Spectrum Math Grade 5 Chapters 1-5 Mid Test Answer Key

Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 1-5 Mid Test regularly and improve your accuracy in solving questions.

Spectrum Math Grade 5 Chapter 1-5 Mid Test Answers Key

Add, Subtract, multiply, or divide

Question 1.
a.

Answer:

Explanation:
275 × 56 = ????
=> Multiplication of 275 by 56, we get the product 15,400.

b.

Answer:

Explanation:
312 × 9 = ????
=> Multiplication of 312 by 9, we get the product 2,808.

c.

Answer:

Explanation:
1717 × 34 = ?????
=> Multiplication of 1717 by 34, we get the product  58,378.

d.

Answer:

Explanation:
5806 × 42 = ?????
=> Multiplication of 5806 by 42, we get the product 2,43,852.

Question 2.
a.

Answer:

Explanation:
72 ÷ 8 = ??
=> Dividing 72 by 8, we get 9 as quotient and 0 as remainder.

b.

Answer:

Explanation:
384 ÷ 19 = ????
=> Dividing 384 by 19, we get 9 as 20 quotient and 4 as remainder.

c.

Answer:

Explanation:
6147 ÷ 52 = ????
=> Dividing 6147 by 52, we get 118 as quotient and 11 as remainder.

d.

Answer:

Explanation:
1352 ÷ 8 = ????
=> Dividing 1352 by 8, we get 169 as quotient and 0 as remainder.

Question 3.
a.

Answer:

Explanation:
Addition:
5.73 + 0.21 + 1.6
=> 5.73 + 0.21 + 1.6
= 7.54.

b.

Answer:

Explanation:
Addition:
28.30 + 1.07 + 5.58
= 29.37 + 5.58
= 34.95.

c.

Answer:

Explanation:
Addition:
93.45 + 28.12 + 23.3
= 121.57 + 23.3
= 144.87.

d.

Answer:

Explanation:
Addition:
27.38 + 92.46 + 84.9
= 119.84 + 84.9
= 204.74.

Question 4.
a.

Answer:

Explanation:
42.5 – 16.30 = ????
=> Subtraction of 42.5 – 16.30 = 26.20.

b.

Answer:

Explanation:
7.28 – 0.95 = ????
=> Subtraction of 7.28 – 0.95 = 6.33.

c.

Answer:

Explanation:
74.27 – 2.56 = ????
=> Subtraction of 74.27 – 2.56 = 71.71.

d.

Answer:

Explanation:
32.56 – 23.65 = ????
=> Subtraction of 32.56 – 23.65 = 8.91.

Question 5.
a.

Answer:

Explanation:
586 × 3.7 = ???
=> Multiplying 586 by 3.7, we get the product as 2,168.20.

b.

Answer:

Explanation:
2.1 × 0.8 = ????
=> Multiplying 586 by 3.7, we get the product as 1.68.

c.

Answer:

Explanation:
3.50 × 2.6 = ????
=> Multiplying 586 by 3.7, we get the product as 9.100.

d.

Answer:

Explanation:
38.2 × 7.58 = ????
Multiplying 586 by 3.7, we get the product as 289.556.

Multiply or Divide.

Question 6.
a.

Answer:

Explanation:
98 × 0.4 = ???
=> Multiplying 98 by 0.4, we get the product as 39.2.

b.

Answer:

Explanation:
370 × 6.4 = ????
=> Multiplying 370 by 6.4, we get the product as 2368.0.

c.

Answer:

Explanation:
7.02 × 9 = ????
=> Multiplying 7.02 by 9, we get the product as 63.18.

d.

Answer:

Explanation:
42.36 × 13 = ????
=> Multiplying 42.36 by 13, we get the product as 550.68.

Question 7.
a.

Answer:
Dividing 10 by 2.5, we get 4 as the quotient and 0 as the remainder.

Explanation:
10 ÷ 2.5 = ???
=> (10 ÷ 2.5) × (10 ÷ 10)
=> 100 ÷ 25
=> 4.

b.

Answer:
Dividing 36 by 0.03, we get 1,200 as the quotient and 0 as the remainder.

Explanation:
36 ÷ 0.03 = ???
=> (36 ÷ 0.03) × (100 ÷ 100)
=> 3600 ÷ 3
=> 1200.

c.

Answer:
Dividing 7.2 by 9, we get 0.8 as the quotient and 0 as the remainder.

Explanation:
7.2 ÷ 9 = ???
=> 7.2 ÷ 9 = 0.8.

d.

Answer:
Dividing 5.6 by 8, we get 0.7 as the quotient and 0 as the remainder.

Explanation:
5.6 ÷ 8 = ???
=> 5.6 ÷ 8 = 0.7.

Question 8.
a.

Answer:
Dividing 24.96 by 4.8, we get 5.2 as the quotient and 0 as the remainder.

Explanation:
24.96 ÷ 4.8 = ???
=> (24.96 ÷ 4.8) ÷ (100 ÷ 100)
=> 2496 ÷ 480
=> 5.2.

b.

Answer:
Dividing 2.96 by 0.37, we get 8 as the quotient and 0 as the remainder.

Explanation:
(2.96 ÷ 0.37) × (100 ÷ 100)
= 296 ÷ 37
= 8.

c.

Answer:
Dividing 63.42 by 9.06, we get 7 as the quotient and 0 as the remainder.

Explanation:
63.42 ÷ 9.06 = ????
=> (63.42 ÷ 9.06) × (100 ÷ 100)
=> 6342 ÷ 906
=> 7.

d.

Answer:
Dividing 4.84 by 1.21, we get 4 as the quotient and 0 as the remainder.

Explanation:
4.84 ÷ 1.21 = ???
=> (4.84 ÷ 1.21) × (100 ÷ 100)
=> 484 ÷ 121
=> 4.

Write each number in expanded form.

Question 9.
a. 732
______
Answer:
Expanded form of 732 is 700 + 30 + 2.

Explanation:
732 = 7(100) + 3(10) + 2(1)
= 700 + 30 + 2

b. 32,132
______
Answer:
Expanded form of 32,132 is 30000 + 2000 + 100 + 30 + 2.

Explanation:
32,132 = 3(10000) + 2(1000) + 1(100) + 3(10) + 2(1)
= 30000 + 2000 + 100 + 30 + 2

c. 4,790
______
Answer:
Expanded form of 4,790 is 4000 + 700 + 90 + 0.

Explanation:
4,790 = 4(1000) + 7(100) + 9(10) + 0(1)
= 4000 + 700 + 90 + 0.

Question 10.
a. 10.03
______
Answer:
Expanded form of 10.03 is 10 + 0 + 0.3.

Explanation:
10.03 = 1(10) + 0(1) + (3÷100)
= 10 + 0 + 0.3
= 10 + 0.3

b. 23,147.32
______
Answer:
Expanded form of 23,147.32 is 20000 + 3000 + 100 + 40 + 7 + 0.32.

Explanation:
23,147.32 = 2(10000) + 3(1000) + 1(100) + 4(10) + 7(1) + (32 ÷ 100)
= 20000 + 3000 + 100 + 40 + 7 + 0.32
= 23000 + 100 + 40 + 7 + 0.32
= 23100 + 40 + 7 + 0.32
= 23140 + 7 + 0.32
= 23147 + 0.32

c. 300.1
______
Answer:
Expanded form of 300.1 is 300 + 00 + 0 + 0.1.

Explanation:
300.1 = 3(100) + 0(10) + 0(1) + (1 ÷ 10)
= 300 + 00 + 0 + 0.1
= 300 + 0.1

What is the value of the underlined digit?

Question 11.
a. 1539.16
Answer:
The value of the underlined digit in 1539.16 is 30 or Thirty.

b. 898,792
Answer:
The value of the underlined digit in 898,792 is 90,000 or Ninety Thousands.

Explanation:
898,792 = 9 × 10000 = 90,000.

c. 35,563.8
Answer:
The value of the underlined digit in 35,563.8 is 5,000 or Five Thousands.

Explanation:
35,563.8 = 5 × 1000 = 5,000.

Question 12.
a. 3,324,291.4
Answer:
The value of the underlined digit in 3,324,291.4 is 3,000,000 or 30 lakhs.

Explanation:
3,324,291.4 = 3 × 1000000 = 3,000,000.

b. 8,524.14
Answer:
The value of the underlined digit in 8,524.14  is four Hundredths or 0.04.

Explanation:
8,524.14  = 4 × 0.01 = 0.04.

c. 82,917.2
Answer:
The value of the underlined digit in 82,917.2 is twoTenths or 0.2.

Explanation:
82,917.2 = 2 × 0.1 = 0.2.

Add or Subtract.

Question 13.
a.

Answer:
Addition of \(\frac{3}{4}\) + \(\frac{1}{4}\), we get the sum of 1.

Explanation:
\(\frac{3}{4}\) + \(\frac{1}{4}\)
= (3 + 1) ÷ 4
= 4 ÷ 4
= 1.

b.

Answer:
Addition of \(\frac{2}{7}\) + \(\frac{3}{5}\), we get the sum of \(\frac{31}{35}\).

Explanation:
\(\frac{2}{7}\) + \(\frac{3}{5}\)
LCM of 7 and 5 = 35.
=> (\(\frac{2}{7}\) × \(\frac{5}{5}\)) + (\(\frac{3}{5}\) × \(\frac{7}{7}\))
=> \(\frac{10}{35}\) +  \(\frac{21}{35}\)
=> (10 + 21) ÷ 35
=> \(\frac{31}{35}\).

c.

Answer:
Addition of \(\frac{7}{8}\) + \(\frac{1}{3}\), we get the sum of \(\frac{29}{24}\) or 1\(\frac{5}{24}\).

Explanation:
\(\frac{7}{8}\) + \(\frac{1}{3}\)
LCM of 8 and 3 = 24.
=> (\(\frac{7}{8}\) × \(\frac{3}{3}\)) + (\(\frac{1}{3}\) × \(\frac{8}{8}\))
=> \(\frac{21}{24}\) +  \(\frac{8}{24}\)
=> (21 + 8) ÷ 24
=> \(\frac{29}{24}\) or 1\(\frac{5}{24}\)

d.

Answer:
Addition of \(\frac{5}{1}\) + \(\frac{2}{3}\), we get the sum of \(\frac{17}{3}\) or 5\(\frac{2}{3}\).

Explanation:
\(\frac{5}{1}\) + \(\frac{2}{3}\)
LCM of 1 and 3 = 3.
=> (\(\frac{5}{1}\) × \(\frac{3}{3}\)) + (\(\frac{2}{3}\) × \(\frac{1}{1}\))
=> \(\frac{15}{3}\) +  \(\frac{2}{3}\)
=> (15 + 2) ÷ 3
=> \(\frac{17}{3}\) or 5\(\frac{2}{3}\)

Question 14.
a.

Answer:
Subtraction of \(\frac{5}{8}\) – \(\frac{1}{8}\), we get the result \(\frac{4}{8}\).

Explanation:
\(\frac{5}{8}\) – \(\frac{1}{8}\)
=> (5 – 1) ÷ 8
=> \(\frac{4}{8}\)

b.

Answer:
Subtraction of \(\frac{6}{9}\) – \(\frac{2}{3}\), we get the result 0.

Explanation:
\(\frac{6}{9}\) – \(\frac{2}{3}\)
LCM of 9 and 3 = 9.
=> (\(\frac{6}{9}\) × \(\frac{1}{1}\)) – (\(\frac{2}{3}\) × \(\frac{3}{3}\))
=> \(\frac{6}{9}\) –  \(\frac{6}{9}\)
=> (6 – 6) ÷ 9
=> 0 ÷ 9
=> 0.

c.

Answer:
Subtraction of \(\frac{10}{11}\) – \(\frac{4}{5}\), we get the result \(\frac{6}{55}\).

Explanation:
\(\frac{10}{11}\) – \(\frac{4}{5}\)
LCM of 11 and 5 = 55.
=> (\(\frac{10}{11}\) × \(\frac{5}{5}\)) – (\(\frac{4}{5}\) × \(\frac{11}{11}\))
=> \(\frac{50}{55}\) –  \(\frac{44}{55}\)
=> (50 – 44) ÷ 55
=> \(\frac{6}{55}\)

d.

Answer:
Subtraction of \(\frac{7}{1}\) – \(\frac{3}{4}\), we get the result \(\frac{25}{4}\) or 6\(\frac{1}{4}\)

Explanation:
\(\frac{7}{1}\) – \(\frac{3}{4}\)
LCM of 1 and 4 = 4.
=> (\(\frac{7}{1}\) × \(\frac{4}{4}\)) – (\(\frac{3}{4}\) × \(\frac{1}{1}\))
=> \(\frac{28}{4}\) –  \(\frac{3}{4}\)
=> (28 – 3) ÷ 4
=> \(\frac{25}{4}\) or 6\(\frac{1}{4}\)

Question 15.
a.

Answer:
Addition of 2\(\frac{3}{4}\) + 4\(\frac{2}{3}\), we get the sum of  \(\frac{89}{12}\) or 7\(\frac{5}{12}\).

Explanation:
2\(\frac{3}{4}\) + 4\(\frac{2}{3}\)
= {[(2 × 4) + 3] ÷ 4} + {[(4 × 3) + 2] ÷ 3}
= [(8 + 3) ÷ 4] + [(12 + 2) ÷ 3]
= (11 ÷ 4) + (14 ÷ 3)
= \(\frac{11}{4}\) + \(\frac{14}{3}\)
LCM of 4 and 3 = 12.
=> (\(\frac{11}{4}\) × \(\frac{3}{3}\)) + (\(\frac{14}{3}\) × \(\frac{4}{4}\))
=> \(\frac{33}{12}\) +  \(\frac{56}{12}\)
=> (33 + 56) ÷ 12
=> \(\frac{89}{12}\) or 7\(\frac{5}{12}\)

b.

Answer:
Addition of 8\(\frac{1}{3}\) + 8\(\frac{5}{7}\), we get the sum of  \(\frac{358}{21}\) or 17\(\frac{1}{12}\).

Explanation:
8\(\frac{1}{3}\) + 8\(\frac{5}{7}\)
= {[(8 × 3) + 1] ÷ 3} + {[(8 × 7) + 5] ÷ 7}
= [(24 + 1) ÷ 3] + [(56 + 5) ÷ 7]
= (25 ÷ 3) + (61 ÷ 7)
= \(\frac{25}{3}\) + \(\frac{61}{7}\)
LCM of 3 and 7 = 21.
=> (\(\frac{25}{3}\) × \(\frac{7}{7}\)) + (\(\frac{61}{7}\) × \(\frac{3}{3}\))
=> \(\frac{175}{21}\) +  \(\frac{183}{21}\)
=> (175 + 183) ÷ 21
=> \(\frac{358}{21}\) or 17\(\frac{1}{12}\)

c.

Answer:
Addition of 2\(\frac{5}{8}\) + 9\(\frac{3}{4}\), we get the sum of \(\frac{99}{8}\) or 12\(\frac{3}{8}\)

Explanation:
2\(\frac{5}{8}\) + 9\(\frac{3}{4}\)
= {[(2 × 8) + 5] ÷ 8} + {[(9 × 4) + 3] ÷ 4}
= [(16 + 5) ÷ 8] + [(36 + 3) ÷ 4]
= (21 ÷ 8) + (39 ÷ 4)
= \(\frac{21}{8}\) + \(\frac{39}{4}\)
LCM of 8 and 4 = 8.
=> (\(\frac{21}{8}\) × \(\frac{1}{1}\)) + (\(\frac{39}{4}\) × \(\frac{2}{2}\))
=> \(\frac{21}{8}\) +  \(\frac{78}{8}\)
=> (21 + 78) ÷ 8
=> \(\frac{99}{8}\) or 12\(\frac{3}{8}\)

d.

Answer:
Addition of 2\(\frac{5}{6}\) + 1\(\frac{1}{8}\), we get the sum of \(\frac{95}{24}\) or 3\(\frac{23}{24}\).

Explanation:
2\(\frac{5}{6}\) + 1\(\frac{1}{8}\)
= {[(2 × 6) + 5] ÷ 6} + {[(1 × 8) + 1] ÷ 8}
= [(12 + 5) ÷ 6] + [(8 + 1) ÷ 8]
= (17 ÷ 6) + (9 ÷ 8)
= \(\frac{17}{6}\) + \(\frac{9}{8}\)
LCM of 6 and 8 = 24.
=> (\(\frac{17}{6}\) × \(\frac{4}{4}\)) + (\(\frac{9}{8}\) × \(\frac{3}{3}\))
=> \(\frac{68}{24}\) +  \(\frac{27}{24}\)
=> (68 + 27) ÷ 24
=> \(\frac{95}{24}\) or 3\(\frac{23}{24}\).

Question 16.
a.

Answer:
Subtraction of 5\(\frac{7}{12}\) – 1\(\frac{5}{12}\), we get the result 4.

Explanation:
5\(\frac{7}{12}\) – 1\(\frac{5}{12}\)
= {[(5 × 12) + 7] ÷ 12} – {[(1 × 12) + 5] ÷ 12}
= [(60 + 7) ÷ 12] – [(12 + 5) ÷ 12]
= (67 ÷ 12) – (19 ÷ 12)
= \(\frac{67}{12}\) – \(\frac{19}{12}\)
=> (67 – 19) ÷ 12
=> \(\frac{48}{12}\) ÷ \(\frac{12}{12}\)
=> \(\frac{4}{1}\)
=> 4.

b.

Answer:
Subtraction of 7\(\frac{1}{4}\) – 3\(\frac{2}{9}\), we get the result  \(\frac{145}{36}\) or 4\(\frac{1}{36}\).

Explanation:
7\(\frac{1}{4}\) – 3\(\frac{2}{9}\)
= {[(7 × 4) + 1] ÷ 4} – {[(3 × 9) + 2] ÷ 9}
= [(28 + 1) ÷ 4] – [(27 + 2) ÷ 9]
= (29 ÷ 4) – (29 ÷ 9)
= \(\frac{29}{4}\) – \(\frac{29}{9}\)
LCM of 4 and 9 = 36.
=> (\(\frac{29}{4}\) × \(\frac{9}{9}\)) – (\(\frac{29}{9}\) × \(\frac{4}{4}\))
=> \(\frac{261}{36}\) – \(\frac{116}{36}\)
=> (261 – 116) ÷ 36
=> \(\frac{145}{36}\) or 4\(\frac{1}{36}\).

c.

Answer:
Subtraction of 8\(\frac{1}{4}\) – 5\(\frac{3}{4}\), we get the result \(\frac{10}{4}\) or 2\(\frac{2}{4}\).

Explanation:
8\(\frac{1}{4}\) – 5\(\frac{3}{4}\)
= {[(8 × 4) + 1] ÷ 4} – {[(5 × 4) + 3] ÷ 4}
= [(32 + 1) ÷ 4] – [(20 + 3) ÷ 4]
= (33 ÷ 4) – (23 ÷ 4)
= \(\frac{33}{4}\) – \(\frac{23}{4}\)
=> (33 – 23) ÷ 4
=> \(\frac{10}{4}\) or 2\(\frac{2}{4}\).

d.

Answer:
Subtraction of 8\(\frac{1}{3}\) – 3\(\frac{1}{2}\), we get the result \(\frac{29}{6}\) or 4\(\frac{5}{6}\).

Explanation:
8\(\frac{1}{3}\) – 3\(\frac{1}{2}\)
= {[(8 × 3) + 1] ÷ 3} – {[(3 × 2) + 1] ÷ 2}
= [(24 + 1) ÷ 3] – [(6 + 1) ÷ 2]
= (25 ÷ 3) – (7 ÷ 2)
= \(\frac{25}{3}\) – \(\frac{7}{2}\)
LCM of 3 and 2 = 6.
=> (\(\frac{25}{3}\) × \(\frac{2}{2}\)) – (\(\frac{7}{2}\) – \(\frac{3}{3}\))
=> \(\frac{50}{6}\) – \(\frac{21}{6}\)
=> (50 – 21) ÷ 6
=> \(\frac{29}{6}\) or 4\(\frac{5}{6}\).

Simplify each of the following.

Question 17.
a. \(\frac{18}{20}\) _____
Answer:
Simplest form of \(\frac{18}{20}\) is \(\frac{9}{10}\).

Explanation:
\(\frac{18}{20}\) ÷ \(\frac{2}{2}\)
=> \(\frac{9}{10}\)

b. \(\frac{28}{35}\) _____
Answer:
Simplest form of \(\frac{28}{35}\) is \(\frac{4}{5}\).

Explanation:
\(\frac{28}{35}\) ÷ \(\frac{7}{7}\)
= \(\frac{4}{5}\).

c. 2\(\frac{2}{12}\) _____
Answer:
Simplest form of 2\(\frac{2}{12}\) is \(\frac{13}{6}\) or 2\(\frac{1}{6}\).

Explanation:
2\(\frac{2}{12}\) = {[(2 × 12) + 2] ÷ 12}
= [(24 + 2) ÷ 12]
= 26 ÷ 12
= \(\frac{26}{12}\) ÷ \(\frac{2}{2}\)
= \(\frac{13}{6}\) or 2\(\frac{1}{6}\).

Question 18.
a. 3\(\frac{4}{6}\) _____
Answer:
Simplest form of 3\(\frac{4}{6}\) is \(\frac{11}{3}\) or 3\(\frac{2}{3}\).

Explanation:
3\(\frac{4}{6}\) = {[(3 × 6) + 4] ÷ 6}
= [(18 + 4) ÷ 6]
= (22 ÷ 6)
= \(\frac{22}{6}\) ÷ \(\frac{2}{2}\)
= \(\frac{11}{3}\) or 3\(\frac{2}{3}\).

b. \(\frac{51}{6}\) _____
Answer:
Simplest form of \(\frac{51}{6}\) is \(\frac{17}{2}\) or 8\(\frac{1}{2}\).

Explanation:
\(\frac{51}{6}\) ÷ \(\frac{3}{3}\)
= \(\frac{17}{2}\) or 8\(\frac{1}{2}\).

c. 7\(\frac{8}{12}\) _____
Answer:
Simplest form of 7\(\frac{8}{12}\) is \(\frac{23}{3}\) or 7\(\frac{2}{3}\)..

Explanation:
7\(\frac{8}{12}\) = {[(7 × 12) + 8] ÷ 12}
= [(84 + 8) ÷ 12]
= 92 ÷ 12
= \(\frac{92}{12}\) ÷ \(\frac{2}{2}\)
= \(\frac{46}{6}\) ÷ \(\frac{2}{2}\)
= \(\frac{23}{3}\) or 7\(\frac{2}{3}\).

Write each improper fraction as a mixed number in simplest form.

Question 19.
a. \(\frac{18}{8}\) _____
Answer:
Simplest form of \(\frac{18}{8}\) is \(\frac{9}{2}\) or 4\(\frac{1}{2}\).

Explanation:
\(\frac{18}{8}\) ÷ \(\frac{2}{2}\)
= \(\frac{9}{2}\) or 4\(\frac{1}{2}\).

b. \(\frac{51}{9}\) _____
Answer:
Simplest form of \(\frac{51}{9}\) is \(\frac{17}{3}\) or 5\(\frac{2}{3}\).

Explanation:
\(\frac{51}{9}\) ÷ \(\frac{3}{3}\)
= \(\frac{17}{3}\) or 5\(\frac{2}{3}\)

c. \(\frac{34}{3}\) _____
Answer:
Simplest form of \(\frac{34}{3}\)  is 11\(\frac{1}{3}\).

Explanation:
\(\frac{34}{3}\) = 11\(\frac{1}{3}\).

Question 20.
a. \(\frac{53}{12}\) _____
Answer:
Simplest form of \(\frac{53}{12}\) is 4\(\frac{5}{12}\).

Explanation:
\(\frac{53}{12}\) = 4\(\frac{5}{12}\)

b. \(\frac{82}{8}\) _____
Answer:
Simplest form of \(\frac{82}{8}\) is \(\frac{41}{4}\) or 10\(\frac{1}{4}\).

Explanation:
\(\frac{82}{8}\) ÷ \(\frac{2}{2}\)
= \(\frac{41}{4}\) or 10\(\frac{1}{4}\).

c. \(\frac{66}{7}\) _____
Answer:
Simplest form of \(\frac{66}{7}\) is 9\(\frac{3}{7}\).

Explanation:
\(\frac{66}{7}\) = 9\(\frac{3}{7}\).

Write each mixed number as an improper fraction.

Question 21.
a. 4\(\frac{1}{3}\) _____
Answer:
Improper fraction of 4\(\frac{1}{3}\) is \(\frac{13}{3}\).

Explanation:
4\(\frac{1}{3}\) = {[(4 × 3) + 1] ÷ 3}
= [(12 + 1) ÷ 3]
= (13 ÷ 3)
= \(\frac{13}{3}\).

b. 7\(\frac{5}{9}\) _____
Answer:
Improper fraction of 7\(\frac{5}{9}\) is \(\frac{68}{9}\).

Explanation:
7\(\frac{5}{9}\) = {[(7 × 9) + 5] ÷ 9}
= [(63 + 5) ÷ 9]
= (68 ÷ 9)
= \(\frac{68}{9}\).

c. 1\(\frac{7}{10}\) _____
Answer:
Improper fraction of 1\(\frac{7}{10}\)  is \(\frac{17}{10}\).

Explanation:
1\(\frac{7}{10}\) = {[(1 × 10) + 7] ÷ 10}
= [(10 + 7) ÷ 10]
= (17 ÷ 10)
= \(\frac{17}{10}\).

Question 22.
a. 3\(\frac{3}{4}\) _____
Answer:
Improper fraction of 3\(\frac{3}{4}\) is \(\frac{15}{4}\).

Explanation:
3\(\frac{3}{4}\) = {[(3 × 4) + 3] ÷ 4}
= [(12 + 3) ÷ 4]
= (15 ÷ 4)
= \(\frac{15}{4}\).

b. 5\(\frac{11}{12}\) _____
Answer:
Improper fraction of 5\(\frac{11}{12}\) is \(\frac{71}{12}\).

Explanation:
5\(\frac{11}{12}\) = {[(5 × 12) + 11] ÷ 12}
= [(60 + 11) ÷ 12]
= (71 ÷ 12)
= \(\frac{71}{12}\).

c. 8\(\frac{2}{9}\) _____
Answer:
Improper fraction of 8\(\frac{2}{9}\) is \(\frac{74}{9}\).

Explanation:
8\(\frac{2}{9}\) = {[(8 × 9) + 2] ÷ 9}
= [(72 + 2) ÷ 9]
= (74 ÷ 9)
= \(\frac{74}{9}\)

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

Question 23.
a. \(\frac{7}{8}\) _____ \(\frac{9}{10}\)
Answer:
\(\frac{7}{8}\) < \(\frac{9}{10}\).

Explanation:
\(\frac{7}{8}\) _____ \(\frac{9}{10}\)
Common multiple of denominators 8 and 10 = 40.
\(\frac{7}{8}\) × \(\frac{5}{5}\) = \(\frac{35}{40}\)
\(\frac{9}{10}\) × \(\frac{4}{4}\) = \(\frac{36}{40}\)
=> \(\frac{35}{40}\) is lesser than \(\frac{36}{40}\).

b. \(\frac{1}{4}\) _____ \(\frac{4}{10}\)
Answer:
\(\frac{1}{4}\) < \(\frac{4}{10}\).

Explanation:
\(\frac{1}{4}\) _____ \(\frac{4}{10}\)
Common multiple of denominators 4 and 10 = 20.
\(\frac{1}{4}\) × \(\frac{5}{5}\) = \(\frac{5}{20}\)
\(\frac{4}{10}\) × \(\frac{2}{2}\) = \(\frac{8}{20}\)
=> \(\frac{5}{20}\) is lesser than \(\frac{8}{20}\).

c. \(\frac{2}{3}\) _____ \(\frac{9}{10}\)
Answer:
\(\frac{2}{3}\) < \(\frac{9}{10}\).

Explanation:
\(\frac{2}{3}\) _____ \(\frac{9}{10}\)
Common multiple of denominators 3 and 10 = 30.
\(\frac{2}{3}\) × \(\frac{10}{10}\) = \(\frac{20}{30}\)
\(\frac{9}{10}\) × \(\frac{3}{3}\) = \(\frac{27}{30}\)
=> \(\frac{20}{30}\) is lesser than \(\frac{27}{30}\).

d. \(\frac{8}{10}\) _____ \(\frac{2}{3}\)
Answer:
\(\frac{8}{10}\) > \(\frac{2}{3}\).

Explanation:
\(\frac{8}{10}\) _____ \(\frac{2}{3}\)
Common multiple of denominators 10 and 3 = 30.
\(\frac{8}{10}\) × \(\frac{3}{3}\) = \(\frac{24}{30}\)
\(\frac{2}{3}\) × \(\frac{10}{10}\) = \(\frac{20}{30}\)
=> \(\frac{24}{30}\) is greater than \(\frac{20}{30}\).

Question 24.
a. 80.59 _____ 80.67
Answer:
80.59 < 80.67.

Explanation:
80.59 _____ 80.67
=> 80.59 is lesser than 80.67. (Checking the decimal points)

b. 46.94 _____ 46.37
Answer:
46.94 > 46.37.

Explanation:
46.94 _____ 46.37
=> 46.94 is greater than 46.37. (Checking the decimal points)

c. 54.72 _____ 54.27
Answer:
54.72 > 54.27.

Explanation:
54.72 _____ 54.27
=> 54.72 is greater than 54.27. (Checking the decimal points)

d. 86.4 _____ 80.40
Answer:
86.4 > 80.40.

Explanation:
86.4 _____ 80.40
=> 86.4 is greater than 80.40.

Put the numbers in order from least to greatest.

Question 25.
0.1, \(\frac{1}{4}\), 3.1, \(\frac{1}{3}\)
Answer:
Numbers from Least to greatest:
0.1
\(\frac{1}{4}\)
\(\frac{1}{3}\)
3.1

Explanation:
0.1 = 0.1.
\(\frac{1}{4}\) = 1 ÷ 4 = 0.25.
3.1 = 3.1.
\(\frac{1}{3}\) = 1 ÷ 3 = 0.33.

Question 26.
0.5, \(\frac{5}{8}\), 0.7, \(\frac{1}{9}\)
Answer:
Numbers from Least to greatest:
\(\frac{1}{9}\)
0.5 = 0.5
0.7
\(\frac{5}{8}\)

Explanation:
0.5 = 0.5
\(\frac{5}{8}\) = 5 ÷ 8 = 0.625.
0.7 = 0.7.
\(\frac{1}{9}\) = 1 ÷ 9 = 0.11.

Question 27.
\(\frac{3}{2}\), 1.7, \(\frac{1}{150}\), \(\frac{8}{3}\)
Answer:
Numbers from Least to greatest:
\(\frac{1}{150}\)
\(\frac{8}{3}\)
\(\frac{3}{2}\)
1.7.

Explanation:
\(\frac{3}{2}\) = 3 ÷ 2 = 1.5.
1.7 = 1.7.
\(\frac{1}{150}\) = 1 ÷ 150 = 0.0067.
\(\frac{8}{3}\) = 8 ÷ 3 = 2.67.