Go through the Spectrum Math Grade 6 Answer Key Chapter 3 Posttest and get the proper assistance needed during your homework.

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Ratios, Rates, and Percents

Solve each proportion.

Question 1.
a.
_______
___15____.

Explanation:
?? ÷ 12 = 5 ÷ 4
Let the unknown number be n.
=> $$\frac{n}{12}$$ = $$\frac{5}{4}$$
=> n = $$\frac{5}{4}$$ × 12
=> n = $$\frac{5}{1}$$ × 3
=> n = $$\frac{15}{1}$$
=> n = 15.

b.
_______
___27____.

Explanation:
18 ÷ 16 = ?? ÷ 24.
Let the unknown number be n.
=> $$\frac{18}{16}$$ = $$\frac{n}{24}$$
=> $$\frac{18}{16}$$ × 24 = n
=> $$\frac{18}{4}$$ × 6 = n
=> $$\frac{18}{2}$$ × 3 = n
=> $$\frac{9}{1}$$ × 3 = n
=> $$\frac{27}{1}$$ = n
=> 27 = n.

c.
_______
___3____.

Explanation:
2 ÷ n = 10 ÷ 15.
Let the unknown number be n.
=> $$\frac{2}{n}$$ = $$\frac{10}{15}$$
=> $$\frac{1}{n}$$ = $$\frac{10}{15}$$ ÷ 2
=> $$\frac{1}{n}$$ = $$\frac{10}{15}$$ × $$\frac{1}{2}$$
=> $$\frac{1}{n}$$ = $$\frac{5}{15}$$ × $$\frac{1}{1}$$
=> $$\frac{1}{n}$$ = $$\frac{1}{3}$$
=> $$\frac{1}{n}$$ = $$\frac{1}{3}$$
=> 1 = $$\frac{1}{3}$$ × n
=> 3 = n.

Question 2.
a.
_______
___5____.

Explanation:
15 ÷ 21 = n ÷ 7.
Let the unknown number be n.
=> $$\frac{15}{21}$$ = $$\frac{n}{7}$$
=> $$\frac{15}{21}$$ × 7 = n
=> $$\frac{15}{3}$$ × 1 = n
=> $$\frac{5}{1}$$ × 1 = n
=> $$\frac{5}{1}$$ = n
=> 5 = n.

b.
_______.
___6____.

Explanation:
n ÷ 8 = 18 ÷ 24.
Let the unknown number be n.
=> $$\frac{n}{8}$$ = $$\frac{18}{24}$$
=> n = $$\frac{18}{24}$$ × 8
=> n = $$\frac{18}{3}$$ × 1
=> n = $$\frac{6}{1}$$ × 1
=> n = $$\frac{6}{1}$$
=> n = 6.

c.
_______
___21____.

Explanation:
10 ÷ 14 = 15 ÷ n.
Let the unknown number be n.
=> $$\frac{10}{14}$$ = $$\frac{15}{n}$$
=> $$\frac{10}{14}$$ = $$\frac{15}{n}$$
=> $$\frac{10}{14}$$ ÷ 15 = $$\frac{1}{n}$$
=> $$\frac{10}{14}$$ × $$\frac{1}{15}$$ = $$\frac{1}{n}$$
=> $$\frac{2}{14}$$ × $$\frac{1}{3}$$ = $$\frac{1}{n}$$
=> $$\frac{1}{7}$$ × $$\frac{1}{3}$$ = $$\frac{1}{n}$$
=> $$\frac{1}{21}$$ = $$\frac{1}{n}$$
=> n = 21.

Question 3.
a.
_______
___6____.

Explanation:
5 ÷ n = 20 ÷ 24.
Let the unknown number be n.
=> $$\frac{5}{n}$$ = $$\frac{20}{24}$$
=> $$\frac{1}{n}$$ = $$\frac{20}{24}$$ ÷ 5
=> $$\frac{1}{n}$$ = $$\frac{20}{24}$$ × $$\frac{1}{5}$$
=> $$\frac{1}{n}$$ = $$\frac{4}{24}$$ × $$\frac{1}{1}$$
=> $$\frac{1}{n}$$ = $$\frac{1}{6}$$ × $$\frac{1}{1}$$
=> $$\frac{1}{n}$$ = $$\frac{1}{6}$$
=> n = 6.

b.
_______
___16____.

Explanation:
4 ÷ 7 = n ÷ 28.
Let the unknown number be n.
=> $$\frac{4}{7}$$ = $$\frac{n}{28}$$
=> $$\frac{4}{7}$$ × 28 = n
=> $$\frac{4}{1}$$ × 4 = n
=> $$\frac{16}{1}$$ = n
=> 16 = n.

c.
_______
___15____.

Explanation:
8 ÷ 6 = 20 ÷ n.
Let the unknown number be n.
=> $$\frac{8}{6}$$ = $$\frac{20}{n}$$
=> $$\frac{8}{6}$$ ÷ 20 = $$\frac{1}{n}$$
=> $$\frac{8}{6}$$ × $$\frac{1}{20}$$ = $$\frac{1}{n}$$
=> $$\frac{4}{6}$$ × $$\frac{1}{10}$$ = $$\frac{1}{n}$$
=> $$\frac{2}{6}$$ × $$\frac{1}{5}$$ = $$\frac{1}{n}$$
=> $$\frac{1}{3}$$ × $$\frac{1}{5}$$ = $$\frac{1}{n}$$
=> $$\frac{1}{15}$$ = $$\frac{1}{n}$$
=> n = 15.

Question 4.
a.
_______
___14____.

Explanation:
n ÷ 10 = 21 ÷ 15.
Let the unknown number be n.
=> $$\frac{n}{10}$$ = $$\frac{21}{15}$$
=> n = $$\frac{21}{15}$$ × 10
=> n = $$\frac{21}{3}$$ × 2
=> n = $$\frac{7}{1}$$ × 2
=> n = $$\frac{14}{1}$$
=> n = 14.

b.
_______
___9____.

Explanation:
15 ÷ n = 20 ÷ 12.
Let the unknown number be n.
=> $$\frac{15}{n}$$ = $$\frac{20}{12}$$
=> $$\frac{1}{n}$$ = $$\frac{20}{12}$$ ÷ 15
=> $$\frac{1}{n}$$ = $$\frac{20}{12}$$ × $$\frac{1}{15}$$
=> $$\frac{1}{n}$$ = $$\frac{4}{12}$$ × $$\frac{1}{3}$$
=> $$\frac{1}{n}$$ = $$\frac{1}{3}$$ × $$\frac{1}{3}$$
=> $$\frac{1}{n}$$ = $$\frac{1}{9}$$
=> 9 = n.

c.
_______
___4____.

Explanation:
3 ÷ 12 = n ÷ 16.
Let the unknown number be n.
=> $$\frac{3}{12}$$ = $$\frac{n}{16}$$
=> $$\frac{3}{12}$$ × 16 = n
=> $$\frac{3}{3}$$ × 4 = n
=> $$\frac{1}{1}$$ × 4 = n
=> 4 = n.

Write the equivalent decimal and fraction for each percent.

Question 5.
Percent 24%
a. Decimal _____
Decimal of 24% is 0.24.

Explanation:
24 % = 24 ÷ 100
= 0.24.

b. Fraction _____
Fraction of 24% is $$\frac{24}{100}$$.

Explanation:
24 % = $$\frac{24}{100}$$

Percent
110%
c. Decimal _____
Decimal of 110% is 1.1.

Explanation:
110% = 110 ÷ 100
= 1.1.

d. Fraction _____
Fraction of 110% is $$\frac{110}{100}$$.

Explanation:
110% = $$\frac{110}{100}$$

Question 6.
Percent
37%
a. Decimal _____
Decimal of 37% is 0.37.

Explanation:
37% = 37 ÷ 100
= 0.37.

b. Fraction _____
Fraction is 37% is $$\frac{37}{100}$$.

Explanation:
37% = $$\frac{37}{100}$$.

Percent
55%
c. Decimal _____
Decimal of 55% is 0.55.

Explanation:
55% = 55 ÷ 100
= 0.55.

d. Fraction _____
Fraction of 55% is $$\frac{55}{100}$$.

Explanation:
55% = $$\frac{55}{100}$$.

Question 7.
Percent
6%
a. Decimal _____
Decimal of 6% is 0.06.

Explanation:
6% = 6 ÷ 100
= 0.06.

b. Fraction _____
Fraction of 6% is $$\frac{6}{100}$$.

Explanation:
6% = $$\frac{6}{100}$$.

Percent
235%
c. Decimal _____
Decimal of 235% is 2.35.

Explanation:
235% = 235 ÷ 100
= 2.35.

d. Fraction _____
Fraction of 235% is $$\frac{235}{100}$$.

Explanation:
235% = $$\frac{235}{100}$$.

For each fraction or decimal, write the equivalent percent.

Question 8.
a. $$\frac{4}{25}$$ = ______
Equivalent percent of $$\frac{4}{25}$$ is $$\frac{12}{75}$$.

Explanation:
$$\frac{4}{25}$$ = $$\frac{4}{25}$$  × $$\frac{3}{3}$$
= $$\frac{12}{75}$$.

b. 0.05 ____
Equivalent percent of 0.05 is $$\frac{5}{100}$$.

Explanation:
0.05 = 5 ÷ 100
= $$\frac{5}{100}$$.

c. $$\frac{3}{5}$$ = ______
Equivalent percent of $$\frac{3}{5}$$ is $$\frac{12}{20}$$.

Explanation:
$$\frac{3}{5}$$ = $$\frac{3}{5}$$ × $$\frac{4}{4}$$
= $$\frac{12}{20}$$.

Question 9.
a. 0.8 = ______
Equivalent percent of 0.8 is $$\frac{80}{100}$$.

Explanation:
0.8 = 80 ÷ 100
= $$\frac{80}{100}$$.

b. $$\frac{7}{8}$$ = ______
Equivalent percent of $$\frac{7}{8}$$ is $$\frac{14}{16}$$.

Explanation:
$$\frac{7}{8}$$ = $$\frac{7}{8}$$ × $$\frac{2}{2}$$
= $$\frac{14}{16}$$.

c. 1.3 = ______
Equivalent percent of 1.3 is $$\frac{130}{100}$$.

Explanation:
1.3 = 130 ÷ 100
= $$\frac{130}{100}$$.

Complete each sentence.

Question 10.
a. 24 is 30% of _____
24 is 30% of 80.

Explanation:
24 = 30% of n
=> 24 = 30% × n
=> 24 = $$\frac{30}{100}$$ × n
=> 24 × $$\frac{100}{30}$$ = n
=> 8 × $$\frac{100}{10}$$ = n
=> 8 × $$\frac{10}{1}$$ = n
=> $$\frac{80}{1}$$ = n
=> 80 = n.

b. 42 is ____% of 50.
42 is 84% of 50.

Explanation:
Let unknown % be n%.
42 = n% × 50
=> 42 = $$\frac{n}{100}$$ × 50
=> 42 ÷ 50 = $$\frac{n}{100}$$
=> $$\frac{42}{50}$$ = $$\frac{n}{100}$$
=> $$\frac{42}{50}$$ × 100 = n
=> $$\frac{42}{1}$$ × 2
=> 84 = n.

Question 11.
a. 20% of 75 is ____
20% of 75 is 15.

Explanation:
20% × 75 is n.
=> $$\frac{20}{100}$$ × 75 = n
=> $$\frac{20}{4}$$ × 3 = n
=> $$\frac{5}{1}$$ × 3 = n
=> $$\frac{15}{1}$$ = n
=> 15 = n.

b. 112 is 70% of ___
112 is 70% of 160.

Explanation:
112 = 70% × n
=> 112 = $$\frac{70}{100}$$ × n
=> 112 × $$\frac{100}{70}$$ = n
=> 112 × $$\frac{10}{7}$$ = n
=> 16 × $$\frac{10}{1}$$ = n
=> $$\frac{160}{1}$$ = n
=> 160 = n.

Question 12.
a. 6.2 is ____% of 124.
6.2 is 5% of 124.

Explanation:
6.2 is n% of 124.
=> 6.2 = $$\frac{n}{100}$$ × 124
=> 6.2 ÷ 124 = $$\frac{n}{100}$$
=> $$\frac{6.2}{124}$$ × 100 = n
=> $$\frac{620}{124}$$ = n
=> $$\frac{5}{1}$$ = n
=> 5 = n.

b. 32% of 85 is ____
32% of 85 is 27.2.

Explanation:
32% × 85 is n.
=> $$\frac{32}{100}$$ × 85 = n.
=> $$\frac{32}{20}$$ × 17 = n.
=> $$\frac{8}{5}$$ × 17 = n.
=> $$\frac{136}{5}$$ = n
=> 27.2 = n.

Question 13.
a. 9 is 12.5% of ___
9 is 12.5% of 72.

Explanation:
9 = 12.5% of n.
9 = 12.5% × n
=> 9 = $$\frac{12.5}{100}$$ × n
=> 9 × $$\frac{100}{12.5}$$ = n
=> $$\frac{900}{12.5}$$ = n
=> $$\frac{72}{1}$$ = n
=> 72 = n.

b. 7 is ___% of 56.
7 is 12.5% of 56.

Explanation:
7 is n% of 56.
=> 7 = $$\frac{n}{100}$$ × 56
=> 7 ÷ 56 = $$\frac{n}{100}$$
=> $$\frac{7}{56}$$  = $$\frac{n}{100}$$
=> $$\frac{1}{8}$$  = $$\frac{n}{100}$$
=> $$\frac{1}{8}$$ × 100 = n
=> $$\frac{1}{2}$$ × 25 = n
=> $$\frac{25}{2}$$  = n
=> 12.5 = n.

Question 14.
a. 125% of 48 is ____
125% of 48 is 60.

Explanation:
125% of 48 is n.
=> 125% × 48 = n.
=> $$\frac{125}{100}$$ × 48 = n
=> $$\frac{25}{20}$$ × 48 = n
=> $$\frac{5}{4}$$ × 48 = n
=> $$\frac{5}{1}$$ × 12 = n
=> $$\frac{60}{1}$$ = n
=> 60 = n.

b. 5.5 is 125% of ____
5.5 is 125% of 4.4.

Explanation:
5.5 is 125% of n.
=> 5.5 = $$\frac{125}{100}$$ × n
=> 5.5 × $$\frac{100}{125}$$ = n
=> 5.5 × $$\frac{4}{5}$$ = n
=> 1.1 × $$\frac{4}{1}$$ = n
=> $$\frac{4.4}{1}$$ = n
=> 4.4 = n.
.

Solve each problem.

Question 15.
Jeans are $20 for 2 pairs. Kerry spent$40 on jeans. How many pairs did she buy?
Kerry bought ____ pairs of jeans.
Number of pairs of jeans she can buy = 4.
Kerry bought 4 pairs of jeans.

Explanation:
Cost of Jeans = $20. Number of pairs of jeans = 2. Cost of each pair of Jeans = Cost of Jeans ÷ Number of pairs of jeans =$20 ÷ 2
= $10. Amount spent by Kerry on jeans =$40.
Number of pairs of jeans she can buy = Amount spent by Kerry on jeans ÷ Cost of each pair of Jeans
= $40 ÷$10
= 4.

Question 16.
Skirts are 4 for $30. Marta and her sisters bought 6 skirts. How much did they pay? They paid ____. Answer: Cost for 6 skirts they pay =$45.

Explanation:
Number of Skirts = 4.
Cost of 4 Skirts = $30. Cost of each Skirt = Cost of 4 Skirts ÷ Number of Skirts =$30 ÷ 4
= $7.5. Number of skirts Marta and her sisters bought = 6. Cost for 6 skirts they pay = Cost of each Skirt × Number of skirts Marta and her sisters bought =$7.5 × 6
= $45. Question 17. Sweaters are 3 for$50. Leslie and her mother spent $100 on sweaters. How many did they buy? They bought ____ sweaters. Answer: Number of sweaters they buy = 6. They bought 6 sweaters. Explanation: Cost of 3 Sweaters =$50.
Number of Sweaters = 3.
Cost of each sweater = Cost of 3 Sweaters ÷ Number of Sweaters
= $50 ÷ 3 =$16.67.
Amount spent by her mother on sweaters = $100. Number of sweaters they buy = Amount spent by her mother on sweaters ÷ Cost of each sweater =$100 ÷ $16.67 = 5.99 = 6. Question 18. T-shirts are 3 for$18. Tia bought 4 T-shirts. How much did she spend?
Tia spent ____.
Amount she spend on T-shirts = $24. Tia spent$24.

Explanation:
Number of T-shirts = 3.
Cost of 3 T-shirts = $18. Cost of each T-shirt = Cost of 3 T-shirts ÷ Number of T-shirts =$18 ÷ 3
= $6. Number of T-shirts Tia bought = 4. Amount she spend on T-shirts = Cost of each T-shirt × Number of T-shirts Tia bought =$6 × 4
= $24. Question 19. In Keon’s homeroom class, $$\frac{3}{5}$$ of the students participate in sports. What percent of students participate in sports? ____ participate in sports. Answer: Percent of students participate in sports = 60. 60% participate in sports. Explanation: Number of the students participate in sports = $$\frac{3}{5}$$. Percent of students participate in sports = Number of the students participate in sports × 100 = $$\frac{3}{5}$$ ×100 = 0.6 × 100 = 60. Question 20. Fifty -five percent of the students at West Side Middle School walk to school. What fraction of the students walk to school? _____ of the students walk to school. Answer: Fraction of the students walk to school = $$\frac{51}{100}$$. Explanation: Percent of the students at West Side Middle School walk to school = 51. Fraction of the students walk to school = 51% = 51 ÷ 100 = $$\frac{51}{100}$$. Question 21. A new car that costs$ 17,500 loses 25% of its value in the first year. How much is the loss of value?
The loss of value is ____.
Amount of the loss of value = $4,375. The loss of value is$4,375.

Explanation:
Cost of the cost price a new car = $17,500. Percentage of the lost value in the first year = 25%. Amount of the loss of value = Cost of the cost price a new car × Percentage of the lost value in the first year =$17,500 × 25%
= $17,500 × $$\frac{25}{100}$$ =$175 × $$\frac{25}{1}$$
= \$4,375.

Question 22.
The 140-member chorus at West Side Middle School wants to add 30 percent more members next year. How many members do they want to add?
They want to add _____ members.
= 140 × $$\frac{30}{100}$$
= 140 × $$\frac{3}{10}$$
= 14 × $$\frac{3}{1}$$
= $$\frac{42}{1}$$