# Free Rational Numbers 02 Practice Test - 8th Grade

### Question 1

The ___ property states that we can add rational numbers in any order.

commutative

#### SOLUTION

Solution :A

The addition of rational numbers can be done in any order and the result remains the same. This is called commutative property.

E.g: 2 + 3 = 3 + 2

### Question 2

Choose the rational numbers whose numerator is (−5)×6, and the denominator is (34−23)×(7−5).

2011

4022

−1511

−3022

#### SOLUTION

Solution :C and D

Rational numbers are the numbers which can be expressed in the form of pq, given q≠0, p and q are integers.

pq=−5×6(34−23)×(7−5)

=−3011×2

=−3022

=−1511

### Question 3

Write down the rational number whose numerator is the smallest four digit number and denominator is the largest five digit number.

100099999

100099900

999999999

100010000

#### SOLUTION

Solution :A

The smallest four digit number is 1000 and largest five digit number is 99999.

Therefore, the required rational number is smallest four digit numberlargest five digit number=100099999 .

### Question 4

Which of the following pair of rational numbers are smaller than -5?

−122 & −202

−105 & −324

−273 & −183

−1005 & −2005

#### SOLUTION

Solution :A, C, and D

a) −122=−6 & −202=−10

-6 and -10 are smaller than -5.

b) −105=−2 & −324=−8

-2 is greater than -5.

c) −273=−9 & −183=−6

-9 and -6 are smaller than -5.

d) −1005=−20 &−2005=−40

-20 and -40 are smaller than -5.

### Question 5

Arrange the following rational numbers in the ascending order

54,23,68,85,92.

23<68<54<85<92

54<68<23<85<92

92<85<54<68 < 23

92<23<54<85<68

#### SOLUTION

Solution :A

To compare the rational numbers, we first make the denominators equal.

L.C.M of the denominators 4, 3, 8, 5, 2 is 120.Equivalent fractions with the denominator 120 are

54×3030=150120

23×4040=80120

68×1515=90120

85×2424=192120

92×6060=540120

Since the denominator is same in the above equivalent fractions, we can decide the ascending order based on the numerator values.Ascending order :

23<68<54<85<92

### Question 6

Product of 76 and reciprocal of 1166 is __________.

16

76

7

711

#### SOLUTION

Solution :C

Reciprocal of 1166=6611

⇒76×6611=7×1111=7

### Question 7

−1551 is a multiplicative inverse of −175.

True

False

#### SOLUTION

Solution :A

Multiplicative inverse of ab is cd if ab×cd=1.

Now, −1551×−175=33=1

### Question 8

Which of the following rational numbers are equivalent to 94?

123

8125

6328

3616

#### SOLUTION

Solution :C and D

When we multiply and divide a rational number by the same number, the value of rational number remains unchanged. Therefore,

94×77=632894×44=3616

### Question 9

Which of the following statements is incorrect?

Every whole number is a rational number

Every integer is a rational number

Zero is a whole number and it is rational number too

Every rational number is not an integer

#### SOLUTION

Solution :C

Zero is a whole number as well as the rational number. Zero can be expressed in the form of pq as 01. Hence zero is a rational number since it satisfies the definition of rational number where p = 0 and q ≠ 0.

### Question 10

Which of the following rational numbers lie betwen 37 and 48 ?

92

2656

-2

1328

#### SOLUTION

Solution :B and D

L.C.M of 7 and 8 is 56.

37 and 48 can be written as 2456 and 2856.

Check for numbers which lie between 2456 and 2856.

Now, 1328 = 2656 lies between 37 and 48.