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Spectrum Math Grade 5 Chapter 4 Pretest Answers Key
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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 = \(\frac{625}{1000}\).