Go through the Spectrum Math Grade 6 Answer Key Chapter 2 Posttest and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 2 Posttest Answers Key
Check What You Learned
Multiplying and Dividing Fractions
Multiply. Write answers in simplest form.
Question 1.
a. \(\frac{2}{3}\) × \(\frac{3}{4}\)
Answer:
Simplest form of \(\frac{2}{3}\) × \(\frac{3}{4}\) is \(\frac{1}{2}\).
Explanation:
\(\frac{2}{3}\) × \(\frac{3}{4}\)
= \(\frac{2}{1}\) × \(\frac{1}{4}\)
= \(\frac{1}{1}\) × \(\frac{1}{2}\)
= \(\frac{1}{2}\)
b. \(\frac{1}{2}\) × \(\frac{3}{8}\)
Answer:
Simplest form of \(\frac{1}{2}\) × \(\frac{3}{8}\) is \(\frac{3}{16}\).
Explanation:
\(\frac{1}{2}\) × \(\frac{3}{8}\)
= \(\frac{3}{16}\)
c. \(\frac{7}{8}\) × \(\frac{3}{5}\)
Answer:
Simplest form of \(\frac{7}{8}\) × \(\frac{3}{5}\) is \(\frac{7}{15}\).
Explanation:
\(\frac{7}{8}\) × \(\frac{3}{5}\)
= \(\frac{21}{45}\) × (3 ÷ 3)
= \(\frac{7}{15}\)
d. \(\frac{2}{7}\) × \(\frac{5}{8}\)
Answer:
Simplest form of \(\frac{2}{7}\) × \(\frac{5}{8}\) is \(\frac{5}{28}\).
Explanation:
\(\frac{2}{7}\) × \(\frac{5}{8}\)
= \(\frac{1}{7}\) × \(\frac{5}{4}\)
= \(\frac{5}{28}\)
Question 2.
a. \(\frac{2}{3}\) × 5
Answer:
Simplest form of \(\frac{2}{3}\) × 5 is \(\frac{10}{3}\) or 3\(\frac{1}{3}\).
Explanation:
\(\frac{2}{3}\) × 5
= \(\frac{10}{3}\) or 3\(\frac{1}{3}\)
b. 4 × \(\frac{7}{8}\)
Answer:
Simplest form of 4 × \(\frac{7}{8}\) is \(\frac{7}{4}\) or 1\(\frac{3}{4}\).
Explanation:
4 × \(\frac{7}{8}\)
= 1 × \(\frac{7}{4}\)
= \(\frac{7}{4}\) or 1\(\frac{3}{4}\)
c. \(\frac{3}{5}\) × 12
Answer:
Simplest form of \(\frac{3}{5}\) × 12 is \(\frac{36}{5}\) or 7\(\frac{1}{5}\).
Explanation:
\(\frac{3}{5}\) × 12
= \(\frac{36}{5}\) or 7\(\frac{1}{5}\)
d. 8 × \(\frac{4}{7}\)
Answer:
Simplest form of 8 × \(\frac{4}{7}\) is \(\frac{32}{7}\) or 4\(\frac{4}{7}\).
Explanation:
8 × \(\frac{4}{7}\)
= \(\frac{32}{7}\) or 4\(\frac{4}{7}\)
Write the reciprocal.
Question 5.
a. \(\frac{3}{8}\) ______
Answer:
Reciprocal of \(\frac{3}{8}\) is \(\frac{8}{3}\) .
Explanation:
\(\frac{3}{8}\) reciprocal = 1 ÷ \(\frac{3}{8}\)
= 1 × \(\frac{8}{3}\)
= \(\frac{8}{3}\)
b. 5 _______
Answer:
Reciprocal of 5 is \(\frac{1}{5}\).
Explanation:
5 reciprocal = 1 ÷ 5
= 1 × \(\frac{1}{5}\)
= \(\frac{1}{5}\)
c.
\(\frac{12}{5}\) ______
Answer:
Reciprocal of \(\frac{12}{5}\) is \(\frac{5}{12}\).
Explanation:
\(\frac{12}{5}\) reciprocal = 1 ÷ \(\frac{12}{5}\)
= 1 × \(\frac{5}{12}\)
= \(\frac{5}{12}\)
d.
\(\frac{4}{7}\) ______
Answer:
Reciprocal of \(\frac{4}{7}\) is \(\frac{7}{4}\).
Explanation:
\(\frac{4}{7}\) reciprocal = 1 ÷ \(\frac{4}{7}\)
= 1 × \(\frac{7}{4}\)
= \(\frac{7}{4}\)
Divide. Write answers in simplest form.
Question 6.
a. 5 ÷ \(\frac{2}{3}\) ______
Answer:
Simplest form of 5 ÷ \(\frac{2}{3}\) is \(\frac{15}{2}\) or 7\(\frac{1}{2}\).
Explanation:
5 ÷ \(\frac{2}{3}\)
= 5 × \(\frac{3}{2}\)
= \(\frac{15}{2}\) or 7\(\frac{1}{2}\)
b. \(\frac{4}{5}\) ÷ 5 ______
Answer:
Simplest form of \(\frac{4}{5}\) ÷ 5 is \(\frac{4}{25}\).
Explanation:
\(\frac{4}{5}\) ÷ 5
= \(\frac{4}{5}\) × \(\frac{1}{5}\)
= \(\frac{4}{25}\)
c. 7 ÷ \(\frac{3}{8}\) ______
Answer:
Simplest form of 7 ÷ \(\frac{3}{8}\) is \(\frac{56}{3}\) or 18\(\frac{2}{3}\).
Explanation:
7 ÷ \(\frac{3}{8}\)
= 7 × \(\frac{8}{3}\)
= \(\frac{56}{3}\) or 18\(\frac{2}{3}\)
d. \(\frac{7}{8}\) ÷ 2 ______
Answer:
Simplest form of \(\frac{7}{8}\) ÷ 2 is \(\frac{7}{16}\).
Explanation:
\(\frac{7}{8}\) ÷ 2
= \(\frac{7}{8}\) × \(\frac{1}{2}\)
= \(\frac{7}{16}\)
Question 7.
a. \(\frac{2}{3}\) ÷ \(\frac{4}{5}\)
Answer:
Simplest form of \(\frac{2}{3}\) ÷ \(\frac{4}{5}\) is \(\frac{5}{6}\).
Explanation:
\(\frac{2}{3}\) ÷ \(\frac{4}{5}\)
= \(\frac{2}{3}\) × \(\frac{5}{4}\)
= \(\frac{1}{3}\) × \(\frac{5}{2}\)
= \(\frac{5}{6}\)
b. \(\frac{7}{8}\) ÷ \(\frac{2}{3}\)
Answer:
Simplest form of \(\frac{7}{8}\) ÷ \(\frac{2}{3}\) is \(\frac{21}{16}\).
Explanation:
\(\frac{7}{8}\) ÷ \(\frac{2}{3}\)
= \(\frac{7}{8}\) × \(\frac{3}{2}\)
= \(\frac{21}{16}\)
c. \(\frac{4}{7}\) ÷ \(\frac{3}{8}\)
Answer:
Simplest form of \(\frac{4}{7}\) ÷ \(\frac{3}{8}\) is \(\frac{32}{21}\) or 1\(\frac{11}{21}\).
Explanation:
\(\frac{4}{7}\) ÷ \(\frac{3}{8}\)
= \(\frac{4}{7}\) × \(\frac{8}{3}\)
= \(\frac{32}{21}\) or 1\(\frac{11}{21}\)
d. \(\frac{5}{12}\) ÷ \(\frac{3}{4}\)
Answer:
Simplest form of \(\frac{5}{12}\) ÷ \(\frac{3}{4}\) is \(\frac{5}{9}\).
Explanation:
\(\frac{5}{12}\) ÷ \(\frac{3}{4}\)
= \(\frac{5}{12}\) × \(\frac{4}{3}\)
= \(\frac{5}{3}\) × \(\frac{1}{3}\)
= \(\frac{5}{9}\)
Question 8.
a. 3\(\frac{1}{8}\) ÷ 2\(\frac{1}{2}\)
Answer:
Simplest form of 3\(\frac{1}{8}\) ÷ 2\(\frac{1}{2}\) is \(\frac{5}{4}\).
Explanation:
3\(\frac{1}{8}\) ÷ 2\(\frac{1}{2}\)
= {[(3 × 8) + 1] ÷ 8} ÷ {[(2 × 2) + 1] ÷ 2}
= [(24 + 1) ÷ 8] ÷ [(4 + 1) ÷ 2]
= \(\frac{25}{8}\) ÷ \(\frac{5}{2}\)
= \(\frac{25}{8}\) × \(\frac{2}{5}\)
= \(\frac{5}{8}\) × \(\frac{2}{1}\)
= \(\frac{5}{4}\) × \(\frac{1}{1}\)
= \(\frac{5}{4}\)
b. 4\(\frac{2}{3}\) ÷ 3\(\frac{1}{2}\)
Answer:
Simplest form of 4\(\frac{2}{3}\) ÷ 3\(\frac{1}{2}\) is \(\frac{4}{3}\) or 1\(\frac{1}{3}\).
Explanation:
4\(\frac{2}{3}\) ÷ 3\(\frac{1}{2}\)
= {[(4 × 3) + 2] ÷ 3} ÷ {[(3 × 2) + 1] ÷ 2}
= [(12 + 2) ÷ 3] ÷ [(6 + 1) ÷ 2]
= \(\frac{14}{3}\) ÷ \(\frac{7}{2}\)
= \(\frac{14}{3}\) × \(\frac{2}{7}\)
= \(\frac{2}{3}\) × \(\frac{2}{1}\)
= \(\frac{4}{3}\) or 1\(\frac{1}{3}\)
c. 2\(\frac{3}{4}\) ÷ 2\(\frac{3}{4}\)
Answer:
Simplest form of 2\(\frac{3}{4}\) ÷ 2\(\frac{3}{4}\) is 1.
Explanation:
2\(\frac{3}{4}\) ÷ 2\(\frac{3}{4}\)
= {[(2 × 4) + 3] ÷ 4} ÷ {[(2 × 4) + 3] ÷ 4}
= [(8 + 3) ÷ 4] ÷ [(8 + 3) ÷ 4]
= \(\frac{11}{4}\) ÷ \(\frac{11}{4}\)
= \(\frac{11}{4}\) × \(\frac{4}{11}\)
= = \(\frac{1}{4}\) × \(\frac{4}{1}\)
= \(\frac{1}{1}\) × \(\frac{1}{1}\)
= \(\frac{1}{1}\)
= 1.
d. 1\(\frac{1}{2}\) ÷ 3\(\frac{1}{8}\)
Answer:
Simplest form of 1\(\frac{1}{2}\) ÷ 3\(\frac{1}{8}\) is \(\frac{6}{25}\).
Explanation:
1\(\frac{1}{2}\) ÷ 3\(\frac{1}{8}\)
= {[(1 × 2) + 1] ÷ 2} ÷ {[(3 × 8) + 1] ÷ 8}
= [(2 + 1) ÷ 2] ÷ [(24 + 1) ÷ 8]
= \(\frac{3}{2}\) ÷ \(\frac{25}{4}\)
= \(\frac{3}{2}\) × \(\frac{4}{25}\)
= \(\frac{3}{1}\) × \(\frac{2}{25}\)
= \(\frac{6}{25}\)
Solve each problem. Write answers in simplest form.
Question 9.
Alice and Samantha watered \(\frac{5}{6}\) of the yard together. Samantha watered \(\frac{1}{3}\) of that amount. What part of the yard did Samantha water?
Samantha watered __________ of the yard.
Answer:
Part of the yard did Samantha water = \(\frac{5}{18}\).
Samantha watered \(\frac{5}{18}\) of the yard.
Explanation:
Total part Alice and Samantha watered together = \(\frac{5}{6}\).
Part Samantha watered of that amount = \(\frac{1}{3}\).
Part of the yard did Samantha water = Total part Alice and Samantha watered together × Part Samantha watered of that amount
= \(\frac{5}{6}\) × \(\frac{1}{3}\)
= \(\frac{5}{18}\)
Question 10.
Ramona sets aside \(\frac{3}{4}\) of an hour for homework after school each day. How many hours does she do homework in 5 days?
Ramona does __________ hours of homework in 5 days.
Answer:
Number of hours she does homework in 5 days = \(\frac{15}{4}\) or 3\(\frac{3}{4}\).
Ramona does \(\frac{15}{4}\) or 3\(\frac{3}{4}\) hours of homework in 5 days.
Explanation:
Part of an hour for homework after school each day Ramona sets aside = \(\frac{3}{4}\)
Number of days = 5.
Number of hours she does homework in 5 days = Part of an hour for homework after school each day Ramona sets aside × Number of days
= \(\frac{3}{4}\) × 5
= \(\frac{15}{4}\) or 3\(\frac{3}{4}\)
Question 11.
Anita can skate 3\(\frac{1}{3}\) miles in 1 hour. How far can she skate in 2\(\frac{1}{2}\) hours?
Anita can skate ___________ miles.
Answer:
Number of miles she can skate = \(\frac{3}{4}\).
Anita can skate \(\frac{3}{4}\) miles.
Explanation:
Number of miles Anita can skate in 1 hour = 3\(\frac{1}{3}\).
Total number of hours she can skate = 2\(\frac{1}{2}\).
Number of miles she can skate = Total number of hours she can skate ÷ Number of miles Anita can skate in 1 hour
= 2\(\frac{1}{2}\) ÷ 3\(\frac{1}{3}\)
= {[(2 × 2) + 1] ÷ 2} ÷ {[(3 × 3) + 1] ÷ 3}
= [(4 + 1) ÷ 2] ÷ [(9 + 1) ÷ 3]
= \(\frac{5}{2}\) ÷ \(\frac{10}{3}\)
= \(\frac{5}{2}\) × \(\frac{3}{10}\)
= \(\frac{1}{2}\) × \(\frac{3}{2}\)
= \(\frac{3}{4}\).
Question 12.
A stack of 5 bricks is on the driveway. Each brick is 2\(\frac{1}{3}\)– inches thick. How high is the stack of bricks?
The stack of bricks is ____________ inches high.
Answer:
Number of inches high is the stack of bricks = \(\frac{35}{3}\) or 11\(\frac{2}{3}\).
The stack of bricks is \(\frac{35}{3}\) or 11\(\frac{2}{3}\) inches high.
Explanation:
Number of bricks a stack has on the driveway = 5.
Number of inches each brick = 2\(\frac{1}{3}\).
Number of inches high is the stack of bricks = Number of bricks a stack has on the driveway × Number of inches each brick
= 5 × 2\(\frac{1}{3}\)
= 5 × {[(2 × 3) + 1] ÷ 3}
= 5 × [(6 + 1) ÷ 3]
= 5 × \(\frac{7}{3}\)
= \(\frac{35}{3}\) or 11\(\frac{2}{3}\)
Question 13.
At the grocery, the bogs of oranges weigh ‘4\(\frac{1}{3}\) pounds. How much would 2\(\frac{1}{2}\) bags of oranges weigh?
The bags would weigh _____ pounds.
Answer:
Number of bags of oranges weighs = \(\frac{26}{15}\) pounds.
The bags would weigh \(\frac{26}{15}\) pounds.
Explanation:
Number of pounds at the grocery, the bogs of oranges weigh = 4\(\frac{1}{3}\).
Total number of pounds bags of oranges weigh = 2\(\frac{1}{2}\).
Number of bags of oranges weighs = Number of pounds at the grocery, the bogs of oranges weigh ÷ Total number of pounds bags of oranges weigh
= 4\(\frac{1}{3}\) ÷ 2\(\frac{1}{2}\)
= {[(4 × 3) + 1] ÷ 3} ÷ {[(2 × 2) + 1] ÷ 2}
= [(12 + 1) ÷ 3] ÷ [(4 + 1) ÷ 2]
= \(\frac{13}{3}\) ÷ \(\frac{5}{2}\)
= \(\frac{13}{3}\) × \(\frac{2}{5}\)
= \(\frac{26}{15}\) pounds.
Question 14.
It takes a baseball team 2 hours to complete a game. How long will it take to complete \(\frac{2}{3}\) of the game?
It will take ___________ hours.
Answer:
Number of hours it takes = \(\frac{1}{3}\).
It will take \(\frac{1}{3}\) hours.
Explanation:
Number of hours it takes a baseball team to complete a game = 2.
Part of the game = \(\frac{2}{3}\).
Number of hours it takes = Part of the game ÷ Number of hours it takes a baseball team to complete a game
= \(\frac{2}{3}\) ÷ 2
= \(\frac{2}{3}\) × \(\frac{1}{2}\)
= \(\frac{1}{3}\) × \(\frac{1}{1}\)
= \(\frac{1}{3}\).
Question 15.
A bag holding 7\(\frac{1}{5}\) pounds of mixed nuts will be divided equally among 9 people. How many pounds of nuts will each person get?
Each person will get ____________ of a pound of nuts.
Answer:
Number of pounds of nuts each person gets = \(\frac{4}{5}\).
Each person will get \(\frac{4}{5}\) of a pound of nuts.
Explanation:
Number of pounds of mixed nuts a bag holds = 7\(\frac{1}{5}\).
Number of people its divided = 9.
Number of pounds of nuts each person gets = Number of pounds of mixed nuts a bag holds ÷ Number of people its divided
= 7\(\frac{1}{5}\) ÷ 9
= {[(7 × 5) + 1] ÷ 5} ÷ 9
= [(35 + 1) ÷ 5] ÷ 9
= \(\frac{36}{5}\) × \(\frac{1}{9}\)
= \(\frac{4}{5}\) × \(\frac{1}{1}\)
= \(\frac{4}{5}\).