Free Printable Rational Numbers Study Guide

1.

-8 + -12

a)

-20

b)

20

c)

-4

d)

4

2.

-9+(-3)

a)

-6

b)

6

c)

-12

d)

12

3.

5-(-3)

a)

8

b)

2

c)

-2

d)

-8

4.

-15 - (-6)

a)

-9

b)

9

c)

21

d)

-21

5.

35 - (-35)

a)

0

b)

-70

c)

70

d)

1

6.

-17 + 2

a)

15

b)

19

c)

-19

d)

-15

7.

-5 + 6 + -3 =

a)

-8

b)

2

c)

-2

d)

-4

8.

What is the opposite of 10?

a)

10

b)

-10

c)

0

d)

20

9.

(-9) + 9

a)

18

b)

-18

c)

0

d)

81

10.

-2 - (-8)

a)

6

b)

-6

c)

-10

d)

10

11.

When you add integers with the same sign, what do you do?

a)

(+) and keep the sign

b)

(-) and keep the sign of the larger

c)

(x) and keep the sign

d)

(-) and keep the sign of the smaller

12.

What do you do when you are adding integers with different signs?

a)

(-) and keep sign of smaller number

b)

(-) and keep sign of larger number

c)

(+) and keep sign of smaller number number

d)

(+) and keep sign of larger number

13.

-9 + (-5)

a)

-14

b)

14

c)

-4

14.

-8 + 20

a)

-28

b)

28

c)

14

d)

12

15.

-22 + (-24)

a)

46

b)

-22

c)

22

d)

-46

16.

-3 + (-2)

a)

-5

b)

-1

c)

1

d)

5

17.

12 + (-2)

a)

-10

b)

-14

c)

14

d)

10

18.

-5 - (-17) ... Which addition sentence represents the same problem?

a)

-5 + 17

b)

-5 + (-17)

c)

5 + (-17)

d)

5 + 17

19.

15 - (-15)

(a)

20.

-12 - 3 =

a)

-15

b)

15

c)

9

d)

-9

21.

The temperature on a cold winter day starts out at 10 degrees, but it drops rapidly 24 degrees due to a strong cold front moving in. What is the current temperature?

a)

14

b)

34

c)

-14

d)

-34

22.

-2 + 9

a)

-11

b)

-7

c)

7

d)

11

23.

-3 + 12

a)

-15

b)

-9

c)

9

d)

15

24.

-9 + (-5)

a)

-14

b)

14

c)

-4

25.

-22 + (-9)

a)

-11

b)

-31

c)

11

d)

31

26.

$-6\cdot-11$

(a)

27.

$-3\cdot-12$

(a)

28.

$-3\cdot7$

(a)

29.

$-10\cdot-2$

(a)

30.

$3\cdot-14$

(a)

31.

$-13\cdot8$

(a)

32.

$10\cdot-2$

(a)

33.

$13\cdot-10$

(a)

34.

$-6\cdot-11$

(a)

35.

$-3\cdot-12$

(a)

36.

$-3\cdot7$

(a)

37.

$-10\cdot-2$

(a)

38.

$3\cdot-14$

(a)

39.

$-13\cdot8$

(a)

40.

$-10\cdot-4$

(a)

41.

$10\cdot-2$

(a)

42.

$13\cdot-10$

(a)

43.

$-7\cdot9$

(a)

44.

$\frac{40}{10}$

(a)

45.

$\frac{210}{-15}$

(a)

46.

$-\frac{78}{13}$

(a)

47.

$\frac{50}{-10}$

(a)

48.

$\frac{169}{13}$

(a)

49.

$\frac{-52}{-13}$

(a)

50.

$\frac{-24}{-3}$

(a)

51.

$\frac{98}{-7}$

(a)

52.

$\frac{84}{7}$

(a)

53.

$\frac{-30}{3}$

(a)

54.

-17(10)=

a)

1710

b)

-170

c)

170

d)

-1710

55.

-3(-4)

a)

-12

b)

7

c)

-7

d)

12

56.

-8(0)=

a)

-8

b)

-0

c)

0

d)

-80

57.

Is the product
–8 • (–3) positive or negative?

a)

negative

b)

positive

c)

both

d)

neither

58.

Every Friday for 8 weeks Kylan withdrew $35 from his savings account. How much did he withdraw in all?

a)

-280

b)

280

c)

27

d)

-27

59.

Multiply
(5) • (–9) • (–2)

a)

90

b)

-45

c)

-90

d)

47

60.

a)

5

b)

6

c)

-5

d)

-6

61.

(-8) x (-4) =

a)

-28

b)

28

c)

32

d)

-32

62.

-8 ÷ (-8)

a)

-1

b)

1

c)

0

d)

-16

63.

45 ÷ (-9) =

a)

8

b)

-8

c)

5

d)

-5

64.

-7(10)=

a)

70

b)

700

c)

-70

d)

-700

65.

Evaluate:
−30÷2

a)

−15

b)

15

c)

10

d)

−10

66.

-20 x 0

a)

20

b)

-20

c)

0

d)

-0

67.

Is the product of -5(2) positive or negative?

a)

positive

b)

negative

c)

Either one

d)

zero

68.

56 ÷ (-7)

a)

-8

b)

-9

c)

8

d)

7

69.

8(-5) =

a)

-40

b)

-13

c)

40

d)

-3

70.

When multiplying or dividing a NEGATIVE and NEGATIVE number your result will be...

a)

POSITIVE

b)

NEGATIVE

c)

DEPENDS ON WHICH NUMBER IS LARGER.

d)

It really doesn't matter.

71.

What is the rule for dividing integers?

a)

Follow the same rules as multiplying integers

b)

Follow the same rules as adding integers

c)

Follow the same rules as subtracting integers

d)

Always do the opposite

72.

$100\ \div\ \left(-2\right)$

a)

50

b)

200

c)

-200

d)

-50

73.

$-33\ \div\ 3$

a)

11

b)

10

c)

-11

d)

-10

74.

At 7:00 a.m., the temperature outside was 10°F below zero. By noon, it rose by 17°F. At 6:00 p.m., the temperature dropped by 6°F. What was the evening temperature?

a)

–33°F

b)

1°F

c)

13°F

d)

33°F

75.

Sharon wants to make cookies for her class bake sale. She found a recipe that calls for 2/3 cups of flour for each batch of cookies. How many batches can she make using 12 cups of flour?

a)

12

b)

18

c)

6

d)

4

76.

Mario paid a total of $12.24 for 4 packs of soda. How much did he pay for each pack?

a)

$36.72

b)

$3.06

c)

$12.28

d)

$3.60

77.

When ADDING one NEGATIVE and one POSITIVE INTEGER, the answer will be...

a)

Negative

b)

Positive

c)

it depends on which number is the "biggest"

d)

you cannot tell without the actual numbers

78.

The temperature was 5.5° C on Monday and was 7.3 degrees lower the next day. What was the temperature on Tuesday?

a)

-2.3* C

b)

12.5* C

c)

-1.8* C

d)

1.8* C

79.

The temperature on Sunday was -15^o C. The temperature on Monday was 12 degrees less than the temperature on Sunday. What was the temperature on Monday?

a)

-27^o C

b)

27^o C

c)

-3^o C

d)

3^o C

80.

Which diagram best represents the relationship among integers, rational numbers, and whole numbers? 7th grade STAAR

a)

b)

c)

d)

81.

Which number would be located in the shaded area of the diagram? STAAR

a)

-1.7

b)

-8

c)

0.66

d)

10

82.

A baby weighed 7.25 lb at birth. At the end of 8 months

the baby weighed 2.5 times its birth weight. How many pounds did the baby weigh at the end of 8 months?

a)

14.5 lb

b)

9.75 lb

c)

18.125 lb

d)

14.125 lbs

83.

A train is traveling at a speed of 75 mph. The train slows down 20 mph to 55 mph. What is the additive inverse of the train’s current speed?

a)

75

b)

-75

c)

55

d)

-55

84.

A roller coaster starts from a deck at an elevation of 25 feet above the ground. On the first hill it climbs 76 feet and then drops 82 feet. On the second hill, the coaster climbs 110 feet and then drops 108 feet. How far below or above the deck is the coaster after the second hill?

a)

25 feet above

b)

25 feet below

c)

4 feet above

d)

4 feet below

85.

Mr. Johnson’s class has 50 students. 12 of the students stay for tutoring on Wednesday. If Mr. Johnson equally divides the students that stay for tutoring into 4 groups, how many students are in each group?

a)

3

b)

5

c)

12

d)

50

86.

Eryn is practicing her free throws. She made ⅘ of the shots she took at basketball practice today. Write ⅘ as a decimal number.

a)

4.5

b)

0.45

c)

0.8

d)

1.25

87.

A family’s vacation destination is 745 miles from their home. They travel by car 5 hours on the first day of the trip. Their average speed is 50 mph. The next day they travel 6 hours averaging the same speed. How many miles are left for the family to travel?

a)

195 miles

b)

184 miles

c)

489 miles

d)

634 miles

88.

Gretchen spends 1/2 an hour grooming Hobo and 1/3 of an hour riding Hobo. How much time did she spend with Hobo?

a)

⅖ hours

b)

⅚ hours

c)

⅔ hours

d)

⅜ hours

89.

Candice and Chris run a relay race at recess. Candice runs 1 ⅓ of a lap around the track. Chris runs ½ of a lap around the track. How much farther does Candice run than Chris?

a)

⅚ laps

b)

⅔ laps

c)

¾ laps

d)

⅙ laps

90.

Tina lives 2 ¼ miles from the library. Sonya lives 3 ½ miles from the library. How much further does Sonya live than Tina?

a)

1 ½ miles

b)

1 ¼ miles

c)

¾ miles

d)

⅔ miles

91.

A Gatorade cooler has 36 cups of water. If a serving is ¾ of a cup how many servings are in the cooler?

a)

48 servings

b)

27 servings

c)

36 ¾ servings

d)

60 servings

92.

If a sheep eats ⅙ of a bale of hay a day how many sheep can be fed off of 2 bales of hay?

a)

3 sheep

b)

6 sheep

c)

9 sheep

d)

12 sheep

93.

The price of a share of stock started the day at $37. During the day it went down $3, up $1, down $7, and up $4.What was the price of a share at the end of the day?

a)

$32

b)

- $32

c)

- $5

d)

$30

94.

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the coaster after the first descent

a)

- 15 feet

b)

15 feet

c)

195 feet

d)

- 195 feet

95.

A football team lost 9 yards on each of three consecutive plays. What was the team’s total change in position for the three plays?

a)

-9 yards

b)

3 yards

c)

-12 yards

d)

-27 yards

96.

64+(-71)

a)

7

b)

-7

c)

135

d)

-135

97.

(- 18) + ( - 9) =

a)

-18

b)

2

c)

- 27

d)

80

98.

(- 12) - (- 4) =

a)

-16

b)

-8

c)

- 3

d)

8

99.

-6 x (-12)

a)

-72

b)

72

c)

2

d)

-2

100.

(-12)(-15)

a)

-180

b)

180

c)

3

d)

-27

101.

(-25) ÷ (-5)

a)

5

b)

-5

c)

-20

d)

-30

102.

-8(0)=

a)

-8

b)

8

c)

0

d)

-80

103.

-3(-4)

a)

-12

b)

7

c)

-7

d)

12

104.

Multiply: (-4) (7)

a)

-28

b)

28

c)

11

d)

-11

105.

-10(4)

a)

40

b)

-14

c)

-40

d)

14

106.

A football team gained 9 yards on one play and then lost 22 yards on the next. Write a sum of integers to find the overall change in field position.

a)

-9 + (-22) = -13

b)

9 + (-22) = 13

c)

9 + (-22) = -13

d)

none

107.

Solve: -1(-3)(-2)(-2) =

a)

12

b)

-12

c)

8

d)

-8

108.

The temperature was 98 degrees last Tuesday. Friday it was 24 degrees cooler. Which expression represents the relationship in the temperature between Tuesday and Friday?

a)

(-98) + (-24)

b)

-98 + - 24

c)

98 + 24

d)

98 + (-24)

109.

Subtract the smallest number you can make from the digits 4, 3, 5 and 2 from the largest number you can make with the same digits.

a)

2086

b)

2187

c)

3087

d)

4087

110.

A shop selling cutlery had 1500 items in stock at the beginning of the month. During the month it sold 732 spoons, 328 forks and 83 knives. How many items of cutlery were left at the end of the month?

a)

2643

b)

357

c)

1143

d)

768

111.

On a number line, what is the distance between -16 and 76?

a)

-60 units

b)

-92 units

c)

60 units

d)

92 units

112.

Write the equivalent addition problem to 5 - (-8)

a)

5 + 8

b)

5 + (-8)

113.

Which of the following has a negative product?

a)

-7 ⋅ (-9)

b)

6(-2)(-11)

c)

8 × 5

d)

-4(12)

114.

In New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now?

a)

-7°F

b)

-21°F

c)

7°F

d)

21°F

115.

(- 8) x ( - 10) =

a)

-18

b)

-2

c)

- 80

d)

80

116.

$-2\frac{1}{10}+\left(1.08\right)$ Find the sum:

a)

$4.151$

b)

$-1.02$

c)

$-1.18$

d)

$0.02$

117.

$-4.68+\left(-1.24\right)$

(a)

118.

(-2.8) ÷ (-⅖)=

a)

7

b)

0.7

c)

0.07

d)

70

119.

$8\ \frac{3}{4}\ +\ 3.5\ =$

(a)

120.

$\left(1\ \frac{1}{5}\ \right)\ +\ 8.5\ =$

(a)

121.

$7\ -\ 3\ \frac{1}{5\ }=$

(a)

122.

$\left(5.25\right)\ \left(-5\right)=$

(a)

123.

$-\ \frac{3}{5}\ \times\ 0.8\ =$

(a)

124.

$14.58\ \div\ \frac{3}{5}\ =$

(a)

125.

$26.95\ \div\ \left(-5\ \frac{1}{2}\right)=$

a)

$-0.49$

b)

$-4.9$

c)

$-3.3$

d)

$-5.3$

126.

Convert this fraction into mixed number

$\frac{14}{5}$

a)

$2\frac{2}{5}$

b)

$1\frac{9}{5}$

c)

$2\frac{4}{5}$

127.

Convert this fraction into mixed number
$\frac{7}{2}$

a)

$3\frac{1}{2}$

b)

$2\frac{3}{2}$

c)

$3\frac{2}{2}$

128.

Convert this fraction into mixed number
$\frac{21}{4}$

a)

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

b)

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

c)

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

129.

Convert this fraction into mixed number

$\frac{22}{9}$

a)

$2\ \frac{3}{9}$

b)

$2\ \frac{4}{9}$

c)

$2\ \frac{2}{9}$

130.

Convert this fraction into mixed number

$\frac{25}{6}$

a)

$4\ \frac{3}{6}$

b)

$4\ \frac{2}{6}$

c)

$4\ \frac{1}{6}$

131.

Convert this fraction into mixed number
$\frac{31}{7}$

a)

$4\ \frac{3}{7}$

b)

$5\ \frac{1}{7}$

c)

$4\ \frac{2}{7}$

132.

Convert this fraction into mixed number

$\frac{76}{9}$

a)

$8\ \frac{5}{9}$

b)

$8\ \frac{2}{9}$

c)

$8\ \frac{4}{9}$

133.

Convert this fraction into mixed number
$\frac{69}{11}$

a)

$6\ \frac{4}{11}$

b)

$6\ \frac{2}{11}$

c)

$6\ \frac{3}{11}$

134.

Convert this fraction into mixed number
$\frac{47}{8}$

a)

$5\ \frac{6}{8}$

b)

$5\ \frac{7}{8}$

c)

$5\ \frac{5}{8}$

135.

Convert this fraction into mixed number
$\frac{103}{10}$

a)

$10\ \frac{3}{10}$

b)

$10\ \frac{1}{10}$

c)

$10\ \frac{7}{10}$

136.

What mixed number does this represent

a)

2 3/8

b)

2 1/4

c)

3 5/8

d)

3 3/8

137.

Which mixed number is represented by the model?

a)

3 1/4

b)

3 4/1

c)

3 3/4

d)

4 1/4

138.

Which mixed number is represented by the model?

a)

3/4

b)

2 4/3

c)

2 3/4

d)

2 1/4

139.

What mixed number is shown by the picture?

a)

13/8

b)

3 1/3

c)

13/4

d)

3 1/4

140.

Which number is represented by the model?

a)

2 3/8

b)

2 5/8

c)

2 3/5

d)

2 3/4

141.

Convert this mixed number to an improper fraction.

a)

$\frac{24}{5}$

b)

$\frac{10}{5}$

c)

$\frac{30}{5}$

d)

$\frac{34}{5}$

142.

Convert this mixed number to an improper fraction.

a)

$\frac{1}{15}$

b)

$\frac{15}{15}$

c)

$\frac{16}{15}$

d)

$\frac{2}{15}$

143.

Write\ \ 6\frac{1}{3}\ as\ an\ improper\ fraction.

a)

$\frac{3}{13}$

b)

$\frac{18}{3}$

c)

$\frac{19}{3}$

d)

$\frac{12}{3}$

144.

Convert $1\frac{\text{6}}{\text{10}}$ to an improper fraction.

a)

$\frac{\text{16}}{\text{10}}$

b)

$\frac{\text{17}}{\text{10}}$

c)

$\frac{\text{16}}{\text{6}}$

d)

$\frac{\text{17}}{\text{6}}$

145.

Convert $1\frac{\text{3}}{\text{5}}$ to an improper fraction.

a)

$\frac{8}{5\ }$

b)

$\frac{9}{5}$

c)

$\frac{6}{3}$

d)

$\frac{15}{5}$

146.

Simplify $\frac{15}{25}$

a)

$\frac{1}{2}$

b)

$\frac{3}{5}$

c)

$\frac{2}{5}$

d)

Cannot be simplified

147.

When the numerator is greater than or equal to the denominator is called____

a)

proper fraction

b)

improper fraction

c)

mixed number

d)

all of the above

148.

When converting a mixed number into an improper fraction, you ___ the whole number by the denominator and then add the numerator.

a)

add

b)

subtract

c)

multiply

d)

divide

149.

Convert this mixed number to an improper fraction.

a)

$\frac{35}{9}$

b)

$\frac{36}{9}$

c)

$\frac{24}{8}$

d)

$\frac{27}{9}$

150.

Joe is making a birdhouse. He uses 3 1/2 feet of lumber. Write this length as an improper fraction.

3\frac{1}{2}\ =\ ?

a)

$\frac{1}{2}$

b)

6

c)

$\frac{7}{2}$

d)

$\frac{6}{2}$

151.

Jody is knitting a scarf. She needs 4 6/7 feet of yarn. Write this number as an improper fraction.

$4\ \frac{6}{7}\ =\ ?$

a)

$\frac{34}{7}$

b)

34

c)

$\frac{34}{4}$

d)

$\frac{17}{7}$

152.

Convert $7\ \frac{1}{5}$ to an improper fraction.

a)

$\frac{13}{5}$

b)

$\frac{13}{1}$

c)

$\frac{36}{5}$

d)

$\frac{7}{6}$

153.

Nick goes running every weekend. Last Sunday, he ran
7 4/5 miles. Write the distance Nick ran as an improper fraction.

7\ \frac{4}{5}\ =\ ?

a)

39

b)

$\frac{39}{7}$

c)

$\frac{16}{5}$

d)

$\frac{39}{5}$

154.

$Convert\ 8\ \frac{7}{10}\ to\ an\ improper\ fraction\$

a)

87

b)

$\frac{87}{10}$

c)

$\frac{87}{7}$

d)

$\frac{25}{10}$

155.

What is the mixed number below as an improper fraction?

9\ \frac{1}{2}

a)

9

b)

$\frac{1}{2}$

c)

$\frac{19}{2}$

d)

$\frac{19}{9}$

156.

Which of the following are integers?

a)

8

b)

-3

c)

-8

d)

$\frac{4}{10}$

157.

Is 2 a natural number?

a)

True

b)

False

158.

Which of the following is a whole number?

a)

9

b)

$\frac{10}{9}$

c)

$-3\ \frac{1}{2}$

d)

$2\ \frac{2}{3}$

159.

Which of the following is a whole number?

a)

-2

b)

-10

c)

10

d)

-1

160.

Which of the following are whole numbers?

a)

0

b)

$\frac{7}{8}$

c)

$\frac{1}{3}$

d)

3

161.

Which of the following are rational numbers?

a)

64

b)

15

c)

$\frac{7}{4}$

d)

7.452

162.

Which of the following are whole numbers?

a)

0

b)

78

c)

35

d)

-88

163.

Is $74.\overline{8}$ a natural number?

a)

Yes

b)

No

164.

Which of the following is a rational number?

a)

$\sqrt[]{75}$

b)

$95.\overline{3}$

c)

$\sqrt[]{44}$

d)

$\pi$

165.

Is ^–23 a rational number?

a)

Yes

b)

No

166.

Which of the following describe ^–77?

Select all that apply.

a)

irrational number

b)

rational number

c)

natural number

d)

whole number

e)

integer

167.

Which of the following describe 91?

Select all that apply.

a)

irrational number

b)

rational number

c)

natural number

d)

whole number

e)

integer

168.

Which of the following describe $\sqrt[]{23}$ ?

Select all that apply.

a)

irrational number

b)

rational number

c)

natural number

d)

whole number

e)

integer

169.

Which of the following describe $\frac{0}{3}$ ?

Select all that apply.

a)

irrational number

b)

rational number

c)

natural number

d)

whole number

e)

integer

170.

Classify this number: 6.7

a)

real

b)

real rational

c)

real rational integer

d)

real rational integer whole

171.

Classify this number: -12

a)

real

b)

real rational

c)

real irrational

d)

real rational integer

172.

-4 is not a whole number because:

a)

It's negative and whole numbers are positive.

b)

it's irrational.

c)

it cannot be turned into a fraction.

d)

it is even.

173.

Which word does NOT describe 5?

a)

Whole

b)

Integer

c)

Rational

d)

Irrational

Rational Numbers Study Guide

Total questions: 173

Worksheet time: 3hrs 8mins

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