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

## Spectrum Math Grade 6 Chapter 3 Posttest Answers Key

**Check What You Learned**

**Ratios, Rates, and Percents**

**Solve each proportion.**

Question 1.

a.

_______

Answer:

___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.

_______

Answer:

___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.

_______

Answer:

___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.

_______

Answer:

___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.

_______.

Answer:

___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.

_______

Answer:

___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.

_______

Answer:

___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.

_______

Answer:

___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.

_______

Answer:

___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.

_______

Answer:

___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.

_______

Answer:

___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.

_______

Answer:

___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 _____

Answer:

Decimal of 24% is 0.24.

Explanation:

24 % = 24 ÷ 100

= 0.24.

b. Fraction _____

Answer:

Fraction of 24% is \(\frac{24}{100}\).

Explanation:

24 % = \(\frac{24}{100}\)

Percent

110%

c. Decimal _____

Answer:

Decimal of 110% is 1.1.

Explanation:

110% = 110 ÷ 100

= 1.1.

d. Fraction _____

Answer:

Fraction of 110% is \(\frac{110}{100}\).

Explanation:

110% = \(\frac{110}{100}\)

Question 6.

Percent

37%

a. Decimal _____

Answer:

Decimal of 37% is 0.37.

Explanation:

37% = 37 ÷ 100

= 0.37.

b. Fraction _____

Answer:

Fraction is 37% is \(\frac{37}{100}\).

Explanation:

37% = \(\frac{37}{100}\).

Percent

55%

c. Decimal _____

Answer:

Decimal of 55% is 0.55.

Explanation:

55% = 55 ÷ 100

= 0.55.

d. Fraction _____

Answer:

Fraction of 55% is \(\frac{55}{100}\).

Explanation:

55% = \(\frac{55}{100}\).

Question 7.

Percent

6%

a. Decimal _____

Answer:

Decimal of 6% is 0.06.

Explanation:

6% = 6 ÷ 100

= 0.06.

b. Fraction _____

Answer:

Fraction of 6% is \(\frac{6}{100}\).

Explanation:

6% = \(\frac{6}{100}\).

Percent

235%

c. Decimal _____

Answer:

Decimal of 235% is 2.35.

Explanation:

235% = 235 ÷ 100

= 2.35.

d. Fraction _____

Answer:

Fraction of 235% is \(\frac{235}{100}\).

Explanation:

235% = \(\frac{235}{100}\).

**For each fraction or decimal, write the equivalent percent.**

Question 8.

a. \(\frac{4}{25}\) = ______

Answer:

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 ____

Answer:

Equivalent percent of 0.05 is \(\frac{5}{100}\).

Explanation:

0.05 = 5 ÷ 100

= \(\frac{5}{100}\).

c. \(\frac{3}{5}\) = ______

Answer:

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 = ______

Answer:

Equivalent percent of 0.8 is \(\frac{80}{100}\).

Explanation:

0.8 = 80 ÷ 100

= \(\frac{80}{100}\).

b. \(\frac{7}{8}\) = ______

Answer:

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 = ______

Answer:

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 _____

Answer:

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.

Answer:

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 ____

Answer:

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 ___

Answer:

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.

Answer:

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 ____

Answer:

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 ___

Answer:

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.

Answer:

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 ____

Answer:

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 ____

Answer:

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.

Answer:

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 ____.

Answer:

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 ____.

Answer:

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.

Answer:

Number of members they want to add =42.

They want to add 42 members.

Explanation:

Number of member chorus at West Side Middle School = 140.

Percentage of more members next year they want to add = 30.

Number of members they want to add = Number of member chorus at West Side Middle School × Percentage of more members next year they want to add

= 140 × 30%

= 140 × \(\frac{30}{100}\)

= 140 × \(\frac{3}{10}\)

= 14 × \(\frac{3}{1}\)

= \(\frac{42}{1}\)

= 42.