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

= \(\frac{27}{4}\) ÷ \(\frac{1}{9}\)

= \(\frac{3}{4}\) ÷ \(\frac{1}{1}\)

= \(\frac{3}{4}\).