Go through the Spectrum Math Grade 6 Answer Key Chapter 2 Pretest and get the proper assistance needed during your homework.

Multiplying and Dividing Fractions

Question 1.
a. $$\frac{7}{8}$$ × $$\frac{3}{4}$$
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 × $$\frac{3}{8}$$
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
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
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$$\frac{3}{5}$$
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
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$$\frac{1}{3}$$
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$$\frac{1}{5}$$
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$$\frac{1}{8}$$
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 ÷ $$\frac{2}{3}$$
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
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 ÷ $$\frac{3}{8}$$
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. $$\frac{4}{5}$$ ÷ $$\frac{7}{8}$$
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. $$\frac{2}{3}$$ ÷ $$\frac{5}{6}$$
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. $$\frac{3}{8}$$ ÷ $$\frac{7}{8}$$
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$$\frac{1}{8}$$
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$$\frac{1}{4}$$
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
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.
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.
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.
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.
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.
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.
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.
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
= $$\frac{27}{4}$$ ÷ $$\frac{1}{9}$$
= $$\frac{3}{4}$$ ÷ $$\frac{1}{1}$$
= $$\frac{3}{4}$$.