Go through the **Spectrum Math Grade 6 Answer Key Chapter 3 Lesson 3.2 Solving Ratios** and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 3 Lesson 3.2 Solving Ratios Answers Key

A proportion can be used in problem solving.

The ratio of apples to oranges is 4 to 5. There are 20 oranges in the basket.

How many apples are there?

\(\frac{4}{5}\) = \(\frac{n}{20}\) Set up a proportion, using n for the missing number.

4 × 20 = 5 × n Cross-multiply.

\(\frac{80}{5}\) = n Solve for n.

16 = n There are 16 apples.

**Solve.
**Question 1.

a. \(\frac{1}{3}\) = \(\frac{n}{24}\) ___________

Answer:

The value of n in \(\frac{1}{3}\) = \(\frac{n}{24}\) is 8.

Explanation:

\(\frac{1}{3}\) = \(\frac{n}{24}\)

=> 1 × 24 = n × 3

=> 24 = 3n

=> 24 ÷ 3 = n

=> 8 = n.

b. \(\frac{4}{9}\) = \(\frac{n}{36}\) ___________

Answer:

The value of n in \(\frac{4}{9}\) = \(\frac{n}{36}\) is 16.

Explanation:

\(\frac{4}{9}\) = \(\frac{n}{36}\)

=> 4 × 36 = n × 9

=>144 = 9n

=> 144 ÷ 9 = n

=> 16 = n.

c. \(\frac{5}{45}\) = \(\frac{n}{9}\) ___________

Answer:

The value of n in \(\frac{5}{45}\) = \(\frac{n}{9}\) is 1.

Explanation:

\(\frac{5}{45}\) = \(\frac{n}{9}\)

=> 5 × 9 = n × 45

=> 45 = 45n

=> 45 ÷ 45 = n

=> 1 = n.

Question 2.

a. \(\frac{3}{5}\) = \(\frac{n}{15}\) ___________

Answer:

The value of n in \(\frac{3}{5}\) = \(\frac{n}{15}\) is 9.

Explanation:

\(\frac{3}{5}\) = \(\frac{n}{15}\)

=> 3 × 15 = n × 5

=> 45 = 5n

=> 45 ÷ 5 = n

=> 9 = n.

b. \(\frac{10}{70}\) = \(\frac{n}{7}\) ___________

Answer:

The value of n in \(\frac{10}{70}\) = \(\frac{n}{7}\) is 1.

Explanation:

\(\frac{10}{70}\) = \(\frac{n}{7}\)

=> 10 × 7 = n × 70

=> 70 = 70n

=> 70 ÷ 70 = n

=> 1 = n.

c. \(\frac{25}{40}\) = \(\frac{n}{16}\) ___________

Answer:

The value of n in \(\frac{25}{40}\) = \(\frac{n}{16}\) is 10.

Explanation:

\(\frac{25}{40}\) = \(\frac{n}{16}\)

=> 25 × 16 = n × 40

=> 400 = 40n

=> 400 ÷ 40 = n

=> 10 = n.

Question 3.

a. \(\frac{7}{12}\) = \(\frac{n}{36}\) ___________

Answer:

The value of n in \(\frac{7}{12}\) = \(\frac{n}{36}\) is 21.

Explanation:

\(\frac{7}{12}\) = \(\frac{n}{36}\)

=> 7 × 36 = n × 12

=> 252 = 12n

=> 252 ÷ 12 = n

=> 21 =n.

b. \(\frac{13}{26}\) = \(\frac{n}{4}\) ___________

Answer:

The value of n in \(\frac{13}{26}\) = \(\frac{n}{4}\) is 2.

Explanation:

\(\frac{13}{26}\) = \(\frac{n}{4}\)

=> 13 × 4 = n × 26

=> 52 = 26n

=> 52 ÷ 26 = n

=> 2 = n.

c. \(\frac{7}{1}\) = \(\frac{n}{3}\) ___________

Answer:

The value of n in \(\frac{7}{1}\) = \(\frac{n}{3}\) is 21.

Explanation:

\(\frac{7}{1}\) = \(\frac{n}{3}\)

=> 7 × 3 = n × 1

=> 21 = 1n

=> 21 ÷ 1 = n

=> 21 = n.

Question 4.

a. \(\frac{8}{5}\) = \(\frac{n}{40}\) ___________

Answer:

The value of n in \(\frac{8}{5}\) = \(\frac{n}{40}\) is 64.

Explanation:

\(\frac{8}{5}\) = \(\frac{n}{40}\)

=> 8 × 40 = n × 5

=> 320 = 5n

=> 320 ÷ 5 = n

=> 64 = n.

b. \(\frac{2}{6}\) = \(\frac{n}{33}\) ___________

Answer:

The value of n in \(\frac{2}{6}\) = \(\frac{n}{33}\) is 11.

Explanation:

\(\frac{2}{6}\) = \(\frac{n}{33}\)

=> 2 × 33 = n × 6

=> 66 = 6n

=> 66 ÷ 6 = n

=> 11 = n.

c. \(\frac{5}{13}\) = \(\frac{n}{39}\) ___________

Answer:

The value of n in latex]\frac{5}{13}[/latex] = \(\frac{n}{39}\) is 15.

Explanation:

latex]\frac{5}{13}[/latex] = \(\frac{n}{39}\)

=> 5 × 39 = n × 13

=> 195 = 13n

=> 195 ÷ 13 = n

=> 15 = n.

Question 5.

a. \(\frac{5}{6}\) = \(\frac{n}{18}\) ___________

Answer:

The value of n in \(\frac{5}{6}\) = \(\frac{n}{18}\) is 15.

Explanation:

\(\frac{5}{6}\) = \(\frac{n}{18}\)

=> 5 × 18 = n × 6

=> 90 = 6n

=> 90 ÷ 6 = n

=> 15 = n.

b. \(\frac{9}{8}\) = \(\frac{n}{32}\) ___________

Answer:

The value of n in \(\frac{9}{8}\) = \(\frac{n}{32}\) is 36.

Explanation:

\(\frac{9}{8}\) = \(\frac{n}{32}\)

=> 9 × 32 = n × 8

=> 288 = 8n

=> 288 ÷ 8 = n

=> 36 = n.

c. \(\frac{2}{3}\) = \(\frac{n}{15}\) ___________

Answer:

The value of n in \(\frac{2}{3}\) = \(\frac{n}{15}\) is 10.

Explanation:

\(\frac{2}{3}\) = \(\frac{n}{15}\)

=> 2 × 15 = n × 3

=> 30 = 3n

=> 30 ÷ 3 = n

=> 10 = n.

A proportion can be used in problem solving.

The ratio of apples to oranges is 4 to 5. There are 20 oranges in the basket. How many apples are there?

\(\frac{4}{5}\) = \(\frac{4}{20}\) ___________ Set up a proportion, using n for the missing number.

4 × 20 = 5 × n Cross-multiply

\(\frac{80}{5}\) =n Solve for n

16 = n There are 16 apples.

**Solve.
**Question 1.

a. \(\frac{1}{3}\) = \(\frac{n}{24}\) _________

Answer:

The value of n in \(\frac{1}{3}\) = \(\frac{n}{24}\) is 8.

Explanation:

\(\frac{1}{3}\) = \(\frac{n}{24}\)

=> 1 × 24 = n × 3

=> 24 = 3n

=> 24 ÷ 3 = n

=> 8 = n.

b. \(\frac{4}{9}\) = \(\frac{n}{36}\) _________

Answer:

The value of n in \(\frac{4}{9}\) = \(\frac{n}{36}\) is 16.

Explanation:

\(\frac{4}{9}\) = \(\frac{n}{36}\)

=> 4 × 36 = n × 9

=> 144 = 9n

=> 144 ÷ 9 = n

=> 16 = n.

c. \(\frac{5}{45}\) = \(\frac{n}{9}\) _________

Answer:

The value of n in \(\frac{5}{45}\) = \(\frac{n}{9}\) is 1.

Explanation:

\(\frac{5}{45}\) = \(\frac{n}{9}\)

= 4 × 9 = n × 45

=> 45 = 45n

=> 45 ÷ 45 = n

=> 1 = n.

Question 2.

a. \(\frac{3}{5}\) = \(\frac{n}{15}\) _________

Answer:

The value of n in \(\frac{3}{5}\) = \(\frac{n}{15}\) is 9.

Explanation:

\(\frac{3}{5}\) = \(\frac{n}{15}\)

=> 3 × 15 = n × 5

=> 45 = 5n

=> 45 ÷ 5 = n

=> 9 = n.

b. \(\frac{10}{70}\) = \(\frac{n}{7}\) _________

Answer:

The value of n in \(\frac{10}{70}\) = \(\frac{n}{7}\) is 1.

Explanation:

\(\frac{10}{70}\) = \(\frac{n}{7}\)

=> 10 × 7 = n × 70

=> 70 = 70n

=> 70 ÷ 70 = n

=> 1 = n.

c. \(\frac{25}{40}\) = \(\frac{n}{16}\) _________

Answer:

The value of n in \(\frac{25}{40}\) = \(\frac{n}{16}\) is 10.

Explanation:

\(\frac{25}{40}\) = \(\frac{n}{16}\)

=> 25 × 16 = n × 40

=> 400 = 40n

=> 400 ÷ 40 = n

=> 10 = n.

Question 3.

a. \(\frac{7}{12}\) = \(\frac{n}{36}\) _________

Answer:

The value of n in \(\frac{7}{12}\) = \(\frac{n}{36}\) is 21.

Explanation:

\(\frac{7}{12}\) = \(\frac{n}{36}\)

=> 7 × 36 = n × 12

=> 252 = 12n

=> 252 ÷ 12 = n

=> 21 = n.

b. \(\frac{13}{26}\) = \(\frac{n}{4}\) _________

Answer:

The value of n in \(\frac{13}{26}\) = \(\frac{n}{4}\) is 2.

Explanation:

\(\frac{13}{26}\) = \(\frac{n}{4}\)

=> 13 × 4 = n × 26

=> 52 = 26n

=> 52 ÷ 26 = n

=> 2 = n.

c. \(\frac{7}{1}\) = \(\frac{n}{3}\) _________

Answer:

The value of n in \(\frac{7}{1}\) = \(\frac{n}{3}\) is 21.

Explanation:

\(\frac{7}{1}\) = \(\frac{n}{3}\)

= 7 × 3 = n × 1

=> 21 = 1n

=> 21 ÷ 1 = n

=> 21 = n.

Question 4.

a. \(\frac{8}{5}\) = \(\frac{n}{40}\) _________

Answer:

The value of n in \(\frac{8}{5}\) = \(\frac{n}{40}\) is 64.

Explanation:

\(\frac{8}{5}\) = \(\frac{n}{40}\)

=> 8 × 40 = n × 5

=> 320 = 5n

=> 320 ÷ 5 = n

=> 64 = n.

b. \(\frac{2}{6}\) = \(\frac{n}{33}\) _________

Answer:

The value of n in \(\frac{2}{6}\) = \(\frac{n}{33}\) is 11.

Explanation:

\(\frac{2}{6}\) = \(\frac{n}{33}\)

=> 2 × 33 = n × 6

=> 66 = 6n

=> 66 ÷ 6 = n

=> 11 = n.

c. \(\frac{5}{13}\) = \(\frac{n}{39}\) _________

Answer:

The value of n in \(\frac{5}{13}\) = \(\frac{n}{39}\) is 15.

Explanation:

\(\frac{5}{13}\) = \(\frac{n}{39}\)

=> 5 × 39 = n × 13

=> 195 = 13n

=> 195 ÷ 13 = n

=> 15 = n.

Question 5.

a. \(\frac{5}{6}\) = \(\frac{n}{18}\) _________

Answer:

The value of n in \(\frac{5}{6}\) = \(\frac{n}{18}\) is 15.

Explanation:

\(\frac{5}{6}\) = \(\frac{n}{18}\)

=> 5 × 18 = n × 6

=> 90 = 6n

=> 90 ÷ 6 = n

=> 15 = n.

b. \(\frac{9}{8}\) = \(\frac{n}{32}\) _________

Answer:

The value of n in \(\frac{9}{8}\) = \(\frac{n}{32}\) is 36.

Explanation:

\(\frac{9}{8}\) = \(\frac{n}{32}\)

=> 9 × 32 = n × 8

=> 288 = 8n

=> 288 ÷ 8 = n

=> 36 = n.

c. \(\frac{2}{3}\) = \(\frac{n}{15}\) _________

Answer:

The value of n in \(\frac{2}{3}\) = \(\frac{n}{15}\) is 10.

Explanation:

\(\frac{2}{3}\) = \(\frac{n}{15}\)

=> 2 × 15 = n × 3

=> 30 = 3n

=> 30 ÷ 3 = n

=> 10 = n.

The missing number can appear any place in a proportion. Solve the same way.

\(\frac{2}{3}\) = \(\frac{6}{n}\)

3 × 6 = 2 × n

\(\frac{18}{2}\) = n

9 = n

\(\frac{3}{5}\) = \(\frac{n}{10}\)

3 × 10 = 5 × n

\(\frac{30}{5}\) = n

6 = n

\(\frac{3}{n}\) = \(\frac{6}{8}\)

3 × 8 = 6 × n

\(\frac{24}{6}\) = n

4 = n

\(\frac{n}{4}\) = \(\frac{3}{6}\)

4 × 3 = 6 × n

\(\frac{12}{6}\) = n

2 = n

**Solve.
**Question 1.

a. \(\frac{n}{3}\) = \(\frac{3}{9}\) _________

Answer:

The value of n in \(\frac{n}{3}\) = \(\frac{3}{9}\) is 1.

Explanation:

\(\frac{n}{3}\) = \(\frac{3}{9}\)

=> n × 9 = 3 × 3

=> 9n = 9

=> n = 9 ÷ 9

=> n = 1.

b. \(\frac{5}{3}\) = \(\frac{15}{n}\) _________

Answer:

The value of n in \(\frac{5}{3}\) = \(\frac{15}{n}\) is 9.

Explanation:

\(\frac{5}{3}\) = \(\frac{15}{n}\)

=> 5 × n = 15 × 3

=> 5n = 45

=> n = 45 ÷ 5

=> n = 9.

c. \(\frac{2}{n}\) = \(\frac{1}{4}\) _________

Answer:

The value of n in \(\frac{2}{n}\) = \(\frac{1}{4}\) is 8.

Explanation:

\(\frac{2}{n}\) = \(\frac{1}{4}\)

= 2 × 4 = 1 × n

=> 8 = 1n

=> 8 ÷ 1 = n

=> 8 = n.

Question 2.

a. \(\frac{15}{30}\) = \(\frac{2}{n}\) _________

Answer:

The value of n in \(\frac{15}{30}\) = \(\frac{2}{n}\) is 4.

Explanation:

\(\frac{15}{30}\) = \(\frac{2}{n}\)

=> 15 × n = 2 × 30

=> 15n = 60

=> n = 60 ÷ 15

=> n = 4.

b. \(\frac{4}{6}\) = \(\frac{n}{24}\) _________

Answer:

The value of n in \(\frac{4}{6}\) = \(\frac{n}{24}\) is 16.

Explanation:

\(\frac{4}{6}\) = \(\frac{n}{24}\)

=> 4 × 24 = n × 6

=> 96 = 6n

=> 96 ÷ 6 = n

=> 16 = n.

c. \(\frac{n}{7}\) = \(\frac{15}{21}\) _________

Answer:

The value of n in \(\frac{n}{7}\) = \(\frac{15}{21}\) is 5.

Explanation:

\(\frac{n}{7}\) = \(\frac{15}{21}\)

=> n × 21 = 15 × 7

=> 21n = 105

=> n = 105 ÷ 21

=> n = 5.

Question 3.

a. \(\frac{6}{n}\) = \(\frac{15}{20}\) _________

Answer:

The value of n in \(\frac{6}{n}\) = \(\frac{15}{20}\) is 8.

Explanation:

\(\frac{6}{n}\) = \(\frac{15}{20}\)

=> 6 × 20 = 15 × n

=> 120 = 15n

=> 120 ÷ 15 = n

=> 8 = n.

b. \(\frac{n}{12}\) = \(\frac{9}{18}\) _________

Answer:

The value of n in \(\frac{n}{12}\) = \(\frac{9}{18}\) is 6.

Explanation:

\(\frac{n}{12}\) = \(\frac{9}{18}\)

=> n × 18 = 9 × 12

=> 18n = 108

=> n = 108 ÷ 18

=> n = 6.

c. \(\frac{9}{2}\) = \(\frac{27}{n}\) _________

Answer:

The value of n in \(\frac{9}{2}\) = \(\frac{27}{n}\) is 6.

Explanation:

\(\frac{9}{2}\) = \(\frac{27}{n}\)

=> 9 × n = 27 × 2

=> 9n = 54

=> n = 54 ÷ 9

=> n = 6.

Question 4.

a. \(\frac{7}{9}\) = \(\frac{n}{63}\) _________

Answer:

The value of n in \(\frac{7}{9}\) = \(\frac{n}{63}\) is 49.

Explanation:

\(\frac{7}{9}\) = \(\frac{n}{63}\)

=> 7 × 63 = n × 9

=> 441 = 9n

=> 441 ÷ 9 = n

=> 49 = n.

b. \(\frac{15}{n}\) = \(\frac{12}{4}\) _________

Answer:

The value of n in \(\frac{15}{n}\) = \(\frac{12}{4}\) is 5.

Explanation:

\(\frac{15}{n}\) = \(\frac{12}{4}\)

=> 15 × 4 = 12 × n

=> 60 = 12n

=> 60 ÷ 12 = n

=> 5 = n.

c. \(\frac{40}{100}\) = \(\frac{n}{25}\) _________

Answer:

The value of n in \(\frac{40}{100}\) = \(\frac{n}{25}\) is 10.

Explanation:

\(\frac{40}{100}\) = \(\frac{n}{25}\)

=> 40 × 25 = n × 100

=> 1000 = 100n

=> 1000 ÷ 100 = n

=> 10 = n.

Question 5.

a. \(\frac{35}{n}\) = \(\frac{4}{8}\) _________

Answer:

The value of n in \(\frac{35}{n}\) = \(\frac{4}{8}\) is 70.

Explanation:

\(\frac{35}{n}\) = \(\frac{4}{8}\)

=> 35 × 8 = 4 × n

=> 280 = 4n

=> 280 ÷ 4 = n

=> 70 = n.

b. \(\frac{16}{4}\) = \(\frac{36}{n}\) _________

Answer:

The value of n in \(\frac{16}{4}\) = \(\frac{36}{n}\) is 9.

Explanation:

\(\frac{16}{4}\) = \(\frac{36}{n}\)

=> 16 × n = 36 × 4

=>16n = 144

=> n = 144 ÷ 16

=> n = 9.

c. \(\frac{n}{12}\) = \(\frac{25}{30}\) _________

Answer:

The value of n in \(\frac{n}{12}\) = \(\frac{25}{30}\) is 10.

Explanation:

\(\frac{n}{12}\) = \(\frac{25}{30}\)

=> n × 30 = 25 × 12

=> 30n = 300

=> n = 300 ÷ 30

=> n = 10.