4}{3}\) or 1\(\frac{1}{3}\) pounds.
Explanation:
Number of pounds a bag of potatoes weighs = 2\(\frac{1}{2}\).
Total number of pounds a bag of potatoes weighs = 3\(\frac{1}{3}\).
Number of pounds the bags weighs = Total number of pounds a bag of potatoes weighs ÷ Number of pounds a bag of potatoes weighs
= 3\(\frac{1}{3}\) ÷ 2\(\frac{1}{2}\)
= {[(3 × 3) + 1] ÷ 3} ÷ {[(2 × 2) + 1] ÷ 2}
= [(9 + 1) ÷ 3] ÷ [(4 + 1) ÷ 2]
= \(\frac{10}{3}\) ÷ \(\frac{5}{2}\)
= \(\frac{10}{3}\) × \(\frac{2}{5}\)
= \(\frac{2}{3}\) × \(\frac{2}{1}\)
= \(\frac{4}{3}\) or 1\(\frac{1}{3}\)
Question 7.
Jason put 6 pieces of chain together to make a fence. Each piece of chain was 3\(\frac{2}{5}\) Feet long. How long was the chain?
The chain was _________________ feet long.
Answer:
Number of feet was the chain = \(\frac{102}{5}\) or 20\(\frac{2}{5}\).
The chain was \(\frac{102}{5}\) or 20\(\frac{2}{5}\) feet long.
Explanation:
Number of pieces of chain Jason puts together to make a fence = 6.
Number of feet each piece of chain = 3\(\frac{2}{5}\).
Number of feet was the chain = Number of pieces of chain Jason puts together to make a fence × Number of feet each piece of chain
= 6 × 3\(\frac{2}{5}\)
= 6 × {[(3 × 5) + 2] ÷ 5}
= 6 × [(15 + 2) ÷ 5]
= 6 × \(\frac{17}{5}\)
= \(\frac{102}{5}\) or 20\(\frac{2}{5}\)