Spectrum Math Grade 6 Chapter 3 Lesson 2 Answer Key Solving Ratios

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. $$\frac{1}{3}$$ = $$\frac{n}{24}$$ ___________
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. $$\frac{4}{9}$$ = $$\frac{n}{36}$$ ___________
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. $$\frac{5}{45}$$ = $$\frac{n}{9}$$ ___________
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. $$\frac{3}{5}$$ = $$\frac{n}{15}$$ ___________
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. $$\frac{10}{70}$$ = $$\frac{n}{7}$$ ___________
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. $$\frac{25}{40}$$ = $$\frac{n}{16}$$ ___________
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. $$\frac{7}{12}$$ = $$\frac{n}{36}$$ ___________
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. $$\frac{13}{26}$$ = $$\frac{n}{4}$$ ___________
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. $$\frac{7}{1}$$ = $$\frac{n}{3}$$ ___________
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. $$\frac{8}{5}$$ = $$\frac{n}{40}$$ ___________
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. $$\frac{2}{6}$$ = $$\frac{n}{33}$$ ___________
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. $$\frac{5}{13}$$ = $$\frac{n}{39}$$ ___________
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. $$\frac{5}{6}$$ = $$\frac{n}{18}$$ ___________
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. $$\frac{9}{8}$$ = $$\frac{n}{32}$$ ___________
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. $$\frac{2}{3}$$ = $$\frac{n}{15}$$ ___________
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. $$\frac{1}{3}$$ = $$\frac{n}{24}$$ _________
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. $$\frac{4}{9}$$ = $$\frac{n}{36}$$ _________
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. $$\frac{5}{45}$$ = $$\frac{n}{9}$$ _________
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. $$\frac{3}{5}$$ = $$\frac{n}{15}$$ _________
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. $$\frac{10}{70}$$ = $$\frac{n}{7}$$ _________
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. $$\frac{25}{40}$$ = $$\frac{n}{16}$$ _________
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. $$\frac{7}{12}$$ = $$\frac{n}{36}$$ _________
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. $$\frac{13}{26}$$ = $$\frac{n}{4}$$ _________
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. $$\frac{7}{1}$$ = $$\frac{n}{3}$$ _________
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. $$\frac{8}{5}$$ = $$\frac{n}{40}$$ _________
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. $$\frac{2}{6}$$ = $$\frac{n}{33}$$ _________
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. $$\frac{5}{13}$$ = $$\frac{n}{39}$$ _________
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. $$\frac{5}{6}$$ = $$\frac{n}{18}$$ _________
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. $$\frac{9}{8}$$ = $$\frac{n}{32}$$ _________
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. $$\frac{2}{3}$$ = $$\frac{n}{15}$$ _________
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. $$\frac{n}{3}$$ = $$\frac{3}{9}$$ _________
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. $$\frac{5}{3}$$ = $$\frac{15}{n}$$ _________
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. $$\frac{2}{n}$$ = $$\frac{1}{4}$$ _________
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. $$\frac{15}{30}$$ = $$\frac{2}{n}$$ _________
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. $$\frac{4}{6}$$ = $$\frac{n}{24}$$ _________
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. $$\frac{n}{7}$$ = $$\frac{15}{21}$$ _________
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. $$\frac{6}{n}$$ = $$\frac{15}{20}$$ _________
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. $$\frac{n}{12}$$ = $$\frac{9}{18}$$ _________
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. $$\frac{9}{2}$$ = $$\frac{27}{n}$$ _________
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. $$\frac{7}{9}$$ = $$\frac{n}{63}$$ _________
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. $$\frac{15}{n}$$ = $$\frac{12}{4}$$ _________
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. $$\frac{40}{100}$$ = $$\frac{n}{25}$$ _________
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. $$\frac{35}{n}$$ = $$\frac{4}{8}$$ _________
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. $$\frac{16}{4}$$ = $$\frac{36}{n}$$ _________
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. $$\frac{n}{12}$$ = $$\frac{25}{30}$$ _________
The value of n in $$\frac{n}{12}$$ = $$\frac{25}{30}$$ is 10.
$$\frac{n}{12}$$ = $$\frac{25}{30}$$