Free Rational Numbers 02 Practice Test - 8th Grade 

Question 1

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

Question 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

Question 3

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 .

Question 4

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.

Question 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

Question 6

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

Question 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

Question 8

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

Question 9

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.

 

Question 10

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.