Go through the Spectrum Math Grade 6 Answer Key Chapter 3 Pretest and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 3 Pretest Answers Key
Check What You Know
Ratios, Rates, and Percents
Solve each proportion.
Question 1.
a.
_____
Answer:
__20__.
Explanation:
Let the unknown number be n.
7 ÷ 5 = 28 ÷ n
=> \(\frac{7}{5}\) = \(\frac{28}{n}\)
=> \(\frac{7}{5}\) ÷ 28 = \(\frac{1}{n}\)
=> \(\frac{7}{5}\) × \(\frac{1}{28}\) = \(\frac{1}{n}\)
=> \(\frac{1}{5}\) × \(\frac{1}{4}\) = \(\frac{1}{n}\)
=> \(\frac{1}{20}\) = \(\frac{1}{n}\)
=> n = 20.
b.
_______
Answer:
Explanation:
Let the unknown number be n.
4 ÷ 6 = n ÷ 21.
=> \(\frac{4}{6}\) = \(\frac{n}{21}\)
=> \(\frac{4}{6}\) × 21 = n
=> \(\frac{4}{2}\) × 7 = n
=> \(\frac{2}{1}\) × 7 = n
=> \(\frac{14}{1}\) = n
=> 14 = n.
c.
_______
Answer:
____20___.
Explanation:
Let the unknown number be n.
6 ÷ n = 15 ÷ 20.
=> \(\frac{6}{n}\) = \(\frac{15}{20}\)
=> \(\frac{1}{n}\) = \(\frac{15}{20}\) ÷ 6
=> \(\frac{1}{n}\) = \(\frac{5}{20}\) × \(\frac{1}{2}\)
=> \(\frac{1}{n}\) = \(\frac{1}{10}\) × \(\frac{1}{2}\)
=> \(\frac{1}{n}\) = \(\frac{1}{20}\)
=> 20 = n.
Question 2.
a.
________
Answer:
___7_____.
Explanation:
Let the unknown number be n.
n ÷ 9 = 14 ÷ 18.
=> \(\frac{n}{9}\) = \(\frac{14}{18}\)
=> n = \(\frac{14}{18}\) × 9
=> n = \(\frac{14}{2}\) × 1
=> n = \(\frac{7}{1}\) × 1
=> n = \(\frac{7}{1}\)
=> n = 7.
b.
_____
Answer:
__12___.
Explanation:
Let the unknown number be n.
15 ÷ 18 = 10 ÷ n.
=> \(\frac{15}{18}\) = \(\frac{10}{n}\)
=> \(\frac{15}{18}\) ÷ 10 = \(\frac{11}{n}\)
=> \(\frac{15}{18}\) × \(\frac{1}{10}\) = \(\frac{1}{n}\)
=> \(\frac{3}{18}\) × \(\frac{1}{2}\) = \(\frac{1}{n}\)
=> \(\frac{1}{6}\) × \(\frac{1}{2}\) = \(\frac{1}{n}\)
=> \(\frac{1}{12}\) = \(\frac{1}{n}\)
=> n = 12.
c.
_____
Answer:
__39___.
Explanation:
Let the unknown number be n.
n ÷ 30 = 13 ÷ 10.
=> \(\frac{n}{30}\) = \(\frac{13}{10}\)
=> n = \(\frac{13}{10}\) × 30
=> n = \(\frac{13}{1}\) × 3
=> n = \(\frac{39}{1}\)
=> n = 39.
Question 3.
a.
_____
Answer:
__30___.
Explanation:
Let the unknown number be n.
10 ÷ 8 = n ÷ 24.
=> \(\frac{10}{8}\) = \(\frac{n}{24}\)
=> \(\frac{10}{8}\) × 24 = n
=> \(\frac{10}{2}\) × 6 = n
=> \(\frac{10}{1}\) × 3 = n
=> \(\frac{30}{1}\) = n
=> 30 = n.
b.
_____
Answer:
__48___.
Explanation:
Let the unknown number be n.
11 ÷ 12 = 44 ÷ n.
=> \(\frac{11}{12}\) = \(\frac{44}{n}\)
=> \(\frac{11}{12}\) ÷ 44 = \(\frac{1}{n}\)
=> \(\frac{11}{12}\) × \(\frac{1}{44}\) = \(\frac{1}{n}\)
=> \(\frac{1}{12}\) × \(\frac{1}{4}\) = \(\frac{1}{n}\)
=> \(\frac{1}{48}\) = \(\frac{1}{n}\)
=> n = 48.
c.
_____
Answer:
__3___.
Explanation:
Let the unknown number be n.
n ÷ 2 = 9 ÷ 6.
=> \(\frac{n}{2}\) = \(\frac{9}{6}\)
=> n = \(\frac{9}{6}\) × 2
=> n = \(\frac{9}{3}\) × 1
=> n = \(\frac{3}{1}\) × 1
=> n = \(\frac{3}{1}\)
=> n = 3.
Question 4.
a.
_____
Answer:
__15___.
Explanation:
Let the unknown number be n.
12 ÷ n = 4 ÷ 5.
=> \(\frac{12}{n}\) = \(\frac{4}{5}\)
=> \(\frac{1}{n}\) = \(\frac{4}{5}\) ÷ 12
=> \(\frac{1}{n}\) = \(\frac{4}{5}\) × \(\frac{1}{12}\)
=> \(\frac{1}{n}\) = \(\frac{1}{5}\) × \(\frac{1}{3}\)
=> \(\frac{1}{n}\) = \(\frac{1}{15}\)
=> 15 = n.
b.
_____
Answer:
__25___.
Explanation:
Let the unknown number be n.
10 ÷ 14 = n ÷ 35.
=> \(\frac{10}{14}\) = \(\frac{n}{35}\)
=> \(\frac{10}{14}\) × 35 = n
=> \(\frac{5}{7}\) × 35 = n
=> \(\frac{5}{1}\) × 5 = n
=> \(\frac{25}{1}\) = n
=> 25 = n.
c.
_______
Answer:
___6____.
Explanation:
Let the unknown number be n.
10 ÷ n = 25 ÷ 15.
=> \(\frac{10}{n}\) = \(\frac{25}{15}\)
=> \(\frac{1}{n}\) = \(\frac{25}{15}\) ÷ 10
=> \(\frac{1}{n}\) = \(\frac{25}{15}\) × \(\frac{1}{10}\)
=> \(\frac{1}{n}\) = \(\frac{5}{15}\) × \(\frac{1}{2}\)
=> \(\frac{1}{n}\) = \(\frac{1}{3}\) × \(\frac{1}{2}\)
=> \(\frac{1}{n}\) = \(\frac{1}{6}\)
=> 6 = n.
Write the equivalent decimal and fraction for each percent.
Question 5-7.
Answer:
Explanation:
5. Percent – 15%
a. Decimal = \(\frac{15}{100}\) = 0.15.
b. Fraction = \(\frac{15}{100}\) = \(\frac{3}{20}\)
Percent – 22%
c. Decimal = \(\frac{22}{100}\) = 0.22.
d. Fraction = \(\frac{22}{100}\) = \(\frac{11}{50}\)
6. Percent – 120%
a. Decimal = \(\frac{120}{100}\) = 1.20.
b. Fraction = \(\frac{120}{100}\) = \(\frac{12}{10}\) = \(\frac{6}{5}\)
Percent – 54%
c. Decimal = \(\frac{54}{100}\) = 0.54.
d. Fraction = \(\frac{54}{100}\) = \(\frac{27}{50}\)
7. Percent – 36%
a. Decimal = \(\frac{36}{100}\) = 0.36.
b. Fraction = \(\frac{36}{100}\) = \(\frac{18}{50}\) = \(\frac{9}{25}\)
Percent – 205%
c. Decimal = \(\frac{205}{100}\) = 2.05.
d. Fraction = \(\frac{205}{100}\) = \(\frac{41}{20}\)
For each fraction or decimal, write the equivalent percent.
Question 8.
a. \(\frac{3}{25}\) = ____
Answer:
Equivalent percent of \(\frac{3}{25}\) is \(\frac{9}{75}\).
Explanation:
\(\frac{3}{25}\) = \(\frac{3}{25}\) × \(\frac{3}{3}\)
= \(\frac{9}{75}\)
b. 0.01 = ____
Answer:
Equivalent percent of 0.01 = \(\frac{1}{100}\).
Explanation:
0.01 = \(\frac{1}{100}\)
c. \(\frac{2}{5}\) = ____
Answer:
Equivalent percent of \(\frac{2}{5}\) is \(\frac{14}{35}\).
Explanation:
\(\frac{2}{5}\) = \(\frac{2}{5}\) × \(\frac{7}{7}\)
= \(\frac{14}{35}\)
Question 9.
a. 4.06 = ____
Answer:
Equivalent percent of 4.06 is \(\frac{406}{100}\).
Explanation:
4.06 = \(\frac{406}{100}\)
b. \(\frac{1}{8}\) = ____
Answer:
Equivalent percent of \(\frac{1}{8}\) is \(\frac{5}{40}\).
Explanation:
\(\frac{1}{8}\) = \(\frac{1}{8}\) × \(\frac{5}{5}\)
= \(\frac{5}{40}\)
c. 0.6 = ____
Answer:
Equivalent percent of 0.6 is \(\frac{60}{100}\).
Explanation:
0.6 = \(\frac{60}{100}\)
Complete each sentence.
Question 10.
a. 90% of 120 is ____.
Answer:
90% of 120 is 108.
Explanation:
90% of 120 = \(\frac{90}{100}\) × 120
= \(\frac{90}{10}\) × 12
= \(\frac{90}{5}\) × 6
= \(\frac{18}{1}\) × 6
=> \(\frac{108}{1}\)
= 108.
b. 18 is 40% of ____.
Answer:
18 is 40% of 45.
Explanation:
18 = 40 % of n.
=> 18 = \(\frac{40}{100}\) × n
=> 18 ÷ \(\frac{40}{100}\) = n
=> 18 × \(\frac{100}{40}\) = n
=> 18 × \(\frac{10}{4}\) = n
=> 9 × \(\frac{10}{2}\) = n
=> 9 × \(\frac{5}{1}\) = n
=> \(\frac{45}{1}\) = n
=> 45 = n.
Question 11.
a. 3.6 is 5% of ____.
Answer:
3.6 is 5% of 72.
Explanation:
3.6 = 5% × n.
=> 3.6 = \(\frac{5}{100}\) × n
=> 3.6 ÷ \(\frac{5}{100}\) = n
=> 3.6 × \(\frac{20}{1}\) = n
=> \(\frac{72}{1}\) = n
=> 72 = n.
b. 27 is ___ % of 108.
Answer:
27 is 25% of 108.
Explanation:
27 = n % of 108
=> 27 = \(\frac{n}{100}\) × 108
=> 27 ÷ 108 = \(\frac{n}{100}\)
=> 1 ÷ 4 = \(\frac{n}{100}\)
=> \(\frac{1}{4}\) × 100 = n
=> \(\frac{1}{1}\) × 25= n
=> 25 = n.
Question 12.
a. 37\(\frac{1}{2}\)% of 64 is ____.
Answer:
37\(\frac{1}{2}\)% of 64 is 24.
Explanation:
37\(\frac{1}{2}\)% × 64 is n.
=> 37\(\frac{1}{2}\)% × 64 = n
=> {[(37 × 2) + 1] ÷ 2}% × 64 = n
=> [(74 + 1) ÷ 2]% × 64 = n
=> {\(\frac{75}{2}\) × \(\frac{1}{100}\)} × 64 = n
=> \(\frac{75}{200}\) × 64 = n
=> \(\frac{15}{40}\) × 64 = n
=> \(\frac{15}{20}\) × 32 = n
=> \(\frac{3}{4}\) × 32 = n
=> \(\frac{3}{1}\) × 8 = n
=> \(\frac{24}{1}\) = n
=> 24 = n.
b. 35 is 25% of ____.
Answer:
35 is 25% of 140.
Explanation:
35 is 25% of n.
=> 35 = \(\frac{25}{100}\) × n
=> 35 = \(\frac{1}{4}\) × n
=> 35 ÷ \(\frac{1}{4}\) = n
=> 35 × \(\frac{4}{1}\) = n
=> \(\frac{140}{1}\) = n
=> 140 = n.
Question 13.
a. 39 is ___% of 52.
Answer:
39 is 75% of 52.
Explanation:
39 = n% of 52.
=> 39 = \(\frac{n}{100}\) × 52
=> 39 ÷ 52 = \(\frac{n}{100}\)
=> 3 ÷ 4 = \(\frac{n}{100}\)
=> \(\frac{3}{4}\) × 100 = n
=> \(\frac{3}{1}\) × 25 = n
=> \(\frac{75}{1}\) = n
=> 75 = n.
b. 28 is ___% of 20.
Answer:
28 is 140% of 20.
Explanation:
28 = n% of 20.
=> 28 = \(\frac{n}{100}\) × 20
=> 28 ÷ 20 = \(\frac{n}{100}\)
=> \(\frac{7}{5}\) = \(\frac{n}{100}\)
=> \(\frac{7}{5}\) × 100 = n
=> \(\frac{7}{1}\) × 20= n
=> \(\frac{140}{1}\) = n
=> 140 = n.
Question 14.
a. 110% of 55 is ____.
Answer:
110% of 55 is 60.5 or 60\(\frac{1}{2}\).
Explanation:
110% of 55 is n.
=> \(\frac{110}{100}\) × 55 = n
=> \(\frac{11}{10}\) × 55 = n
=> \(\frac{11}{2}\) × 11 = n
=> \(\frac{121}{2}\) = n
=> 60\(\frac{1}{2}\) or 60.5 = n.
b. 82 is ____ % of 40.
Answer:
82 is 205% of 40.
Explanation:
82 is n% of 40.
=> 82 = \(\frac{n}{100}\) × 40
=> 82 ÷ 40 = \(\frac{n}{100}\)
=> \(\frac{82}{40}\) = \(\frac{n}{100}\)
=> \(\frac{41}{20}\) = \(\frac{n}{100}\)
=> \(\frac{41}{20}\) × 100 = n
=> \(\frac{41}{1}\) × 5 = n
=> \(\frac{205}{1}\) = n
=> 205 = n.
Solve each problem.
Question 15.
Corn costs $2 for 6 ears. Carmen bought 214 ears of corn. How much did she spend?
Carmen spent ____.
Answer:
Amount spent by Carmen of corns = $71.33.
Carmen spent $71.33.
Explanation:
Cost of corn = $2.
Number of ears of corn = 6.
Cost of each ear of corn = Cost of corn ÷ Number of ears of corn
= $2 ÷ 6
= $0.33.
Number of ears of corn Carmen bought = 214.
Amount spent by Carmen of corns = Number of ears of corn Carmen bought × Cost of each ear of corn
= 214 × $0.33
= $71.33.
Question 16.
Tomatoes are 5 for $2. Keith spent $8 on tomatoes. How many tomatoes did he get?
Keith got ________________ tomatoes.
Answer:
Number of tomatoes Keith buys = 20.
Keith got 20 tomatoes.
Explanation:
Number of tomatoes = 5.
Cost of 5 tomatoes = $2.
Cost of each tomato = Cost of 5 tomatoes ÷ Number of tomatoes
= $2 ÷ 5
= $0.4.
Cost spent on tomatoes by Keith = $8.
Number of tomatoes Keith buys = Cost spent on tomatoes by Keith ÷ Cost of each tomato
= $8 ÷ $0.4
= 20.
Question 17.
Peaches are 8 for $2. Jill bought 12 peaches. How much did she spend?
Jill spent ____.
Answer:
Amount spent on peaches by Jill = $3.
Jill spent #3.
Explanation:
Cost of 8 Peaches = $2.
Number of peaches = 8.
Cost of each peach = Cost of 8 Peaches ÷ Number of peaches
= $2 ÷ 8
= $0.25.
Number of peaches Jill bought = 12.
Amount spent on peaches by Jill = Number of peaches Jill bought × Cost of each peach
= 12 × $0.25
= $3.
Question 18.
Corn costs $2 for 6 ears. Isabel spent $3 on corn. How many ears did she get?
Isabel got ________________ ears.
Answer:
Number of corns bought by Isabel = 10.
Isabel got 10 ears.
Explanation:
Cost of corn = $2.
Number of ears of corn = 6.
Cost of each ears of corn = Cost of corn ÷ Number of ears of corn
= $2 ÷ 6
= $0.33.
Amount spent on corn by Isabel = $3.
Number of corns bought by Isabel = Amount spent on corn by Isabel ÷ Cost of each ears of corn
= $3 ÷ $0.33
= 10.
Question 19.
At East Side Middle School, \(\frac{3}{4}\) of the students ride the bus to school. What percent of the students ride the bus?
__________________ of the students ride the bus.
Answer:
Percent of the students ride the bus = 75.
75 of the students ride the bus.
Explanation:
Total number of students At East Side Middle School = 4.
Number of students ride the bus to school = 3.
Percent of the students ride the bus = (Number of students ride the bus to school ÷ Total number of students At East Side Middle School) × 100
= (3 ÷ 4) × 100
= 0.75 × 100
= 75.
Question 20.
Morgan got \(\frac{17}{20}\) of the questions on a science test correct. What percent of the questions did she get correct?
Morgan got _________________ of the questions correct.
Answer:
Percent of the questions did she get correct = 85.
Morgan got 85 of the questions correct.
Explanation:
Total number of questions on a science test = 20.
Number of marks he scored = 17.
Percent of the questions did she get correct = (Number of marks he scored ÷ Total number of questions on a science test) × 100
= (17 ÷ 20) × 100
= 0.85 × 100
= 85.
Question 21.
The band at East Side Middle School lost 20 percent of its 230 members from last year. How many band members left?
________________ band members left.
Answer:
Number of members band members left = 46.
46 band members left.
Explanation:
Percent lost by the band at East Side Middle School = 20%.
Members from last year the band at East Side Middle School = 230.
Number of members band members left = Members from last year the band at East Side Middle School × Percent lost by the band at East Side Middle School
= 230 × 20%
= 230 × \(\frac{20}{100}\)
= 230 × \(\frac{2}{10}\)
= 23 × \(\frac{2}{1}\)
= \(\frac{46}{1}\)
= 46.
Question 22.
A sweater is on sale for 40 percent off its original price of $29.95. What is the amount of savings?
The savings is ____.
Answer:
Amount of savings of sweater = $11.98.
The savings is $11.98.
Explanation:
Sale percent of a sweater = 40.
Original cost of a sweater = $29.95.
Amount of savings of sweater = Original cost of a sweater × Sale percent of a sweater
= $29.95 × 40%
= $29.95 × \(\frac{40}{100}\)
= $29.95 × \(\frac{4}{10}\)
= $5.99 × \(\frac{4}{2}\)
= $5.99 × \(\frac{2}{1}\)
= $11.98.