# Free Rational Numbers 01 Practice Test - 8th Grade

A number which can be represented in the form of pq, q0 where p and q are integers is called a ___ number.

#### SOLUTION

Solution :

A number which can be represented in the form of pq, q0 where p and q are integers is called a rational number.

For example, 23,5, 4 etc are all rational numbers as they can be expressed in pq form with p and q as integers and q0.

The product of two whole numbers is always a whole number.

A.

True

B.

False

#### SOLUTION

Solution : A

If 'a' and 'b' are any two whole numbers, their product will also be a whole number. We know that the multiplication of any two numbers can be expressed as repeated addition of one number. So, if we are adding any whole number to itself again and again, then we will surely get a whole number.
Let's assume a=2,b=3.
a×b=2×3 which is same as adding '2' three times to itself, which will result in a whole number.

Which of the following lies between 254 and 223?

A. 132
B. 152
C. 172
D. 8

#### SOLUTION

Solution : A

Rational numbers can be compared by making their denominators equal.

Here, we need to compare all given rational numbers 254,223,132,152,172 and 81.

We know LCM of 1, 2, 3 and 4, i.e., the denominators of the above fractions, is 12.

Converting all the above fractions into like fractions, we get

254=25×34×3=7512

223=22×43×4=8812

132=13×62×6=7812

152=15×62×6=9012

172=17×62×6=10212

8=81=8×121×12=9612

Arranging these fractions in an ascending order, we have
7512,7812,8812,9012,9612,10212

Thus, 132 lies between 254 and 223.

Which operations on whole numbers are commutative?

A.

B.

Multiplication

C.

Division

D.

Subtraction

#### SOLUTION

Solution : A and B

An operation is commutative if changing the order of operands does not change the result.

Addition and multiplication are commutative for whole numbers.

For example, 2+3=5,  3+2=5.

Also, 3×4=12,  4×3=12

The reciprocal of -10 is

A.

0.1

B.

- 0.1

C.

0.01

D.

- 0.01

#### SOLUTION

Solution : B

The reciprocal of any non-zero number 'a' is 1a.

​​​​​​The reciprocal of '-10' = 1(10)=0.1

Division of the reciprocal of 511 by 5518 results in 1825.

A.

True

B.

False

#### SOLUTION

Solution : A

Reciprocal of 511 is 115.

115÷5518

=11×185×(55)

=1825

By what rational number should we divide 227 so as to get the number 1114?

A.

- 2

B.

57

C.

127

D.

-4

#### SOLUTION

Solution : D

Let the rational number be x.

227÷x  = 1114 (given)

227=x×1114

227÷1114=x

227×1411=x

x=4

Therefore, 227 should be divided by -4 to get 1114.

For what value of x, 12x is equal to 3?

A.

4

B.

4

C.

3

D. 3

#### SOLUTION

Solution : A

12x=3

123=x

Or
x=4

Which of the following is a rational number between 13 and  53 ?

A.

73

B.

43

C. 53
D. 63

#### SOLUTION

Solution : B

In the fractions 13 and  53, the denominators are same.

So, considering numerator values, we can find the required rational number.

4 lies between 1 and 5.

So, keep 4 in the numerator and keep the same denominator as it is.

The required rational number is 43.

(59÷13)÷52=59÷(13÷52).

A.

True

B.

False

#### SOLUTION

Solution : B

Let's first evaluate LHS.

(5913)×152=59676

Now, RHS

59×(5213)

=306813

We see that both LHS and RHS are not equal.