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## 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. \(\frac{27}{5}\) ________

Answer:

Mixed fraction of \(\frac{27}{5}\) is 5\(\frac{2}{5}\).

Explanation:

\(\frac{27}{5}\)

= 5\(\frac{2}{5}\)

b. \(\frac{35}{8}\) ________

Answer:

Mixed fraction of \(\frac{35}{8}\) is 4\(\frac{3}{8}\).

Explanation:

\(\frac{35}{8}\)

= 4\(\frac{3}{8}\)

c. \(\frac{15}{7}\) ________

Answer:

Mixed fraction of \(\frac{15}{7}\) is 2\(\frac{1}{7}\).

Explanation:

\(\frac{15}{7}\)

= 2\(\frac{1}{7}\)

d. \(\frac{25}{4}\) ________

Answer:

Mixed fraction of \(\frac{25}{4}\) is 6\(\frac{1}{4}\).

Explanation:

\(\frac{25}{4}\)

= 6\(\frac{1}{4}\)

e.

\(\frac{17}{3}\) ________

Answer:

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\(\frac{5}{16}\) ________

Answer:

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\(\frac{3}{5}\) ________

Answer:

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\(\frac{3}{7}\) ________

Answer:

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\(\frac{3}{16}\) ________

Answer:

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\(\frac{1}{3}\) ________

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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. \(\frac{6}{9}\) _________

Answer:

Simplest form of\(\frac{6}{9}\) is \(\frac{2}{3}\).

Explanation:

\(\frac{6}{9}\) ÷ \(\frac{3}{3}\)

= \(\frac{2}{3}\)

b. \(\frac{12}{36}\) _________

Answer:

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. \(\frac{20}{32}\) _________

Answer:

Simplest form of \(\frac{20}{32}\) is \(\frac{5}{8}\).

Explanation:

\(\frac{20}{32}\) ÷ \(\frac{4}{4}\)

= \(\frac{5}{8}\)

d. \(\frac{21}{49}\) _________

Answer:

Simplest form of \(\frac{21}{49}\) is \(\frac{3}{7}\).

Explanation:

\(\frac{21}{49}\) ÷ \(\frac{7}{7}\)

= \(\frac{3}{7}\)

Question 8.

a. \(\frac{15}{18}\) _________

Answer:

Simplest form of \(\frac{15}{18}\) is \(\frac{5}{6}\).

Explanation:

\(\frac{15}{18}\) ÷ \(\frac{3}{3}\)

= \(\frac{5}{6}\)

b. \(\frac{40}{45}\) _________

Answer:

Simplest form of \(\frac{40}{45}\) is \(\frac{8}{9}\).

Explanation:

\(\frac{40}{45}\) ÷ \(\frac{5}{5}\)

= \(\frac{8}{9}\)

c. \(\frac{12}{14}\) _________

Answer:

Simplest form of \(\frac{12}{14}\) is \(\frac{6}{7}\).

Explanation:

\(\frac{12}{14}\) ÷ \(\frac{2}{2}\)

= \(\frac{6}{7}\)

d. \(\frac{19}{38}\) _________

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

\(\frac{8}{12}\) ______ \(\frac{1}{12}\)

Answer:

\(\frac{8}{12}\) > \(\frac{1}{12}\).

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. \(\frac{2}{3}\) ______ \(\frac{1}{2}\)

Answer:

\(\frac{2}{3}\) > \(\frac{1}{2}\).

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. \(\frac{6}{9}\) ______ \(\frac{2}{5}\)

Answer:

\(\frac{6}{9}\) > \(\frac{2}{5}\).

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. \(\frac{4}{6}\) ______ \(\frac{5}{9}\)

Answer:

. \(\frac{4}{6}\) > \(\frac{5}{9}\).

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. \(\frac{3}{6}\) ______ \(\frac{7}{9}\)

Answer:

\(\frac{3}{6}\) < \(\frac{7}{9}\).

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. \(\frac{2}{5}\) ______ \(\frac{1}{4}\)

Answer:

\(\frac{2}{5}\) > \(\frac{1}{4}\).

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. \(\frac{2}{7}\) ______ \(\frac{2}{3}\)

Answer:

\(\frac{2}{7}\) < \(\frac{2}{3}\).

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. \(\frac{6}{7}\) ______ \(\frac{1}{5}\)

Answer:

\(\frac{6}{7}\) > \(\frac{1}{5}\).

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. \(\frac{2}{5}\) ________

Answer:

Decimal of \(\frac{2}{5}\) is 0.4.

Explanation:

\(\frac{2}{5}\) = 2 ÷ 5

= 0.4.

b. \(\frac{3}{6}\) ________

Answer:

Decimal of \(\frac{3}{6}\) is 0.5.

Explanation:

\(\frac{3}{6}\) ÷ \(\frac{3}{3}\)

= \(\frac{1}{2}\)

= 0.5.

c. \(\frac{2}{8}\) ________

Answer:

Decimal of \(\frac{2}{8}\) is 0.25.

Explanation:

\(\frac{2}{8}\) ÷ \(\frac{2}{2}\)

= \(\frac{1}{4}\)

= 0.25.

d. \(\frac{7}{8}\) ________

Answer:

Decimal of \(\frac{7}{8}\) is 0.875.

Explanation:

\(\frac{7}{8}\) = 7 ÷ 8

= 0.875.

Question 14.

a. 0.5 ________

Answer:

Fraction of 0.5 is \(\frac{5}{10}\).

Explanation:

0.5 = \(\frac{5}{10}\)

b. 0.6 ________

Answer:

Fraction of 0.6 is \(\frac{6}{10}\).

Explanation:

0.6 = \(\frac{6}{10}\).

b. 0.6 ________

Answer:

Fraction of 0.6 is \(\frac{6}{10}\).

Explanation:

0.6 = \(\frac{6}{10}\).

c. 0.75 ________

Answer:

Fraction of 0.75 is \(\frac{75}{100}\).

Explanation:

0.75 = \(\frac{75}{100}\).

d. 0.625 ________

Answer:

Fraction of 0.625 is \(\frac{625}{1000}\).

Explanation:

0.625 = \(\frac{625}{1000}\).