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Spectrum Math Grade 5 Chapter 4 Posttest Answers Key
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Understanding Fractions
Change each improper fraction to a mixed number in simplest form.
Question 1.
a. \(\frac{22}{4}\) ______
Answer:
Simplest form of \(\frac{22}{4}\) is \(\frac{11}{2}\) or 5\(\frac{1}{2}\).
Explanation:
\(\frac{22}{4}\)
= \(\frac{22}{4}\) ÷ \(\frac{2}{2}\)
= \(\frac{11}{2}\) or 5\(\frac{1}{2}\)
b. \(\frac{9}{8}\) ______
Answer:
Simplest form of \(\frac{9}{8}\) is 1\(\frac{1}{8}\).
Explanation:
\(\frac{9}{8}\)
= \(\frac{9}{8}\) or 1\(\frac{1}{8}\)
c. \(\frac{17}{6}\) ______
Answer:
Simplest form of \(\frac{17}{6}\) is 2\(\frac{5}{6}\).
Explanation:
\(\frac{17}{6}\)
= 2\(\frac{5}{6}\)
d. \(\frac{23}{9}\) ______
Answer:
Simplest form of \(\frac{23}{9}\) is 2\(\frac{5}{9}\).
Explanation:
\(\frac{23}{9}\)
= 2\(\frac{5}{9}\)
e. \(\frac{26}{12}\) ______
Answer:
Simplest form of \(\frac{26}{12}\) is \(\frac{13}{6}\) or 2\(\frac{13}{6}\).
Explanation:
\(\frac{26}{12}\)
= \(\frac{26}{12}\) ÷ \(\frac{2}{2}\)
= \(\frac{13}{6}\) or 2\(\frac{13}{6}\)
Question 2.
a. \(\frac{48}{21}\) ______
Answer:
Simplest form of \(\frac{48}{21}\) is \(\frac{16}{7}\) or 2\(\frac{2}{7}\).
Explanation:
\(\frac{48}{21}\)
= \(\frac{48}{21}\) ÷ \(\frac{3}{3}\)
= \(\frac{16}{7}\) or 2\(\frac{2}{7}\)
b. \(\frac{25}{3}\) ______
Answer:
Simplest form of \(\frac{25}{3}\) is 8\(\frac{1}{3}\).
Explanation:
\(\frac{25}{3}\)
= \(\frac{25}{3}\) or 8\(\frac{1}{3}\)
c. \(\frac{10}{7}\) ______
Answer:
Simplest form of \(\frac{10}{7}\) is 1\(\frac{3}{7}\).
Explanation:
\(\frac{10}{7}\)
= 1\(\frac{3}{7}\)
d. \(\frac{30}{7}\) ______
Answer:
Simplest form of \(\frac{30}{7}\) is 4\(\frac{2}{7}\).
Explanation:
\(\frac{30}{7}\)
= 4\(\frac{2}{7}\)
e. \(\frac{22}{8}\) ______
Answer:
Simplest form of \(\frac{22}{8}\) is \(\frac{11}{4}\) or 2 \(\frac{3}{4}\).
Explanation:
\(\frac{22}{8}\)
= \(\frac{22}{8}\) ÷ \(\frac{2}{2}\)
= \(\frac{11}{4}\) or 2 \(\frac{3}{4}\)
Change each mixed number to an improper fraction.
Question 3.
a. 3\(\frac{6}{8}\) ______
Answer:
Improper fraction of 3\(\frac{6}{8}\) is \(\frac{15}{4}\).
Explanation:
3\(\frac{6}{8}\)
{[(3 × 8) + 6] ÷ 8}
= [(24 + 6) ÷ 8
= 30 ÷ 8
= \(\frac{30}{8}\) ÷ \(\frac{2}{2}\)
= \(\frac{15}{4}\)
b. 9\(\frac{8}{12}\) ______
Answer:
Improper fraction of 9\(\frac{8}{12}\) is \(\frac{29}{3}\).
Explanation:
9\(\frac{8}{12}\)
{[(9 × 12) + 8] ÷ 12}
= [(108 + 8) ÷ 12
= 116 ÷ 12
= \(\frac{116}{12}\) ÷ \(\frac{4}{4}\)
= \(\frac{29}{3}\)
c. 4\(\frac{7}{14}\) ______
Answer:
Improper fraction of 4\(\frac{7}{14}\) is \(\frac{9}{2}\).
Explanation:
4\(\frac{7}{14}\)
{[(4 × 14) + 7] ÷ 14}
= [(56 + 7) ÷ 14
= 63 ÷ 14
= \(\frac{63}{14}\) ÷ \(\frac{7}{7}\)
= \(\frac{9}{2}\)
d. 6\(\frac{3}{8}\) ______
Answer:
Improper fraction of 6\(\frac{3}{8}\) is \(\frac{51}{8}\).
Explanation:
6\(\frac{3}{8}\)
{[(6 × 8) + 3] ÷ 8}
= [(48 + 3) ÷ 8
= 51 ÷ 8
= \(\frac{51}{8}\)
e. 2\(\frac{9}{8}\) ______
Answer:
Improper fraction of 2\(\frac{9}{8}\) is \(\frac{25}{8}\).
Explanation:
2\(\frac{9}{8}\)
{[(2 × 8) + 9] ÷ 8}
= [(16 + 9) ÷ 8
= 25 ÷ 8
= \(\frac{25}{8}\)
Question 4.
a. 2\(\frac{3}{4}\) ______
Answer:
Improper fraction of 2\(\frac{3}{4}\) is \(\frac{11}{4}\).
Explanation:
2\(\frac{3}{4}\)
{[(2 × 4) + 3] ÷ 4}
= [(8 + 3) ÷ 4
= 11 ÷ 4
= \(\frac{11}{4}\)
b. 6\(\frac{8}{9}\) ______
Answer:
Improper fraction of 6\(\frac{8}{9}\) is \(\frac{62}{9}\).
Explanation:
6\(\frac{8}{9}\)
{[(6 × 9) + 8] ÷ 9}
= [(54 + 8) ÷ 9
= 62÷ 9
= \(\frac{62}{9}\)
c. 8\(\frac{11}{12}\) ______
Answer:
Improper fraction of 8\(\frac{11}{12}\) is \(\frac{107}{12}\).
Explanation:
8\(\frac{11}{12}\)
{[(8 × 12) + 11] ÷ 12}
= [(96 + 11) ÷ 12
= 107 ÷ 12
= \(\frac{107}{12}\)
d. 4\(\frac{4}{9}\) ______
Answer:
Improper fraction of 4\(\frac{4}{9}\) is \(\frac{40}{9}\).
Explanation:
4\(\frac{4}{9}\)
{[(4 × 9) + 4] ÷ 9}
= [(36 + 4) ÷ 9
= 40 ÷ 9
= \(\frac{40}{9}\)
e. 5\(\frac{2}{7}\) ______
Answer:
Improper fraction of 5\(\frac{2}{7}\) is \(\frac{37}{7}\).
Explanation:
5\(\frac{2}{7}\)
= {[(5 × 7) + 2] ÷ 7}
= [(35 + 2) ÷ 7
= 37 ÷ 7
= \(\frac{37}{7}\)
Find the greatest common factor for each set of numbers.
Question 5.
a. 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.
b. 21 and 14
_________
Answer:
The greatest common factor of 21 and 14 is 7.
Explanation:
Factors of 21:
1,3,7,21.
Factors of 14:
1,2,7,14.
c. 9 and 45
_________
Answer:
The greatest common factor of 9 and 45 is 9.
Explanation:
Factors of 9:
1,3,9.
Factors of 45:
1,3,5,9,15,45.
d. 13 and 25
_________
Answer:
The greatest common factor of 13 and 25 is 1.
Explanation:
Factors of 13:
1,13.
Factors of 25:
1,5,25.
e. 12 and 45
_________
Answer:
The greatest common factor of 12 and 45 is 3.
Explanation:
Factors of 12:
1,2,3,4,6,12.
Factors of 45:
1,3,5,9,15,45.
Find the least common multiple for each set of numbers.
Question 6.
a. 3 and 4
_________
Answer:
The least common multiple of 3 and 4 is 12.
Explanation:
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Multiples of 4:
4, 8, 12, 26, 20, 24, 28, 32, 36, 40.
b. 4 and 12
_________
Answer:
The least common multiple of 4 and 12 is 12.
Explanation:
Multiples of 4:
4, 8, 12, 26, 20, 24, 28, 32, 36, 40.
Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
c. 15 and 20
_________
Answer:
The least common multiple of 15 and 20 is 60.
Explanation:
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150.
Multiples of 20:
20, 40, 60, 80, 100, 120, 140, 160, 180, 200.
d. 10 and 6
_________
Answer:
The least common multiple of 10 and 6 is 30.
Explanation:
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
Multiples of 6:
6, 12,18, 24, 30, 36, 42, 48, 54, 60.
e. 10 and 3
_________
Answer:
The least common multiple of 10 and 3 is 30.
Explanation:
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
Multiples of 3:
3, 6, 9,12,15, 18, 21, 24, 27, 30.
Write each fraction in simplest form.
Question 7.
a. \(\frac{10}{25}\) ______
Answer:
Simplest form of \(\frac{10}{25}\) is \(\frac{2}{5}\).
Explanation:
\(\frac{10}{25}\)
= \(\frac{10}{25}\) ÷ \(\frac{5}{5}\)
= \(\frac{2}{5}\)
b. \(\frac{21}{35}\) ______
Answer:
Simplest form of \(\frac{21}{35}\) is \(\frac{3}{5}\).
Explanation:
\(\frac{21}{35}\)
= \(\frac{21}{35}\) ÷ \(\frac{7}{7}\)
= \(\frac{3}{5}\)
c. \(\frac{15}{24}\) ______
Answer:
Simplest form of \(\frac{15}{24}\) is \(\frac{5}{8}\).
Explanation:
\(\frac{15}{24}\)
= \(\frac{15}{24}\) ÷ \(\frac{3}{3}\)
= \(\frac{5}{8}\)
d. \(\frac{16}{20}\) ______
Answer:
Simplest form of \(\frac{16}{20}\) is \(\frac{4}{5}\).
Explanation:
\(\frac{16}{20}\)
= \(\frac{16}{20}\) ÷ \(\frac{4}{4}\)
= \(\frac{4}{5}\)
Question 8.
a. \(\frac{21}{24}\) ______
Answer:
Simplest form of \(\frac{21}{24}\) is \(\frac{7}{8}\).
Explanation:
\(\frac{21}{24}\)
= \(\frac{21}{24}\) ÷ \(\frac{3}{3}\)
= \(\frac{7}{8}\)
b. \(\frac{6}{21}\) ______
Answer:
Simplest form of \(\frac{6}{21}\) is \(\frac{2}{7}\).
Explanation:
\(\frac{6}{21}\)
= \(\frac{6}{21}\) ÷ \(\frac{3}{3}\)
= \(\frac{2}{7}\)
c. \(\frac{20}{32}\) ______
Answer:
Simplest form of \(\frac{20}{32}\) is \(\frac{5}{8}\).
Explanation:
\(\frac{20}{32}\)
= \(\frac{20}{32}\) ÷ \(\frac{4}{4}\)
= \(\frac{5}{8}\)
d. \(\frac{48}{54}\) ______
Answer:
Simplest form of \(\frac{48}{54}\) is \(\frac{8}{9}\).
Explanation:
\(\frac{48}{54}\)
= \(\frac{48}{54}\) ÷ \(\frac{3}{3}\)
= \(\frac{16}{18}\) ÷ \(\frac{2}{2}\)
= \(\frac{8}{9}\)
Find the equivalent fraction.
Question 9.
a.
Answer:
The equivalent fraction of \(\frac{7}{12}\) = \(\frac{35}{60}\).
Explanation:
\(\frac{7}{12}\) = \(\frac{n}{60}\)
=> \(\frac{7}{12}\) × 60 = n
=> \(\frac{7}{1}\) × 5 = n
=> \(\frac{35}{1}\) = n
= > 35 = n.
b.
Answer:
The equivalent fraction of \(\frac{8}{9}\) = \(\frac{72}{81}\).
Explanation:
\(\frac{8}{9}\) = \(\frac{n}{81}\)
=> \(\frac{8}{9}\) × 81 = n
=> \(\frac{8}{1}\) × 9 = n
=> \(\frac{72}{1}\) = n
= > 72 = n.
c.
Answer:
The equivalent fraction of 4 = \(\frac{32}{8}\).
Explanation:
\(\frac{4}{1}\) = \(\frac{n}{8}\)
=> \(\frac{4}{1}\) × 8 = n
=> \(\frac{32}{1}\) × 1 = n
=> 32 = n.
d.
Answer:
The equivalent fraction of \(\frac{7}{10}\) = \(\frac{21}{30}\).
Explanation:
\(\frac{7}{10}\) = \(\frac{n}{30}\)
=> \(\frac{7}{10}\) × 30 = n
=> \(\frac{7}{1}\) × 3 = n
=> \(\frac{21}{1}\) = n
= > 21 = n.
Question 10.
a.
Answer:
The equivalent fraction of 7 = \(\frac{49}{7}\).
Explanation:
\(\frac{7}{1}\) = \(\frac{n}{7}\)
=> \(\frac{7}{1}\) × 7 = n
=> \(\frac{49}{1}\) = n
=> 49 = n.
b.
Answer:
The equivalent fraction of \(\frac{5}{11}\) = \(\frac{15}{33}\).
Explanation:
\(\frac{5}{11}\) = \(\frac{n}{33}\)
=> \(\frac{5}{11}\) × 33 = n
=> \(\frac{5}{1}\) × 3 = n
=> \(\frac{15}{1}\) = n
= > 15 = n.
c.
Answer:
The equivalent fraction of 3 = \(\frac{18}{6}\).
Explanation:
\(\frac{3}{1}\) = \(\frac{n}{6}\)
=> \(\frac{3}{1}\) × 6 = n
=> \(\frac{18}{1}\) = n
=> 18 = n.
d.
Answer:
The equivalent fraction of 9 = \(\frac{36}{4}\).
Explanation:
\(\frac{9}{1}\) = \(\frac{n}{4}\)
=> \(\frac{9}{1}\) × 4 = n
=> \(\frac{36}{1}\) = n
=> 36 = n
Compare each pair of fractions using <, >, or =.
Question 11.
a. \(\frac{8}{6}\) _____ \(\frac{6}{8}\)
Answer:
\(\frac{8}{6}\) > \(\frac{6}{8}\).
Explanation:
\(\frac{8}{6}\) _____ \(\frac{6}{8}\).
Common multiple of denominators 6 and 8 = 24.
\(\frac{8}{6}\) × \(\frac{4}{4}\) = \(\frac{32}{24}\)
\(\frac{6}{8}\) × \(\frac{3}{3}\) = \(\frac{18}{24}\)
=> \(\frac{32}{24}\) is greater than \(\frac{18}{24}\).
b. \(\frac{10}{8}\) _____ \(\frac{6}{5}\)
Answer:
\(\frac{10}{8}\) > \(\frac{6}{5}\).
Explanation:
\(\frac{10}{8}\) _____ \(\frac{6}{5}\)
Common multiple of denominators 5 and 8 = 40.
\(\frac{10}{8}\) × \(\frac{5}{5}\) = \(\frac{50}{40}\)
\(\frac{6}{5}\) × \(\frac{8}{8}\) = \(\frac{48}{40}\)
=> \(\frac{50}{40}\) is greater than \(\frac{48}{40}\).
c. \(\frac{7}{9}\) _____ \(\frac{6}{8}\)
Answer:
\(\frac{7}{9}\) > \(\frac{6}{8}\).
Explanation:
\(\frac{7}{9}\) _____ \(\frac{6}{8}\)
Common multiple of denominators 9 and 8 = 72.
\(\frac{7}{9}\) × \(\frac{8}{8}\) = \(\frac{56}{72}\)
\(\frac{6}{8}\) × \(\frac{9}{9}\) = \(\frac{54}{72}\)
=> \(\frac{56}{72}\) is greater than \(\frac{54}{72}\).
d. \(\frac{12}{10}\) _____ \(\frac{6}{5}\)
Answer:
\(\frac{12}{10}\) = \(\frac{6}{5}\)
Explanation:
\(\frac{12}{10}\) _____ \(\frac{6}{5}\)
Common multiple of denominators 10 and 5 = 10.
\(\frac{12}{10}\) × \(\frac{1}{1}\) = \(\frac{12}{10}\)
\(\frac{6}{5}\) × \(\frac{2}{2}\) = \(\frac{12}{10}\)
=> \(\frac{12}{10}\) is equals to \(\frac{12}{10}\).
Question 12.
a. \(\frac{4}{6}\) _____ \(\frac{10}{5}\)
Answer:
\(\frac{4}{6}\) < \(\frac{10}{5}\).
Explanation:
\(\frac{4}{6}\) _____ \(\frac{10}{5}\)
Common multiple of denominators 6 and 5 = 30.
\(\frac{4}{6}\) × \(\frac{5}{5}\) = \(\frac{20}{30}\)
\(\frac{10}{5}\) × \(\frac{6}{6}\) = \(\frac{60}{30}\)
=> \(\frac{20}{30}\) is lesser than \(\frac{60}{30}\).
b. \(\frac{6}{7}\) _____ \(\frac{5}{6}\)
Answer:
\(\frac{6}{7}\) > \(\frac{5}{6}\).
Explanation:
\(\frac{6}{7}\) _____ \(\frac{5}{6}\)
Common multiple of denominators 7 and 6 = 42.
\(\frac{6}{7}\) × \(\frac{6}{6}\) = \(\frac{36}{42}\)
\(\frac{5}{6}\) × \(\frac{7}{7}\) = \(\frac{35}{42}\)
=> \(\frac{36}{42}\) is greater than \(\frac{35}{42}\).
c. \(\frac{8}{5}\) _____ \(\frac{10}{8}\)
Answer:
\(\frac{8}{5}\) > \(\frac{10}{8}\).
Explanation:
\(\frac{8}{5}\) _____ \(\frac{10}{8}\)
Common multiple of denominators 5 and 8 = 40.
\(\frac{8}{5}\) × \(\frac{8}{8}\) = \(\frac{64}{40}\)
\(\frac{10}{8}\) × \(\frac{5}{5}\) = \(\frac{50}{40}\)
=> \(\frac{64}{30}\) is greater than \(\frac{50}{30}\).
d. \(\frac{4}{9}\) _____ \(\frac{4}{5}\)
Answer:
\(\frac{4}{9}\) < \(\frac{4}{5}\).
Explanation:
\(\frac{4}{9}\) _____ \(\frac{4}{5}\).
Common multiple of denominators 9 and 5 = 45.
\(\frac{4}{9}\) × \(\frac{5}{5}\) = \(\frac{20}{45}\)
\(\frac{4}{5}\) × \(\frac{9}{9}\) = \(\frac{36}{45}\)
=> \(\frac{20}{45}\) is lesser than \(\frac{36}{45}\).
Convert each fraction into a decimal. Convert each decimal into a fraction.
Question 13.
a. \(\frac{8}{20}\) ______
Answer:
Decimal of \(\frac{8}{20}\) is 0.4.
Explanation:
\(\frac{8}{20}\) ÷ \(\frac{4}{4}\)
= \(\frac{2}{5}\) or 0.4.
b. \(\frac{3}{5}\) ______
Answer:
Decimal of \(\frac{3}{5}\) is 0.6.
Explanation:
\(\frac{3}{5}\) = 0.6.
c. \(\frac{7}{14}\) ______
Answer:
Decimal of \(\frac{7}{14}\) is 0.5.
Explanation:
\(\frac{7}{14}\) ÷ \(\frac{7}{7}\)
= \(\frac{1}{2}\)
= 0.5.
d. \(\frac{9}{30}\) ______
Answer:
Decimal of \(\frac{9}{30}\) is 0.3.
Explanation:
\(\frac{9}{30}\) ÷ \(\frac{3}{3}\)
= \(\frac{3}{10}\)
= 0.3.
Question 14.
a. 7.26 ______
Answer:
Fraction of 7.26 is \(\frac{726}{100}\).
Explanation:
7.26 = \(\frac{726}{100}\)
b. 10.4 ______
Answer:
Fraction of 10.4 is \(\frac{104}{10}\).
Explanation:
10.4 = \(\frac{104}{10}\)
c. 0.7 ______
Answer:
Fraction of 0.7 is \(\frac{7}{10}\).
Explanation:
0.7 = \(\frac{7}{10}\)
d. 6.25 ______
Answer:
Fraction of 6.25 is \(\frac{625}{100}\).
Explanation:
6.25 = \(\frac{625}{100}\)