# Free Rational Numbers 02 Practice Test - 8th Grade

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

A.

commutative

B. associative
C. closure
D. distributive

#### 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

Choose the rational numbers whose numerator is (5)×6, and the denominator is (3423)×(75).

A.

2011

B.

4022

C.

1511

D.

3022

#### SOLUTION

Solution : C and D

Rational numbers are the numbers which can be expressed in the form of pq, given q0, p and q are integers.

pq=5×6(3423)×(75)

=3011×2

=3022

=1511

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

A.

100099999

B.

100099900

C.

999999999

D.

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 .

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

A.

122 & 202

B.

105 & 324

C.

273 & 183

D.

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.

Arrange the following rational numbers in the ascending order
54,23,68,85,92.

A.

23<68<54<85<92

B.

54<68<23<85<92

C.

92<85<54<68 < 23

D.

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

Product of 76 and reciprocal of 1166 is __________.

A.

16

B.

76

C.

7

D.

711

#### SOLUTION

Solution : C

Reciprocal of 1166=6611

76×6611=7×1111=7

1551 is a multiplicative inverse of 175.

A.

True

B.

False

#### SOLUTION

Solution : A

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

Now, 1551×175=33=1

Which of the following rational numbers are equivalent to 94?

A.

123

B.

8125

C.

6328

D.

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

Which of the following statements is incorrect?

A.

Every whole number is a rational number

B.

Every integer is a rational number

C.

Zero is a whole number and it  is rational number too

D.

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.

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

A.

92

B.

2656

C.

-2

D.

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.