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

**Add, Subtract, multiply, or divide**

Question 1.

a.

Answer:

275×56 = 15,400.

Explanation:

By multiplying 275 and 56 we will get the product as 15,400.

b.

Answer:

312×9 = 2,808.

Explanation:

By multiplying 312 and 9 we will get the product as 2,808.

c.

Answer:

1717×34 = 58,378.

Explanation:

By multiplying 1717 and 34 we will get the product as 58,378.

d.

Answer:

5806×42 = 243,852.

Explanation:

By multiplying 5806 and 42 we will get the product as 243,852.

Question 2.

a.

Answer:

72÷8 = 9.

Explanation:

The division of 72 by 8 we will get the result as 8.

b.

Answer:

384÷19 = 20.21.

Explanation:

The division of 384 by 19 we will get the result as 20.21.

c.

Answer:

6147÷52 = 118

Explanation:

The division of 6147 by 52 we will get the result as 118.

d.

Answer:

1352÷8 = 169.

Explanation:

The division of 1352 by 8 we will get the result as 169.

Question 3.

a.

Answer:

5.73+0.21+1.6 = 7.54.

Explanation:

The addition of 5.73, 0.21 and 1.6 we will get the result as 7.54.

b.

Answer:

28.30+1.07+5.58 = 34.95.

Explanation:

The addition of 28.30, 1.07 and 5.58 we will get the result as 34.95.

c.

Answer:

93.45+28.12+23.3 = 144.87.

Explanation:

The addition of 93.45, 28.12 and 23.3 we will get the result as 144.87.

d.

Answer:

Explanation:

The addition of 27.38, 92.46 and 84.9 we will get the result as 204.74.

Question 4.

a.

Answer:

42.5-16.30 = 26.20.

Explanation:

By subtracting 16.30 from 42.5 we will get the result as 26.20.

b.

Answer:

7.28-0.95 = 6.33.

Explanation:

By subtracting 0.95 from 7.28 we will get the result as 6.33.

c.

Answer:

74.27-2.56 = 71.71.

Explanation:

By subtracting 2.56 from 74.27 we will get the result as 71.71.

d.

Answer:

32.56-23.65 = 8.91.

Explanation:

By subtracting 23.65 from 32.56 we will get the result as 8.91.

Question 5.

a.

Answer:

586×3.7 = 2168.2

Explanation:

By multiplying 586 and 3.7 we will get the product as 2168.2.

b.

Answer:

2.1×0.8 = 1.68.

Explanation:

By multiplying 2.1 and 0.8 we will get the product as 1.68.

c.

Answer:

3.50×2.6 = 9.1

Explanation:

By multiplying 3.50 and 2.6 we will get the product as 9.1.

d.

Answer:

38.2×7.58 = 289.556.

Explanation:

By multiplying 38.2 and 7.58 we will get the product as 289.556.

**Multiply or Divide.**

Question 6.

a.

Answer:

98×0.4 = 39.2.

Explanation:

By multiplying 98 and 0.4 we will get the product as 39.2.

b.

Answer:

370×6.4 = 2368.0

Explanation:

By multiplying 370 and 6.4 we will get the product as 2368.0

c.

Answer:

7.02×9 = 63.18.

Explanation:

By multiplying 7.02 and 9 we will get the product as 63.18.

d.

Answer:

42.36×13 = 550.68.

Explanation:

By multiplying 42.36 and 13 we will get the product as 550.68.

Question 7.

a.

Answer:

10÷2.5 = 4.

Explanation:

The division of 10 by 2.5 we will get the result as 4.

b.

Answer:

36÷0.03 = 1200.

Explanation:

The division of 36 by 0.03 we will get the result as 1200.

c.

Answer:

7.2÷9 = 0.8.

Explanation:

The division of 7.2 by 9 we will get the result as 0.8.

d.

Answer:

5.6÷8 = 0.7.

Explanation:

The division of 5.6 by 8 we will get the result as 0.7.

Question 8.

a.

Answer:

24.96÷4.8 = 5.2.

Explanation:

The division of 24.96 by 4.8 we will get the result as 5.2

b.

Answer:

2.96÷0.37 = 8.

Explanation:

The division of 2.96 by 0.37 we will get the result as 8.

c.

Answer:

63.42÷9.06 = 7.

Explanation:

The division of 63.42 by 9.06 we will get the result as 7.

d.

Answer:

4.84÷1.21 = 4.

Explanation:

The division of 4.84 by 1.21 we will get the quotient as 4.

**Write each number in expanded form.**

Question 9.

a. 732

______

Answer:

732 = 700+30+2

Explanation:

The expanded form of 732 which is 700+30+2.

b. 32,132

______

Answer:

32,132 = 30,000+2,000+100+30+2.

Explanation:

The expanded form of 32,132 which is 30,000+2,000+100+30+2.

c. 4,790

______

Answer:

4,790 = 4000+700+90.

Explanation:

The expanded form of 4,790 which is 4,000+700+90.

Question 10.

a. 10.03

______

Answer:

10.03 = 10+0.3.

Explanation:

The expanded form of 10.03 which is 10+0.3

b. 23,147.32

______

Answer:

23,147.32 = 20,000+3,000+100+40+7+0.3+0.02.

Explanation:

The expanded form of 23,147.32 which is 20,000+3,000+100+40+7+0.3+0.02

c. 300.1

______

Answer:

300.1= 300+0.1

Explanation:

The expanded form of 300.1 which is 300+0.1

**What is the value of the underlined digit?**

Question 11.

a. 15__3__9.16

Answer:

3 – Tens place.

Explanation:

Here, the underlined digit is 3, so the value of the digit 3 is Tens place.

b. 8__9__8,792

Answer:

8__9__8,792 = Ten Thousands.

Explanation:

Here, the underlined digit is 9 in 8__9__8,792, so the value of the digit 9 is Ten Thousands place.

c. 3__5__,563.8

Answer:

3__5__,563.8 = Thousands.

Explanation:

Here, the underlined digit is 5 in 3__5__,563.8, so the value of the digit 5 is Thousands place.

Question 12.

a. __3__,324,291.4

Answer:

3 = Million.

Explanation:

Here, the underlined digit is 3 in __3__,324,291.4, so the value of the digit 3 is million place.

b. 8,524.1__4__

Answer:

.04 = Hundredths.

Explanation:

Here, the underlined digit is .04 in 8,524.1__4__, so the value of the digit .04 is hundredths.

c. 82,917.__2__

Answer:

.2= Hundredths.

Explanation:

Here, the underlined digit is .2 in 82,917.__2__, so the value of the digit .2 is hundredths.

**Add or Subtract.**

Question 13.

a.

Answer:

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

Explanation:

The addition of \(\frac{3}{4}\)+\(\frac{1}{4}\) is \(\frac{4}{4}\) which is 1.

b.

Answer:

\(\frac{2}{7}\)+\(\frac{3}{5}\) = \(\frac{31}{35}\).

Explanation:

The addition of \(\frac{2}{7}\)+\(\frac{3}{5}\) which is \(\frac{10+21}{35}\)

= \(\frac{31}{35}\).

c.

Answer:

\(\frac{7}{8}\)+\(\frac{1}{3}\) = \(\frac{29}{24}\).

Explanation:

The addition of \(\frac{7}{8}\)+\(\frac{1}{3}\) which is \(\frac{21+8}{24}\)

= \(\frac{29}{24}\).

d.

Answer:

5+\(\frac{2}{3}\) = \(\frac{17}{3}\).

Explanation:

The addition of 5+\(\frac{2}{3}\) which is \(\frac{15+2}{3}\)

= \(\frac{17}{3}\).

Question 14.

a.

Answer:

\(\frac{5}{8}\)–\(\frac{1}{8}\) = \(\frac{1}{2}\).

Explanation:

The subtraction of \(\frac{5}{8}\)–\(\frac{1}{8}\) which is \(\frac{5-1}{8}\)

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

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

b.

Answer:

\(\frac{6}{9}\)–\(\frac{2}{3}\) = 0.

Explanation:

The subtraction of \(\frac{6}{9}\)–\(\frac{2}{3}\) which is

= \(\frac{18-18}{9}\)

= 0.

c.

Answer:

\(\frac{10}{11}\)–\(\frac{4}{5}\) = \(\frac{6}{55}\).

Explanation:

The subtraction of \(\frac{10}{11}\)–\(\frac{4}{5}\) which is

= \(\frac{50-44}{55}\)

= \(\frac{6}{55}\).

d.

Answer:

7-\(\frac{3}{4}\) = 6\(\frac{1}{4}\).

Explanation:

The subtraction of 7-\(\frac{3}{4}\) which is

= \(\frac{28-3}{4}\)

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

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

Question 15.

a.

Answer:

2\(\frac{3}{4}\)+4\(\frac{2}{3}\) = 8\(\frac{1}{12}\).

Explanation:

The addition of 2\(\frac{3}{4}\)+4\(\frac{2}{3}\) which is

= \(\frac{11}{4}\)+\(\frac{14}{3}\)

= \(\frac{33+64}{12}\)

= \(\frac{97}{12}\)

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

b.

Answer:

8\(\frac{1}{3}\)+8\(\frac{5}{7}\) = 17\(\frac{1}{21}\).

Explanation:

The addition of 8\(\frac{1}{3}\)+8\(\frac{5}{7}\) which is

= \(\frac{25}{3}\)+\(\frac{61}{7}\)

= \(\frac{175+183}{21}\)

= \(\frac{358}{21}\)

= 17\(\frac{1}{21}\).

c.

Answer:

2\(\frac{5}{8}\)+9\(\frac{3}{4}\) = 12\(\frac{3}{8}\).

Explanation:

The addition of 2\(\frac{5}{8}\)+9\(\frac{3}{4}\) which is

= \(\frac{21}{8}\)+\(\frac{39}{4}\)

= \(\frac{84+312}{32}\)

= \(\frac{396}{32}\)

= 12\(\frac{12}{32}\)

= 12\(\frac{3}{8}\).

d.

Answer:

2\(\frac{5}{6}\)+1\(\frac{1}{8}\) = 3\(\frac{23}{24}\).

Explanation:

The addition of 2\(\frac{5}{6}\)+1\(\frac{1}{8}\) which is

= \(\frac{17}{6}\)+\(\frac{9}{8}\)

= \(\frac{136+54}{48}\)

= \(\frac{190}{48}\)

= \(\frac{1}{48}\)

= 3\(\frac{46}{48}\)

= 3\(\frac{23}{24}\).

Question 16.

a.

Answer:

5\(\frac{7}{12}\)-1\(\frac{5}{12}\) = 4\(\frac{1}{6}\).

Explanation:

The subtraction of 5\(\frac{7}{12}\)-1\(\frac{5}{12}\) which is

= \(\frac{67}{12}\)–\(\frac{17}{12}\)

= \(\frac{67-17}{12}\)

= \(\frac{50}{12}\)

= 4\(\frac{2}{12}\)

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

b.

Answer:

7\(\frac{1}{4}\)-3\(\frac{2}{9}\) = 4\(\frac{1}{36}\).

Explanation:

The subtraction of 7\(\frac{1}{4}\)-3\(\frac{2}{9}\) which is

= \(\frac{29}{4}\)–\(\frac{29}{9}\)

= \(\frac{261-116}{36}\)

= \(\frac{145}{36}\)

= 4\(\frac{1}{36}\).

c.

Answer:

8\(\frac{1}{4}\)-5\(\frac{3}{4}\) = 2\(\frac{1}{2}\).

Explanation:

The subtraction of 8\(\frac{1}{4}\)-5\(\frac{3}{4}\) which is

= \(\frac{33}{4}\)–\(\frac{23}{4}\)

= \(\frac{33-23}{4}\)

= \(\frac{10}{4}\)

= 2\(\frac{2}{4}\)

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

d.

Answer:

8\(\frac{1}{3}\)-3\(\frac{1}{2}\) = 4\(\frac{5}{6}\).

Explanation:

The subtraction of 8\(\frac{1}{3}\)-3\(\frac{1}{2}\) which is \(\frac{25}{3}\)–\(\frac{7}{2}\)

= \(\frac{50-21}{6}\)

= \(\frac{29}{6}\)

= 4\(\frac{5}{6}\).

**Simplify each of the following.**

Question 17.

a. \(\frac{18}{20}\) _____

Answer:

\(\frac{9}{10}\).

Explanation:

The simplest form of \(\frac{18}{20}\) is \(\frac{9}{10}\) as the both numbers are divisible by 2. So we will divide them with 2.

b. \(\frac{28}{35}\) _____

Answer:

\(\frac{4}{5}\).

Explanation:

The simplest form of \(\frac{28}{35}\) is \(\frac{4}{5}\) as the both numbers are divisible by 7. So we will divide them with 7.

c. 2\(\frac{2}{12}\) _____

Answer:

2\(\frac{1}{6}\)

Explanation:

The simplest form of 2\(\frac{2}{12}\) which is \(\frac{26}{12}\) = \(\frac{13}{6}\) which is 2\(\frac{1}{6}\) as the both numbers are divisible by 2. So we will divide them with 2.

Question 18.

a. 3\(\frac{4}{6}\) _____

Answer:

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

Explanation:

The simplest form of 3\(\frac{4}{6}\) which is \(\frac{22}{6}\) as the both numbers are divisible by 2. So we will divide them with 2. Then \(\frac{11}{3}\) which is 3\(\frac{2}{3}\).

b. \(\frac{51}{6}\) _____

Answer:

8\(\frac{1}{2}\).

Explanation:

The simplest form of \(\frac{51}{6}\) is \(\frac{17}{2}\) as the both numbers are divisible by 3. So we will divide them with 3. Then 8\(\frac{1}{2}\).

c. 7\(\frac{8}{12}\) _____

Answer:

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

Explanation:

The simplest form of 7\(\frac{8}{12}\) which is \(\frac{92}{12}\) as the both numbers are divisible by 4. So we will divide them with 4. Then \(\frac{23}{3}\) which is 7\(\frac{2}{3}\).

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

Question 19.

a. \(\frac{18}{8}\) _____

Answer:

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

Explanation:

The mixed fraction of \(\frac{18}{8}\) is 2\(\frac{2}{8}\) which is 2\(\frac{1}{4}\).

b. \(\frac{51}{9}\) _____

Answer:

5\(\frac{2}{3}\).

Explanation:

The mixed fraction of \(\frac{51}{9}\) is 5\(\frac{6}{9}\) which is 5\(\frac{2}{3}\).

c. \(\frac{34}{3}\) _____

Answer:

11\(\frac{1}{3}\).

Explanation:

The mixed fraction of \(\frac{34}{3}\) is 11\(\frac{1}{3}\).

Question 20.

a. \(\frac{53}{12}\) _____

Answer:

4\(\frac{5}{12}\).

Explanation:

The mixed fraction of \(\frac{53}{12}\) is 4\(\frac{5}{12}\).

b. \(\frac{82}{8}\) _____

Answer:

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

Explanation:

The mixed fraction of \(\frac{82}{8}\) is 5\(\frac{1}{4}\).

c. \(\frac{66}{7}\) _____

Answer:

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

Explanation:

The mixed fraction of \(\frac{66}{7}\) is 9\(\frac{3}{7}\).

**Write each mixed number as an improper fraction.**

Question 21.

a. 4\(\frac{1}{3}\) _____

Answer:

\(\frac{13}{3}\).

Explanation:

The improper fraction of 4\(\frac{1}{3}\) is \(\frac{13}{3}\).

b. 7\(\frac{5}{9}\) _____

Answer:

\(\frac{68}{9}\).

Explanation:

The improper fraction of 7\(\frac{5}{9}\) which is \(\frac{68}{9}\).

c. 1\(\frac{7}{10}\) _____

Answer:

\(\frac{17}{10}\).

Explanation:

The improper fraction of 1\(\frac{7}{10}\) which is \(\frac{17}{10}\).

Question 22.

a. 3\(\frac{3}{4}\) _____

Answer:

\(\frac{15}{4}\).\(\frac{15}{4}\).

Explanation:

The improper fraction of 3\(\frac{3}{4}\) which is \(\frac{15}{4}\).

b. 5\(\frac{11}{12}\) _____

Answer:

\(\frac{71}{12}\).

Explanation:

The improper fraction of 5\(\frac{11}{12}\) which is \(\frac{71}{12}\).

c. 8\(\frac{2}{9}\) _____

Answer:

\(\frac{74}{9}\).

Explanation:

The improper fraction of 8\(\frac{2}{9}\) which is \(\frac{74}{9}\).

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

Question 23.

a. \(\frac{7}{8}\) _____ \(\frac{9}{10}\)

Answer:

\(\frac{7}{8}\) < \(\frac{9}{10}\).

Explanation:

As \(\frac{7}{8}\) is 0.875 and \(\frac{9}{10}\) is 0.9. So \(\frac{7}{8}\) < \(\frac{9}{10}\).

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

Answer:

\(\frac{1}{4}\) < \(\frac{4}{10}\).

Explanation:

As \(\frac{1}{4}\) is 0.25 and \(\frac{4}{10}\) is 0.4. So \(\frac{1}{4}\) < \(\frac{4}{10}\).

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

Answer:

\(\frac{2}{3}\) < \(\frac{9}{10}\).

Explanation:

As \(\frac{2}{3}\) is 0.67 and \(\frac{9}{10}\) is 0.9. So \(\frac{2}{3}\) < \(\frac{9}{10}\).

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

Answer:

\(\frac{8}{10}\) > \(\frac{2}{3}\).

Explanation:

As \(\frac{8}{10}\) is 0.8 and \(\frac{2}{3}\) is 0.67. So \(\frac{8}{10}\) > \(\frac{2}{3}\).

Question 24.

a. 80.59 _____ 80.67

Answer:

80.59<80.67.

Explanation:

Here, 80.59 is less than 80.67. So 80.59<80.67.

b. 46.94 _____ 46.37

Answer:

46.94>46.37.

Explanation:

Here, 46.94 is greater than 46.37. So 46.94>46.37.

c. 54.72 _____ 54.27

Answer:

54.72>54.27.

Explanation:

Here, 54.72 is greater than 54.27. So 54.72>54.27.

d. 86.4 _____ 80.40

Answer:

86.4>80.40.

Explanation:

Here, 86.4 is greater than 80.40. So 86.4>80.40.

**Put the numbers in order from least to greatest.**

Question 25.

0.1, \(\frac{1}{4}\), 3.1, \(\frac{1}{3}\)

Answer:

0.1, 0.25, 0.33, 3.1.

Explanation:

Given the values are 0.1, \(\frac{1}{4}\) which is 0.25, 3.1 and \(\frac{1}{3}\) which is 0.33. So the numbers from least to greatest are 0.1, 0.25, 0.33, 3.1.

Question 26.

0.5, \(\frac{5}{8}\), 0.7, \(\frac{1}{9}\)

Answer:

0.11, 0.5, 0.625, 0.7.

Explanation:

Given the values are 0.5, \(\frac{5}{8}\) which is 0.625, 0.7, \(\frac{1}{9}\) which is 0.11. So the numbers from least to greatest are 0.11, 0.5, 0.625, 0.7.

Question 27.

\(\frac{3}{2}\), 1.7, \(\frac{1}{150}\), \(\frac{8}{3}\)

Answer:

0.0067, 1.5, 1.7, 2.67.

Explanation:

Given the values are \(\frac{3}{2}\) which is 1.5, 1.7, \(\frac{1}{150}\) which is 0.0067, \(\frac{8}{3}\) which is 2.67. So the numbers from least to greatest are 0.0067, 1.5, 1.7, 2.67.