Go through the Spectrum Math Grade 6 Answer Key Chapter 2 Pretest and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 2 Pretest Answers Key
Multiplying and Dividing Fractions
Question 1.
a. \(\frac{7}{8}\) × \(\frac{3}{4}\)
Answer:
Product of \(\frac{7}{8}\) × \(\frac{3}{4}\) is \(\frac{21}{28}\).
Explanation:
\(\frac{7}{8}\) × \(\frac{3}{4}\)
= (7 × 3) ÷ (8 × 4)
= \(\frac{21}{28}\)
b. 9 × \(\frac{3}{8}\)
Answer:
Product of 9 × \(\frac{3}{8}\) is \(\frac{27}{8}\) or 3\(\frac{3}{8}\).
Explanation:
9 × \(\frac{3}{8}\)
= (9 × 3) ÷ (1 × 8)
= \(\frac{27}{8}\) or 3\(\frac{3}{8}\)
c. \(\frac{5}{8}\) × 5
Answer:
Product of \(\frac{5}{8}\) × 5 is \(\frac{25}{8}\) or 3\(\frac{1}{8}\).
Explanation:
\(\frac{5}{8}\) × 5
= (5 × 5) ÷ (8 × 1)
= \(\frac{25}{8}\) or 3\(\frac{1}{8}\)
Question 2.
a. 3\(\frac{1}{8}\) × 4
Answer:
Product of 3\(\frac{1}{8}\) × 4 is \(\frac{25}{2}\) or 12\(\frac{1}{2}\).
Explanation:
3\(\frac{1}{8}\) × 4
= {[(3 × 8) + 1] ÷ 8} × 4
= [(24 + 1) ÷ 8] × 4
= \(\frac{25}{8}\) × 4
= \(\frac{25}{2}\) × 1
= \(\frac{25}{2}\) or 12\(\frac{1}{2}\)
b. 8 × 2\(\frac{3}{5}\)
Answer:
Product of 8 × 2\(\frac{3}{5}\) is \(\frac{104}{5}\) or 20\(\frac{4}{5}\).
Explanation:
8 × 2\(\frac{3}{5}\)
= 8 × {[(2 × 5) + 3] ÷ 5}
= 8 × [(10 + 3) ÷ 5]
= 8 × \(\frac{13}{5}\)
= (8 × 13) ÷ (1 × 5)
= \(\frac{104}{5}\) or 20\(\frac{4}{5}\)
c. 4\(\frac{1}{2}\) × 9
Answer:
Product of 4\(\frac{1}{2}\) × 9 is \(\frac{81}{2}\) or 40\(\frac{1}{2}\).
Explanation:
4\(\frac{1}{2}\) × 9
= {[(4 × 2) + 1] ÷ 2} × 9
= [(8 + 1) ÷ 2] × 9
= \(\frac{9}{2}\) × 9
= (9 × 9) ÷ (2 × 1)
= \(\frac{81}{2}\) or 40\(\frac{1}{2}\)
Question 3.
a. 5\(\frac{3}{4}\) × 2\(\frac{1}{3}\)
Answer:
Product of 5\(\frac{3}{4}\) × 2\(\frac{1}{3}\) is \(\frac{161}{12}\) or 13\(\frac{5}{12}\).
Explanation:
5\(\frac{3}{4}\) × 2\(\frac{1}{3}\)
= {[(5 × 4) + 3] ÷ 4} × {[(2 × 3) + 1] ÷ 3}
= [(20 + 3) ÷ 4] × [(6 + 1) ÷ 3]
= \(\frac{23}{4}\) × \(\frac{7}{3}\)
= (23 × 7) ÷ (4 × 3)
= \(\frac{161}{12}\) or 13\(\frac{5}{12}\)
b. 2\(\frac{1}{4}\) × 3\(\frac{1}{5}\)
Answer:
Product of 2\(\frac{1}{4}\) × 3\(\frac{1}{5}\) is \(\frac{36}{5}\) or 7\(\frac{1}{5}\).
Explanation:
2\(\frac{1}{4}\) × 3\(\frac{1}{5}\)
= {[(2 × 4) + 1] ÷ 4} × {[(3 × 5) + 1] ÷ 5}
= [(8 + 1) ÷ 4] × [(15 + 1) ÷ 5]
= \(\frac{9}{4}\) × \(\frac{16}{5}\)
= \(\frac{9}{1}\) × \(\frac{4}{5}\)
= (9 × 4) ÷ (1 × 5)
= \(\frac{36}{5}\) or 7\(\frac{1}{5}\)
c. 3\(\frac{2}{3}\) × 1\(\frac{1}{8}\)
Answer:
Product of 3\(\frac{2}{3}\) × 1\(\frac{1}{8}\) is \(\frac{33}{8}\) or 4\(\frac{1}{8}\).
Explanation:
3\(\frac{2}{3}\) × 1\(\frac{1}{8}\)
= {[(3 × 3) + 2] ÷ 3} × {[(1 × 8) + 1] ÷ 8}
= [(9 + 2) ÷ 3] × [(8 + 1) ÷ 8]
= \(\frac{11}{3}\) × \(\frac{9}{8}\)
= \(\frac{11}{1}\) × \(\frac{3}{8}\)
= (11 × 3) ÷ (1 × 8)
= \(\frac{33}{8}\) or 4\(\frac{1}{8}\)
Question 4.
a. 8 ÷ \(\frac{2}{3}\)
Answer:
Dividing 8 by \(\frac{2}{3}\), we get the answer 12.
Explanation:
8 ÷ \(\frac{2}{3}\)
= 8 × \(\frac{3}{2}\)
= 4 × \(\frac{3}{1}\)
= \(\frac{12}{1}\)
= 12.
b. \(\frac{4}{5}\) ÷ 3
Answer:
Dividing 3 by \(\frac{4}{5}\), we get the answer \(\frac{4}{15}\).
Explanation:
\(\frac{4}{5}\) ÷ 3
= \(\frac{4}{5}\) × \(\frac{1}{3}\)
= (4 × 1) ÷ (5 × 3)
= \(\frac{4}{15}\)
c. 10 ÷ \(\frac{3}{8}\)
Answer:
Dividing 10 by \(\frac{3}{8}\),we get the answer \(\frac{80}{3}\) or 23\(\frac{2}{3}\).
Explanation:
10 ÷ \(\frac{3}{8}\)
= 10 × \(\frac{8}{3}\)
= \(\frac{80}{3}\) or 23\(\frac{2}{3}\)
Question 5.
a. \(\frac{4}{5}\) ÷ \(\frac{7}{8}\)
Answer:
Dividing \(\frac{4}{5}\) by \(\frac{7}{8}\), we get the answer \(\frac{32}{35}\).
Explanation:
\(\frac{4}{5}\) ÷ \(\frac{7}{8}\)
= \(\frac{4}{5}\) × \(\frac{8}{7}\)
= (4 × 8) ÷ (5 × 7)
= \(\frac{32}{35}\)
b. \(\frac{2}{3}\) ÷ \(\frac{5}{6}\)
Answer:
Dividing \(\frac{2}{3}\) by \(\frac{5}{6}\), we get the answer \(\frac{4}{5}\).
Explanation:
\(\frac{2}{3}\) ÷ \(\frac{5}{6}\)
= \(\frac{2}{3}\) × \(\frac{6}{5}\)
= \(\frac{2}{1}\) × \(\frac{2}{5}\)
= (2 × 2) ÷ (1 × 5)
= \(\frac{4}{5}\)
c. \(\frac{3}{8}\) ÷ \(\frac{7}{8}\)
Answer:
Dividing \(\frac{3}{8}\) by \(\frac{7}{8}\), we get the answer \(\frac{3}{7}\).
Explanation:
\(\frac{3}{8}\) ÷ \(\frac{7}{8}\)
= \(\frac{3}{8}\) × \(\frac{8}{7}\)
= \(\frac{3}{1}\) × \(\frac{1}{7}\)
= (3 × 1) ÷ (1 × 7)
= \(\frac{3}{7}\)
Question 6.
a. 2\(\frac{3}{4}\) ÷ 3\(\frac{1}{8}\)
Answer:
Dividing 2\(\frac{3}{4}\) by 3\(\frac{1}{8}\), we get the answer \(\frac{22}{25}\).
Explanation:
2\(\frac{3}{4}\) ÷ 3\(\frac{1}{8}\)
= {[(2 × 4) + 3] ÷ 4} ÷ {[(3 × 8) + 1] ÷ 8}
= [(8 + 3) ÷ 4] ÷ [(24 + 1) ÷ 8]
= \(\frac{11}{4}\) ÷ \(\frac{25}{8}\)
= \(\frac{11}{4}\) × \(\frac{8}{25}\)
= \(\frac{11}{1}\) × \(\frac{2}{25}\)
= (11 × 2) ÷ (1 × 25)
= \(\frac{22}{25}\)
b. 7 ÷ 3\(\frac{1}{4}\)
Answer:
Dividing 7 by 3\(\frac{1}{4}\), we get the answer \(\frac{28}{13}\) or 2\(\frac{2}{13}\).
Explanation:
7 ÷ 3\(\frac{1}{4}\)
= 7 ÷ {[(3 × 4) + 1] ÷ 4}
= 7 ÷ [(12 + 1) ÷ 4]
= 7 ÷ \(\frac{13}{4}\)
= 7 × \(\frac{4}{13}\)
= (7 × 4) ÷ (1 × 13)
= \(\frac{28}{13}\) or 2\(\frac{2}{13}\)
c. 7\(\frac{3}{8}\) ÷ 9
Answer:
Dividing 7\(\frac{3}{8}\) by 9, we get the answer \(\frac{59}{72}\).
Explanation:
7\(\frac{3}{8}\) ÷ 9
= {[(7 × 8) + 3] ÷ 8} ÷ 9
= [(56 + 3) ÷ 8] ÷ 9
= \(\frac{59}{8}\) ÷ 9
= \(\frac{59}{8}\) × \(\frac{1}{9}\)
= \(\frac{59}{72}\)
Solve each problem. Write answers in simplest form.
Question 7.
John and George together raked \(\frac{7}{8}\) of the yard. John raked \(\frac{3}{4}\) of that amount. What part of the yard did John rake?
John raked ____ of the yard.
Answer:
Part of the yard did John raked = \(\frac{21}{32}\).
John raked \(\frac{21}{32}\) of the yard.
Explanation:
Part of the yard John and George together raked = \(\frac{7}{8}\).
Part of that amount John raked = \(\frac{3}{4}\).
Part of the yard did John raked = Part of the yard John and George together raked × Part of that amount John raked
= \(\frac{7}{8}\) × \(\frac{3}{4}\)
= (7 × 3) ÷ (8 × 4)
= \(\frac{21}{32}\)
Question 8.
Felipe has track practice for \(\frac{5}{8}\) of an hour after school each day. How many hours does he have track practice in 5 days?
Felipe his track practice for ____________ hours.
Answer:
Number of hours Felipe has track practice in 5days = \(\frac{25}{8}\) or 3\(\frac{1}{8}\).
Felipe his track practice for \(\frac{25}{8}\) or 3\(\frac{1}{8}\) hours.
Explanation:
Number of hours Felipe has track practice after school each day = \(\frac{5}{8}\).
Number of days = 5.
Number of hours Felipe has track practice in 5days = Number of hours Felipe has track practice after school each day × Number of days
= \(\frac{5}{8}\) × 5
= (5 × 5) ÷ (8 × 1)
= \(\frac{25}{8}\) or 3\(\frac{1}{8}\)
Question 9.
Paul can walk 2\(\frac{1}{2}\) miles in 1 hour. How far can he walk in 1\(\frac{3}{4}\) hours?
Paul can walk ___________ miles.
Answer:
Number of miles he walks in 1\(\frac{3}{4}\) hours = \(\frac{7}{10}\).
Paul can walk \(\frac{7}{10}\) miles.
Explanation:
Number of miles in 1 hour Paul can walk = 2\(\frac{1}{2}\).
Total number of hours he walks = 1\(\frac{3}{4}\).
Number of miles he walks in 1\(\frac{3}{4}\) hours = Total number of hours he walks ÷ Number of miles in 1 hour Paul can walk
= 1\(\frac{3}{4}\) ÷ 2\(\frac{1}{2}\)
= {[(1 × 4) + 3] ÷ 4} ÷ {[(2 × 2) + 1] ÷ 2}
= [(4 + 3) ÷ 4] ÷ [(4 + 1) ÷ 2]
= \(\frac{7}{4}\) ÷ \(\frac{5}{2}\)
= \(\frac{7}{4}\) × \(\frac{2}{5}\)
= \(\frac{7}{2}\) × \(\frac{1}{5}\)
= \(\frac{7}{10}\)
Question 10.
Brad has a stack of 7 books on his desk. Each book is 1\(\frac{7}{8}\) inches thick. How tall is the stack?
The stack is ____________ inches tall.
Answer:
Number of inches is the stack = \(\frac{105}{8}\) or 13\(\frac{1}{8}\).
The stack is \(\frac{105}{8}\) or 13\(\frac{1}{8}\) inches tall.
Explanation:
Number of books on his desk Brad has a stack = 7.
Number of inches each book = 1\(\frac{7}{8}\).
Number of inches is the stack = Number of books on his desk Brad has a stack × Number of inches each book
= 7 × 1\(\frac{7}{8}\)
= 7 × {[(1 × 8) + 7] ÷ 8}
= 7 × [(8 + 7) ÷ 8]
= 7 × \(\frac{15}{8}\)
= (7 × 15) ÷ (1 × 8)
= \(\frac{105}{8}\) or 13\(\frac{1}{8}\)
Question 11.
A bag of candy weighs 3\(\frac{2}{3}\) ounces. How much would 4\(\frac{1}{2}\) bags of candy weigh?
The bags would weigh __________ ounces.
Answer:
Number of ounces bags weighs = \(\frac{27}{22}\) or 1\(\frac{5}{22}\).
The bags would weigh \(\frac{27}{22}\) or 1\(\frac{5}{22}\) ounces.
Explanation:
Number of ounces a bag of candy weighs = 3\(\frac{2}{3}\).
Total number of ounces bags of candy weighs = 4\(\frac{1}{2}\).
Number of ounces bags weighs = Total number of ounces bags of candy weighs ÷ Number of ounces a bag of candy weighs
= 4\(\frac{1}{2}\) ÷ 3\(\frac{2}{3}\)
= {[(4 × 2) + 1] ÷ 2} ÷ {[(3 × 3) + 2] ÷ 3}
= [(8 + 1) ÷ 2] ÷ [(9 + 2) ÷ 3]
= \(\frac{9}{2}\) ÷ \(\frac{11}{3}\)
= \(\frac{9}{2}\) × \(\frac{3}{11}\)
= (9 × 3) ÷ (2 × 11)
= \(\frac{27}{22}\) or 1\(\frac{5}{22}\)
Question 12.
It takes 8 hours to paint a room. How long will it take to paint \(\frac{2}{3}\) of the room?
It will take ____________ hours to paint \(\frac{2}{3}\) of the room.
Answer:
Number of hours it takes to paint \(\frac{2}{3}\) of the room = \(\frac{1}{12}\).
It will take \(\frac{1}{12}\) hours to paint \(\frac{2}{3}\) of the room.
Explanation:
Number of hours it takes to paint a room = 8.
Part of the room it takes to paint = \(\frac{2}{3}\).
Number of hours it takes to paint \(\frac{2}{3}\) of the room = Part of the room it takes to paint ÷ Number of hours it takes to paint a room
= \(\frac{2}{3}\) ÷ 8
= \(\frac{2}{3}\) × \(\frac{1}{8}\)
= \(\frac{1}{3}\) × \(\frac{1}{4}\)
= (1 × 1) ÷ (3 × 4)
= \(\frac{1}{12}\)
Question 13.
Jim vill divide 6\(\frac{3}{4}\) pounds of candy equally among 9 friends. How much candy will each friend get?
Each friend will get ___________ of a pound.
Answer:
Number of pounds of candy will each friend gets = \(\frac{3}{4}\).
Each friend will get \(\frac{3}{4}\) of a pound.
Explanation:
Total number of pounds of candy Jim vill divide = 6\(\frac{3}{4}\).
Number of friends equally he divides the candy = 9.
Number of pounds of candy will each friend gets = Total number of pounds of candy Jim vill divide ÷ Number of friends equally he divides the candy
= 6\(\frac{3}{4}\) ÷ 9
= {[(6 × 4) + 3] ÷ 4} ÷ 9
= [(24 + 3) ÷ 4] ÷ 9
= \(\frac{27}{4}\) ÷ 9
= \(\frac{27}{4}\) ÷ \(\frac{1}{9}\)
= \(\frac{3}{4}\) ÷ \(\frac{1}{1}\)
= \(\frac{3}{4}\).