Free Printable Study Guide - 1.2 Understanding Rational Numbers

1.

An expression is shown.

$\left|2\frac{2}{3}\right|$

Which statement best describes the expression shown?

a)

$\left|2\frac{2}{3}\right|$ = $-2\frac{2}{3}$ because the opposite of $2\frac{2}{3}$ is $-2\frac{2}{3}$

b)

$\left|2\frac{2}{3}\right|$ = $2\frac{2}{3}$ because the distance from $2\frac{2}{3}$ to 0 is $2\frac{2}{3}$

c)

$\left|2\frac{2}{3}\right|$ = $-2\frac{2}{3}$ because the distance from $2\frac{2}{3}$ to 0 is $-2\frac{2}{3}$

d)

$\left|2\frac{2}{3}\right|$ = $5\frac{1}{3}$ because the distance from $2\frac{2}{3}$ to $-2\frac{2}{3}$ is $5\frac{1}{3}$

2.

Amsterdam is at an elevation of -12 feet, and Orlando has an elevation of 89 feet. How many feet below sea level is Amsterdam?

Amsterdam is (a) feet below sea level.

Choose from the below words

12

-12

89

-89

3.

This question has two parts.

Jake borrowed $112 from his friend. He also owes his parents $32 for a video game they bought for him.

Part A: Which mathematical statement correctly represents Jake's total debt? (a)

Part B: What is Jake's total debt? (b)

Choose from the below words

$\left|-112\right|+\left|-32\right|$

Jake owes a total of $144

$\left|112\right|-\left|32\right|$

$\left|-112\right|+\left|32\right|$

$\left|-112\right|-\left|-32\right|$

Jake owes a total of $80

Jake owes a total of -$144

Jake owes a total of -$80

4.

Tasty Ice Cream financial statement shows a balance of -$12,830. Their competitor, Tasty Italian Ice financial statement shows a balance of -$13,027.

Which statement correctly compares the two amounts?

a)

$\left|-12,830\right|<\left|-13,027\right|$

b)

$-13,027>\left|-12,830\right|$

c)

$\left|-12,830\right|>\left|-13,027\right|$

d)

$\left|-13,027\right|<-12,830$

5.

|-12| - |- 8|=

6.

Singapore is at an elevation of -50 feet, and Fort Lauderdale has an elevation of 9 feet. How many feet above sea level is Fort Lauderdale?

Fort Lauderdale is (a) feet above sea level.

Choose from the below words

9

-9

50

-50

7.

| -13| + | 24| =

8.

| 15 - 5 | =

9.

|- 10| - |5|=

10.

4 + 4 + $\left|-\ 4\right|$ =

11.

40 - l - 10 l =

12.

$\frac{\left|10\ +\ 8\right|}{3}$ =

13.

32____l40l

a)

<

b)

>

c)

=

14.

Compare these Integers using the symbols:
< > =
| -13 | ____ | 4 |

a)

<

b)

>

c)

=

15.

Compare these Integers using the symbols:
< > =
| -4 | _____ 4

a)

<

b)

>

c)

=

16.

|-10|____|-7|

a)

<

b)

>

c)

=

17.

l-6l____6

a)

<

b)

>

c)

=

18.

Compare |-5| to the |-10|

a)

|-5| > |-10|

b)

|-5| = |-10|

c)

|-5| < |-10|

19.

Evaluate the expression.
|-2| + |-5|

a)

7

b)

-7

c)

3

d)

-3

20.

The absolute value of -6 is ___ the absolute value of 6.

a)

greater than

b)

equal to

c)

less than

21.

What are 2 integers with an absolute value of 15?

a)

15 and -10

b)

30 and 15

c)

15 and -15

d)

0 and -15

22.

Find the Absolute Value of -18

a)

18

b)

-18

c)

36

d)

-36

23.

What is the absolute value of $-\left|14\right|$ ?

a)

-14

b)

14

c)

This cannot be solved.

24.

What is the distance between 5 and 0?

a)

6

b)

4

c)

5

d)

-5

25.

Evaluate the expression.
|–4| – |–4|

a)

-8

b)

0

c)

8

d)

-4

26.

Desmond's monthly Netflix subscription costs $10. If he charges it to his credit card each month for 5 months without making any payments, what will his debt be?

a)

He will owe -$45

b)

He will owe -$50

c)

He will owe $45

d)

He will owe $50

27.

Emma's monthly gym membership costs $15. If she charges it to her credit card each month for 4 months without making any payments, what will her debt be?

a)

She will owe -$60

b)

She will owe -$75

c)

She will owe $60

d)

She will owe $75

28.

John's monthly subscription to a music service costs $12. If he charges it to his credit card each month for 6 months without making any payments, what will his debt be?

a)

He will owe -$60

b)

He will owe -$72

c)

He will owe $60

d)

He will owe $72

29.

Compare the absolute values: |-8| ____ |8|

a)

<

b)

>

c)

=

30.

What is the absolute value of -20?

a)

20

b)

-20

c)

0

d)

Cannot be determined

31.

Evaluate the expression: |-3| + |-7|

a)

10

b)

-10

c)

4

d)

-4

32.

A whale is at the surface of the ocean, then swims down 300 feet to feed. What is the whale's elevation?

a)

-300

b)

300

c)

0

d)

-0

33.

Write an integer that represents an elevation of 25 feet below sea level.

a)

25

b)

- 25

c)

0

d)

- 2.5

34.

Morgan drove from Los Angeles (elevation 330 feet) to Death Valley (elevation -282 feet). What is the difference in elevation between Los Angeles and Death Valley?

a)

48 feet

b)

582 feet

c)

148 feet

d)

612 feet

35.

If the temperature was 3 degrees below zero in the morning and it dropped 7 more degrees, what was the temperature then?

a)

4 degrees below zero

b)

10 degrees below zero

c)

-4 degrees

d)

-10 degrees

36.

A hiker starts at an elevation of 200 feet below sea level and hikes up to an elevation of 150 feet above sea level. What is the total change in elevation?

a)

350 feet

b)

50 feet

c)

-350 feet

d)

-50 feet

37.

Choose the integer for: Being in debt $14

a)

14

b)

-14

38.

What is the absolute value of -25?

a)

25

b)

-25

c)

0

d)

Cannot be determined

39.

Compare the absolute values: |-12| ____ |9|

a)

<

b)

>

c)

=

40.

Evaluate the expression: |-6| + |-8|

a)

14

b)

-14

c)

2

d)

-2

41.

what is the absolute value of -|14|?

a)

14

b)

21

c)

33

d)

-14

42.

what is the absolute value of -|24|?

a)

-24

b)

24

c)

98

d)

11

43.

What is the absolute value of |55|?

a)

-55

b)

45

c)

55

d)

--55

44.

What is the absolute value of | 8 |?

a)

8

b)

-8

c)

0

d)

16

45.

Order the numbers from least to greatest.
-2, I8I, 5, I-10I, 6

a)

-2, I8I, 5, I-10I, 6

b)

-2, 5, 6, I8I, I-10I

c)

-2, 5, 6, 8, 10

d)

I-10I, -2, 5, 6. I8I

46.

Is absolute value always positive?

a)

yes

b)

no

47.

What is the opposite of zero?

a)

1

b)

-1

c)

0

48.

What is the opposite of -3?

a)

3

b)

0

c)

-1/3

d)

1/3

49.

-3 and 3 are opposites .
True or False?

a)

True

b)

False

50.

l - 4 l + l -1 l

a)

5

b)

3

c)

4

d)

-5

51.

Evaluate the expression.
|–5| + 8

a)

3

b)

13

c)

-13

d)

-3

52.

∣-61∣ ____ ∣5∣

a)

<

b)

>

c)

=

53.

∣-5∣ _____ ∣5∣

a)

<

b)

>

c)

=

54.

-12 _____ 12

a)

<

b)

>

c)

=

55.

-13 < -22

a)

True

b)

False

56.

Evaluate.
| 15 - 5 | =

a)

20

b)

10

c)

-20

d)

-10

57.

Evaluate.
| -13| + | 24| =

a)

12

b)

-37

c)

37

d)

10

58.

Evaluate.
| -56| - 10 =

a)

66

b)

36

c)

26

d)

46

59.

| -25| / 5

a)

5

b)

-5

c)

20

d)

-20

60.

45/ |9|

a)

-5

b)

30

c)

5

d)

20

61.

Which list orders the integers from least to greatest?

a)

-5, 3, -2, l -4l

b)

-2, 3, l-4l, -5

c)

-5, -2, 3, l-4l

d)

-2, -5, 3, l-4l

62.

Which represents the absolute value of 10?

a)

10

b)

-10

c)

-1/10

d)

11

63.

95 feet above sea level would be expressed by the integer:

a)

-95

b)

-100

c)

95

d)

0

64.

Which statement best describes l -4 l?

a)

the distance from -4 to 4 on a number line

b)

the distance from 4 to 0 on a number line

c)

the distance from -4 to 0 on a number line

d)

the distance from 0 to 4 on a number line

65.

What is another way to write -( -6)?

a)

66

b)

6

c)

-6

d)

-66

66.

Which number represents the opposite of 67?

a)

-67

b)

76

c)

67

d)

0

67.

Which situation can be represented by the integer 13?

a)

a withdrawal of $13 from a bank account

b)

a deposit of $13 into a bank account

c)

a drop of 13 feet

d)

a plane descending 13 kilometers

68.

Which situation would you represent with a negative integer?

a)

a mountain climber descending a mountain

b)

a price increase

c)

a person winning a sum of money

d)

an elevator going from the 3rd floor to the 5th floor

69.

The change, in yards, of a football team's position on the field for each of their last four plays is shown below. Which shows their yardage from least to greatest?

a)

0<-4<-7<7

b)

0<-7<-4< 7

c)

-4<-7<0<7

d)

-7<-4<0<7

70.

l-4l

a)

-4

b)

0

c)

4

d)

-0

71.

Drag each value to each blank on the number line.

Put the value that is in in the MIDDLE of the box you are filling in.

a)50%

b)1

c)

2\frac{3}{4}

d)

\frac{3}{2}

e)225%

f)0

g)25%

h)75%

i)3

j)1.25

1

2

3

4

5

1)

2)

3)

4)

5)

72.

Drag each value to each blank on the number line.

Put the value that is in in the MIDDLE of the box you are filling in.

a)

\frac{1}{2}

b)1

c)

2.75

d)

150\%

e)

2\frac{1}{4}

f)0

g)25%

h)75%

i)3

j)1.25

1

2

3

4

5

1)

2)

3)

4)

5)

73.

$8\frac{4}{5}>2$

The statement above is true.

Based on this statement, is the following statement also true? Why or why not?

$-8\frac{4}{5}>-2$

a)

The second statement is not true because both values are negative. The larger value would be -2.

b)

The second statement is not true because $-8\frac{4}{5}$ is located to the right of -2, so it should be greater.

c)

The second statement is true because if the positive version is true above, the same is true if they are both negative.

d)

The second statement is true because on a numberline, $-8\frac{4}{5}$ is to the left of -2, so it should be greater.

74.

The value represented by point M is the opposite of the value represented by the point (a) because they are the same distance from (b) on the number line.

(select a letter for the first blank and a number for the second blank.)

Choose from the below words

K

0

R

T

W

B

H

-1

1

75.

Order the following values from least to greatest.

a)

-4.099

b)

-3

c)

-0.02

d)

1.2223

e)

1.68

1)

2)

3)

4)

5)

76.

Order the following values from least to greatest.

a)

-29%

b)

-0.28

c)

2%

d)

4

e)

$\frac{17}{4}$

1)

2)

3)

4)

5)

77.

Mr. Siedell and his brother John went scuba diving. After 10 seconds, Mr. Siedell is at a depth of $29\frac{5}{6}\ feet$ and John is at a depth of $18\frac{1}{3}\ feet$ .

Select all the statements that are true.

a)

Mr. Siedell is closer to sea level than his brother.

b)

John is closer to sea level than Mr. Siedell.

c)

Mr. Siedell has to swim further to get to the surface than John.

d)

Mr. Siedell's depth can be described as $29\frac{5}{6}feet$ below sea level.

e)

John's depth can be described as $-18\frac{1}{3}$ below sea level.

78.

Before school, Terry wants to get donuts with her friends and then go to school. The donut shop is 3 blocks east of her house. School is 3 blocks west of her house. Which location represents "zero" in this scenario?

a)

Donut shop

b)

Terry's house

c)

School

d)

Her friend's house

79.

Order the following values from least to greatest.

a)

-12.8

b)

-900%

c)

$-\frac{5}{4}$

d)

0

e)

120%

1)

2)

3)

4)

5)

80.

$5\frac{3}{4}>1$

The statement above is true.

Based on this statement, is the following statement also true? Why or why not?

$-5\frac{3}{4}>-1$

a)

The second statement is not true because both values are negative. The larger value would be -1.

b)

The second statement is not true because $-5\frac{3}{4}$ is located to the right of -1, so it should be greater.

c)

The second statement is true because if the positive version is true above, the same is true if they are both negative.

d)

The second statement is true because on a numberline, $-5\frac{3}{4}$ is to the left of -1, so it should be greater.

81.

Mrs. Johnson and her sister Mary went snorkeling. After 15 seconds, Mrs. Johnson is at a depth of $35\frac{2}{3}\ feet$ and Mary is at a depth of $22\frac{1}{2}\ feet$ .

Select all the statements that are true.

a)

Mrs. Johnson is closer to sea level than her sister.

b)

Mary is closer to sea level than Mrs. Johnson.

c)

Mrs. Johnson has to swim further to get to the surface than Mary.

d)

Mrs. Johnson's depth can be described as $35\frac{2}{3}feet$ below sea level.

e)

Mary's depth can be described as $-22\frac{1}{2}$ below sea level.

82.

Order the following integers from greatest to least
3, -4, 6

a)

3, -4, 6

b)

6, 3, -4

c)

6, -4, 3

d)

3, -4, 6

83.

Order from least to greatest
0, -3, 2

a)

0, 2, -3

b)

0, -3, 2

c)

-3, 0, 2

d)

2, -3, 0

84.

Negative integers are ____ than zero

a)

greater

b)

equal

c)

less

d)

bigger

85.

Positive integers are ____ than zero

a)

greater

b)

equal

c)

less

d)

smaller

86.

Compare
-10 ____ -2

a)

=

b)

<

c)

>

d)

=

87.

Compare
-6 _____ 6

a)

<

b)

=

c)

=

d)

>

88.

Compare
-7 ____ -8

a)

=

b)

<

c)

>

d)

=

89.

Monday's temperature was -3°F and Tuesday's was -5°F. Which day was colder?

a)

neither they were equal

b)

Monday

c)

Tuesday

d)

Friday

90.

List the numbers in order from least to greatest
-6, 0, 8, -9

a)

-9, -6, 0, 8

b)

0, -6, 8, -9

c)

-9, 8, -6, 0

d)

1, 2, 3, 4

91.

List in order from greatest to least
12, -9, -6, 10

a)

12, 9, 6, 10

b)

-6, -9, 10, 12

c)

5, 4, 3, 21

d)

12, 10, -6, -9

92.

Fill in the blank with the correct sign >, < , or =
-3.4 ________ -2.5

a)

>

b)

<

c)

=

93.

Fill in the blank with the correct sign >, < , or =

3/4 ________ 4/5

a)

>

b)

<

c)

=

94.

Paige rode her bike 4/5 mile. Megan rode her bike 1/3 mile. Which girl rode the greatest distance?

a)

Paige; 4/5 > 1/3

b)

Megan; 4/5 < 1/3

95.

What is the decimal equivalent of 3/5?

a)

0.3

b)

3.5

c)

0.6

d)

0.2

96.

Put the following in order LEAST to GREATEST:

0.54, 2/5, 0.45

a)

2/5, 0.45, 0.54

b)

0.54, 2/5, 0.45

c)

0.54, 0.45, 2/5

d)

0.45, 2/5, 0.54

97.

Fill in the blank with the correct sign >, < , or =
-1.8_____ 0.8

a)

>

b)

<

c)

=

98.

Order from least to greatest:
[-8, 7, -6, 5, -4, 3, -2]

a)

^{-2, 3, -4, 5, -6, 7, -8}

b)

^{-2, -4, -6, -8, 3, 5, 7}

c)

^{-6, -8, -4, -2, 7, 5, 3}

d)

^{-8, -6, -4, -2, 3, 5, 7}

99.

Put the rational numbers in order from least to greatest.
-4.2, -4 1/2, -4, 0, 4

a)

^{0, -4 1/2, -4.2, 4, -4}

b)

^{-4 1/2, -4.2, -4, 0, 4}

c)

^{-4 1/2, -4.2, -4, 4, 0}

100.

Put the rational numbers in order from least to greatest.
-1, -1.1, -1.5, -1.15, -0.5

a)

^{-1.5, -1.15, -1.1, -1, -0.5}

b)

^{-1.1, -1, -1.5, -1.15, -0.5}

c)

^{-0.5, -1.1, -1, -1.5, -1.15}

101.

Which is ordered in ascending order?

a)

^{1/2, 3/4, 1/4, 2/3}

b)

^{1/2, 2/3, 1/4, 3/4}

c)

^{1/4, 1/2, 2/3, 3/4}

102.

What decimal represents point L on the number line?

a)

0.5

b)

0.3

c)

5

d)

.05

103.

What decimal represents point J on the number line?

a)

0.4

b)

0.3

c)

3

d)

.03

104.

What decimal does the green dot represent on the number line?

a)

7.88

b)

7.8

c)

7.80

d)

7.89

105.

What fraction and decimal represents where point "a" is on the number line?

a)

2/10 or 0.2

b)

2/100 or 0.02

c)

3/10 or 0.3

d)

3/100 or 0.03

106.

What fraction and decimal represents where point "e" is on the number line?

a)

10/10 or 1.0

b)

10/10 or .10

c)

10/100 or .010

d)

10/100 or .10

107.

Find the value of a.

a)

0.55

b)

0.61

c)

0.56

d)

0.59

108.

Which of the marks would represent 7.3 correctly?

a)

Blue

b)

Green

c)

Red

d)

Orange

109.

a)

4/5

b)

3/4

c)

3/1

d)

1/3

110.

Which number line shows 1/2

a)

A

b)

B

c)

C

d)

D

111.

Label Point C

a)

5/6

b)

-2/6

c)

-2/3

d)

-1/2

112.

Which decimal is located at point B

a)

4.0

b)

0.5

c)

1.4

d)

0.4

113.

a)

-5.2

b)

-0.1

c)

-1.8

d)

1.6

114.

What is the value of point A

a)

2/7

b)

-4/7

c)

-5/8

d)

7/7

115.

a)

3.5

b)

-3.5

c)

-4.5

d)

-2.5

116.

What numbers represent points A, B and C on the number line? Check all that apply

a)

-4/5

b)

0.2

c)

-0.2

d)

-0.4

e)

2/5

117.

Which point on the number line best represents -1.2?

a)

A

b)

B

c)

C

d)

D

e)

E

118.

Complete the statement using < , >, or =

$-5.65$ (a) $-5.6$

Choose from the below words

<

>

=

119.

Complete the statement using < , >, or =

$\frac{14}{8}$ (a) $1\ \frac{3}{4}$

Choose from the below words

=

<

>

120.

Compare the following numbers:

3.25 (a) 3 1/10

Choose from the below words

>

<

=

121.

A set of numbers is shown below.

$-\left|-6\right|,\ 6,\ -2,\ -\left(-4\right)$

Which choice shows the numbers in order from least to greatest? (a) (b) (c) (d)

Choose from the below words

$-\left|-6\right|$

-2

-(-4)

6

122.

List the following in ascending order.

(a) (b) (c)

Choose from the below words

0.63%

0.6

$\frac{2}{3}$

123.

Which list of integers is in order from greatest to least?

a)

24, 9, -33, -24, -11

b)

24, 9, -11, -24, -33

c)

-33, 24, -18, -11, 9

124.

Convert the fraction 3/4 to a decimal.

a)

0.25

b)

1.25

c)

0.75

d)

0.5

125.

Convert the fraction 5/8 to a decimal.

a)

0.85

b)

0.75

c)

0.45

d)

0.625

126.

Convert the fraction 2/5 to a decimal.

a)

0.2

b)

0.5

c)

0.6

d)

0.4

127.

Convert the fraction 7/10 to a decimal.

a)

0.9

b)

0.75

c)

0.7

d)

0.5

128.

Convert the fraction 1/3 to a decimal.

a)

0.333

b)

0.33

c)

0.3

d)

$0.\overline{3}$

129.

Convert the fraction 9/12 to a decimal.

a)

0.25

b)

0.75

c)

0.5

d)

0.9

130.

Convert the fraction 6/9 to a decimal.

a)

0.6

b)

$0.\overline{6}$

c)

0.67

d)

0.666

131.

Convert the fraction 11/15 to a decimal.

a)

$0.7\overline{3}$

b)

0.7332

c)

0.7334

d)

0.733

132.

Convert the mixed number 3 6/25 into a decimal

a)

0.868

b)

3.067

c)

3.24

d)

-2.75

e)

1.254

133.

Josh wrote 483 out of an expected

500 words for his essay.

How would this ratio be expressed in decimal form?

a)

-1.354

b)

1.178

c)

3.012

d)

0.966

e)

-0.127

134.

What is today's price change if the quote change is -3 $\frac{7}{16}$ .

a)

2.4671

b)

-3.867

c)

-3.4375

d)

3.4375

e)

1.456

135.

Determine the decimal equivalent of 11/8.

a)

0.935

b)

2.34

c)

0.563

d)

1.375

e)

-1.92

136.

Determine the decimal equivalent of $\frac{1}{11}$ .

a)

.091

b)

1.076

c)

2.87

d)

$\overline{.09}$

e)

.192

137.

Determine the decimal equivalent of $\frac{7}{6}$ .

a)

1.24

b)

1.67

c)

0.924

d)

$1.1\overline{66}$

e)

.156

138.

Determine the decimal equivalent of $\frac{13}{5}$ .

a)

1.431

b)

0.0263

c)

2.6

d)

1.723

e)

0.0512

139.

Determine the decimal equivalent of $\frac{11}{19}$ .

a)

0.578947368........

b)

.0438

c)

.6231

d)

.51119

e)

.453845

Study Guide - 1.2 Understanding Rational Numbers

Total questions: 139

Worksheet time: 6hrs 52mins

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