# Spectrum Math Grade 5 Chapter 4 Pretest Answer Key

Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 4 Pretest regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 4 Pretest Answers Key

Check What You Know

Understanding Fractions

Change each improper fraction to a mixed number.

Question 1.
a. $$\frac{27}{5}$$ ________
Mixed fraction of $$\frac{27}{5}$$ is 5$$\frac{2}{5}$$.

Explanation:
$$\frac{27}{5}$$
= 5$$\frac{2}{5}$$

b. $$\frac{35}{8}$$ ________
Mixed fraction of $$\frac{35}{8}$$ is 4$$\frac{3}{8}$$.

Explanation:
$$\frac{35}{8}$$
= 4$$\frac{3}{8}$$

c. $$\frac{15}{7}$$ ________
Mixed fraction of $$\frac{15}{7}$$ is 2$$\frac{1}{7}$$.

Explanation:
$$\frac{15}{7}$$
= 2$$\frac{1}{7}$$

d. $$\frac{25}{4}$$ ________
Mixed fraction of $$\frac{25}{4}$$ is 6$$\frac{1}{4}$$.

Explanation:
$$\frac{25}{4}$$
= 6$$\frac{1}{4}$$

e.
$$\frac{17}{3}$$ ________
Mixed fraction of $$\frac{17}{3}$$ is 5$$\frac{2}{3}$$.

Explanation:
$$\frac{17}{3}$$
= 5$$\frac{2}{3}$$

Change each mixed number to an improper fraction.

Question 2.
a. 3$$\frac{5}{16}$$ ________
Improper fraction of 3$$\frac{5}{16}$$ is $$\frac{53}{16}$$.

Explanation:
3$$\frac{5}{16}$$
= {[(3 × 16) + 5] ÷ 16]
= [(48 + 5) ÷ 16]
= 53 ÷ 16
= $$\frac{53}{16}$$

b. 3$$\frac{3}{5}$$ ________
Improper fraction of 3$$\frac{3}{5}$$  is $$\frac{18}{5}$$.

Explanation:
3$$\frac{3}{5}$$
= {[(3 × 5) + 3] ÷ 5]
= [(15 + 3) ÷ 5]
= 18 ÷ 5
= $$\frac{18}{5}$$

c. 2$$\frac{3}{7}$$ ________
Improper fraction of 2$$\frac{3}{7}$$ is $$\frac{17}{7}$$.

Explanation:
2$$\frac{3}{7}$$
= {[(2 × 7) + 3] ÷ 7]
= [(14 + 3) ÷ 7]
= 17 ÷ 7
= $$\frac{17}{7}$$

d. 1$$\frac{3}{16}$$ ________
Improper fraction of 1$$\frac{3}{16}$$ is $$\frac{19}{16}$$.

Explanation:
1$$\frac{3}{16}$$
= {[(1 × 16) + 3] ÷ 16]
= [(16 + 3) ÷ 16]
= 19 ÷ 16
= $$\frac{19}{16}$$

e. 4$$\frac{1}{3}$$ ________
Improper fraction of 4$$\frac{1}{3}$$ is $$\frac{17}{3}$$.

Explanation:
4$$\frac{1}{3}$$
= {[(4 × 3) + 1] ÷ 3]
= [(16 + 1) ÷ 3]
= 17 ÷ 3
= $$\frac{17}{3}$$

Find the greatest common factor for each set of numbers.

Question 3.
a. 18 and 22
The greatest common factor of 18 and 22 is 2.

Explanation:
Factors of 18:
1,2,3,6,9,18.
Factors of 22:
1,2,11,22.

b. 25 and 50
The greatest common factor of 25 and 50 is 25.

Explanation:
Factors of 25:
1,5,25.
Factors of 50:
1,2,5,10,25,50.

c. 54 and 36
The greatest common factor of 54 and 36 is 9.

Explanation:
Factors of 54:
1,2,3,6,9,16,27,54.
Factors of 36:
1,2,3,4,9,12,28,36.

d. 40 and 8
The greatest common factor of 40 and 8 is 8.

Explanation:
Factors of 40:
1,2,4,5,8,10,20,40.
Factors of 8:
1,2,4,8.

e. 16 and 24
The greatest common factor of 16 and 24 is 8.

Explanation:
Factors of 16:
1,2,4,8,16.
Factors of 24:
1,2,3,4,6,8,12,24.

Question 4.
a. 10 and 15
The greatest common factor of 10 and 15 is 5.

Explanation:
Factors of 10:
1,2,5,10.
Factors of 15:
1,3,5,15.

b. 24 and 30
The greatest common factor of 24 and 30 is 6.

Explanation:
Factors of 24:
1,2,3,4,6,8,12,24.,
Factors of 30:
1,2,3,5,6,10,15,30.

c. 8 and 10
The greatest common factor of 8 and 10 is 2.

Explanation:
Factors of 8:
1,2,4,8.
Factors of 10:
1,2,5,10.

d. 5 and 24
The greatest common factor of 5 and 24 is 1.

Explanation:
Factors of 5:
1,5.
Factors of 24:
1,2,3,4,6,8,12,24.

e. 24 and 40
The greatest common factor of 24 and 40 is 8.

Explanation:
Factors of 24:
1,2,3,4,6,8,12,24.
Factors of 40:
1,2,4,5,8,10,20,40.

Find the least common multiple for each set of numbers.

Question 5.
a. 8 and 12
The least common multiple of 8 and 12 is 24.

Explanation:
Multiple of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
Multiple of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120.

b. 15 and 4
The least common multiple of 15 and 4 is 60.

Explanation:
Multiple of 15:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150.
Multiple of 4:
4, 8, 12, 26, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.

c. 20 and 4
The least common multiple of 20 and 4 is 20.

Explanation:
Multiple of 20:
20, 40, 60, 80, 100, 120, 140, 160, 180, 200.
Multiple of 4:
4, 8, 12, 26, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.

d. 3 and 24
The least common multiple of 3 and 24 is 24.

Explanation:
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Multiples of 24:
24, 48, 72, 96, 120, 144, 168, 192, 216, 240.

e. 12 and 4
The least common multiple of 12 and 4 is 12.

Explanation:
Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
Multiples of 4:
4, 8, 12, 26, 20, 24, 28, 32, 36, 40.

Question 6.
a. 15 and 2
The least common multiple of 15 and 2 is 30.

Explanation:
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150.
Multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30.

b. 12 and 30
The least common multiple of 12 and 30 is 60.

Explanation:
Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
Multiples of 30:
30, 60, 90, 120, 150, 180, 210, 240, 270, 300.

c. 4 and 30
The least common multiple of 4 and 30 is 60.

Explanation:
Multiples of 4:
4, 8, 12, 26, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.
Multiples of 30:
30, 60, 90, 120, 150, 180, 210, 240, 270, 300.

d. 6 and 40
The least common multiple of 6 and 40 is 240.

Explanation:
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180,186, 192, 198, 204, 210, 216, 222, 228, 234, 240.
Multiples of 40:
40, 80, 120, 160, 200, 240, 280, 320, 360, 400.

e. 10 and 2
The least common multiple of 10 and 2 is 10.

Explanation:
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
Multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

Write each fraction in simplest form.

Question 7.
a. $$\frac{6}{9}$$ _________
Simplest form of$$\frac{6}{9}$$ is $$\frac{2}{3}$$.

Explanation:
$$\frac{6}{9}$$ ÷ $$\frac{3}{3}$$
= $$\frac{2}{3}$$

b. $$\frac{12}{36}$$ _________
Simplest form of $$\frac{12}{36}$$  is $$\frac{1}{3}$$.

Explanation:
$$\frac{12}{36}$$ ÷ $$\frac{4}{4}$$
= $$\frac{3}{9}$$ ÷ $$\frac{3}{3}$$
= $$\frac{1}{3}$$

c. $$\frac{20}{32}$$ _________
Simplest form of $$\frac{20}{32}$$ is $$\frac{5}{8}$$.

Explanation:
$$\frac{20}{32}$$ ÷ $$\frac{4}{4}$$
= $$\frac{5}{8}$$

d. $$\frac{21}{49}$$ _________
Simplest form of $$\frac{21}{49}$$ is $$\frac{3}{7}$$.

Explanation:
$$\frac{21}{49}$$ ÷ $$\frac{7}{7}$$
= $$\frac{3}{7}$$

Question 8.
a. $$\frac{15}{18}$$ _________
Simplest form of $$\frac{15}{18}$$ is $$\frac{5}{6}$$.

Explanation:
$$\frac{15}{18}$$ ÷ $$\frac{3}{3}$$
= $$\frac{5}{6}$$

b. $$\frac{40}{45}$$ _________
Simplest form of $$\frac{40}{45}$$ is $$\frac{8}{9}$$.

Explanation:
$$\frac{40}{45}$$ ÷ $$\frac{5}{5}$$
= $$\frac{8}{9}$$

c. $$\frac{12}{14}$$ _________
Simplest form of $$\frac{12}{14}$$ is $$\frac{6}{7}$$.

Explanation:
$$\frac{12}{14}$$ ÷ $$\frac{2}{2}$$
= $$\frac{6}{7}$$

d. $$\frac{19}{38}$$ _________
Simplest form of $$\frac{19}{38}$$ is $$\frac{1}{2}$$.

Explanation:
$$\frac{19}{38}$$ ÷ $$\frac{19}{19}$$
= $$\frac{1}{2}$$

Find the equivalent fraction.

Question 9.
a.

The equivalent fraction of $$\frac{4}{6}$$ = $$\frac{8}{12}$$.

Explanation:
$$\frac{4}{6}$$ = $$\frac{n}{12}$$
=> $$\frac{4}{6}$$ × 12 = n
=> $$\frac{4}{1}$$ × 2 = n
=> $$\frac{8}{1}$$ = n
=> 8 = n.

b.

The equivalent fraction of $$\frac{1}{9}$$ = $$\frac{2}{18}$$.

Explanation:
$$\frac{1}{9}$$ = $$\frac{n}{18}$$
=> $$\frac{1}{9}$$ × 18 = n
=> $$\frac{1}{1}$$ × 2 = n
=> $$\frac{2}{1}$$ = n
=> 2 = n.

c.

The equivalent fraction of $$\frac{5}{6}$$ = $$\frac{10}{12}$$.

Explanation:
$$\frac{5}{6}$$ = $$\frac{n}{12}$$
=> $$\frac{5}{6}$$ × 12 = n
=> $$\frac{5}{1}$$ × 2 = n
=> $$\frac{10}{1}$$ = n
=> 10 = n.

d.

The equivalent fraction of $$\frac{5}{12}$$ = $$\frac{25}{60}$$.

Explanation:
$$\frac{5}{12}$$ = $$\frac{n}{60}$$
=> $$\frac{5}{12}$$ × 60 = n
=> $$\frac{5}{1}$$ × 5 = n
=> $$\frac{25}{1}$$ = n
=> 25 = n.

Question 10.
a.

The equivalent fraction of $$\frac{2}{5}$$ = $$\frac{8}{20}$$.

Explanation:
$$\frac{2}{5}$$ = $$\frac{n}{20}$$
=> $$\frac{2}{5}$$ × 20 = n
=> $$\frac{2}{1}$$ × 4 = n
=> $$\frac{8}{1}$$ = n
=> 8 = n.

b.

The equivalent fraction of $$\frac{7}{1}$$ = $$\frac{42}{6}$$.

Explanation:
$$\frac{7}{1}$$ = $$\frac{n}{6}$$
=> $$\frac{7}{1}$$ × 6 = n
=> $$\frac{42}{1}$$ = n
=> 42 = n

c.

The equivalent fraction of $$\frac{6}{1}$$ = $$\frac{66}{11}$$.

Explanation:
$$\frac{6}{1}$$ = $$\frac{n}{11}$$
=> $$\frac{6}{1}$$ × 11 = n
=> $$\frac{66}{1}$$ = n
=> 66 = n

d.

The equivalent fraction of $$\frac{4}{1}$$ = $$\frac{28}{7}$$.

Explanation:
$$\frac{4}{1}$$ = $$\frac{n}{7}$$
=> $$\frac{4}{1}$$ × 7 = n
=> $$\frac{28}{1}$$ = n
=> 28= n

Compare each pair of fractions using <, >, or =.

Question 11.
a.
$$\frac{8}{12}$$ ______ $$\frac{1}{12}$$
$$\frac{8}{12}$$ > $$\frac{1}{12}$$.

Explanation:
$$\frac{8}{12}$$ ______ $$\frac{1}{12}$$
Same denominators. So, numerators 8 is big than 1.
=> $$\frac{8}{12}$$ is greater than $$\frac{1}{12}$$.

b. $$\frac{2}{3}$$ ______ $$\frac{1}{2}$$
$$\frac{2}{3}$$ > $$\frac{1}{2}$$.

Explanation:
$$\frac{2}{3}$$ ______ $$\frac{1}{2}$$
Common multiple of 3 and 2 = 6.
=> $$\frac{2}{3}$$ × $$\frac{2}{2}$$ = $$\frac{4}{6}$$.
$$\frac{1}{2}$$ × $$\frac{3}{3}$$ = $$\frac{3}{6}$$.
=> $$\frac{4}{6}$$ is greater than $$\frac{3}{6}$$.

c. $$\frac{6}{9}$$ ______ $$\frac{2}{5}$$
$$\frac{6}{9}$$ > $$\frac{2}{5}$$.

Explanation:
$$\frac{6}{9}$$ ______ $$\frac{2}{5}$$
Common multiple of 9 and 5 = 45.
=> $$\frac{6}{9}$$ × $$\frac{5}{5}$$ = $$\frac{30}{45}$$.
$$\frac{2}{5}$$ × $$\frac{9}{9}$$ = $$\frac{18}{45}$$.
=> $$\frac{30}{45}$$ is greater than $$\frac{18}{45}$$.

d. $$\frac{4}{6}$$ ______ $$\frac{5}{9}$$
. $$\frac{4}{6}$$ > $$\frac{5}{9}$$.

Explanation:
. $$\frac{4}{6}$$ ______ $$\frac{5}{9}$$
Common multiple of 6 and 9 = 54.
=> $$\frac{4}{6}$$ × $$\frac{9}{9}$$ = $$\frac{36}{54}$$.
$$\frac{5}{9}$$ × $$\frac{6}{6}$$ = $$\frac{30}{54}$$.
=> $$\frac{36}{54}$$ is greater than $$\frac{30}{54}$$.

Question 12.
a. $$\frac{3}{6}$$ ______ $$\frac{7}{9}$$
$$\frac{3}{6}$$ < $$\frac{7}{9}$$.

Explanation:
$$\frac{3}{6}$$ ______ $$\frac{7}{9}$$
Common multiple of 6 and 9 = 54.
=> $$\frac{3}{6}$$ × $$\frac{9}{9}$$ = $$\frac{27}{54}$$.
$$\frac{7}{9}$$ × $$\frac{6}{6}$$ = $$\frac{42}{54}$$.
=> $$\frac{27}{54}$$ is lesser than $$\frac{42}{54}$$.

b. $$\frac{2}{5}$$ ______ $$\frac{1}{4}$$
$$\frac{2}{5}$$ > $$\frac{1}{4}$$.

Explanation:
$$\frac{2}{5}$$ ______ $$\frac{1}{4}$$
Common multiple of 5 and 4 = 20.
=> $$\frac{2}{5}$$ × $$\frac{4}{4}$$ = $$\frac{8}{20}$$.
$$\frac{1}{4}$$ × $$\frac{5}{5}$$ = $$\frac{5}{20}$$.
=> $$\frac{8}{20}$$ is greater than $$\frac{5}{20}$$.

c. $$\frac{2}{7}$$ ______ $$\frac{2}{3}$$
$$\frac{2}{7}$$ < $$\frac{2}{3}$$.

Explanation:
$$\frac{2}{7}$$ ______ $$\frac{2}{3}$$
Common multiple of 7 and 3 = 21.
=> $$\frac{2}{7}$$ × $$\frac{3}{3}$$ = $$\frac{6}{21}$$.
$$\frac{2}{3}$$ × $$\frac{7}{7}$$ = $$\frac{14}{21}$$.
=> $$\frac{6}{21}$$ is lesser than $$\frac{14}{21}$$.

d. $$\frac{6}{7}$$ ______ $$\frac{1}{5}$$
$$\frac{6}{7}$$ > $$\frac{1}{5}$$.

Explanation:
$$\frac{6}{7}$$ ______ $$\frac{1}{5}$$
Common multiple of 7 and 5 = 35.
=> $$\frac{6}{7}$$ × $$\frac{5}{5}$$ = $$\frac{30}{35}$$.
$$\frac{1}{5}$$ × $$\frac{7}{7}$$ = $$\frac{7}{35}$$.
=> $$\frac{30}{35}$$ is greater than $$\frac{7}{35}$$.

Convert each fraction into a decimal. Convert each decimal into a fraction.

Question 13.
a. $$\frac{2}{5}$$ ________
Decimal of $$\frac{2}{5}$$ is 0.4.

Explanation:
$$\frac{2}{5}$$ = 2 ÷ 5
= 0.4.

b. $$\frac{3}{6}$$ ________
Decimal of $$\frac{3}{6}$$ is 0.5.

Explanation:
$$\frac{3}{6}$$  ÷ $$\frac{3}{3}$$
= $$\frac{1}{2}$$
= 0.5.

c. $$\frac{2}{8}$$ ________
Decimal of $$\frac{2}{8}$$ is 0.25.

Explanation:
$$\frac{2}{8}$$ ÷ $$\frac{2}{2}$$
= $$\frac{1}{4}$$
= 0.25.

d. $$\frac{7}{8}$$ ________
Decimal of $$\frac{7}{8}$$ is 0.875.

Explanation:
$$\frac{7}{8}$$ = 7 ÷ 8
= 0.875.

Question 14.
a. 0.5 ________
Fraction of 0.5 is $$\frac{5}{10}$$.

Explanation:
0.5 = $$\frac{5}{10}$$

b. 0.6 ________
Fraction of 0.6 is $$\frac{6}{10}$$.

Explanation:
0.6 = $$\frac{6}{10}$$.

b. 0.6 ________
Fraction of 0.6 is $$\frac{6}{10}$$.

Explanation:
0.6 = $$\frac{6}{10}$$.

c. 0.75 ________
Fraction of 0.75 is $$\frac{75}{100}$$.
0.75 = $$\frac{75}{100}$$.
Fraction of 0.625 is $$\frac{625}{1000}$$.
0.625 = $$\frac{625}{1000}$$.