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.