MCQ Questions on Rational Numbers for Class 8 with Answers

Answer: (a) -1/3

Explanation: Given Number = 36/(−108)

In order to reduce the given number into its standard form, we would first need to make the Denominator positive

Multiplying both the Numerator and Denominator (to make the Denominator positive) by (-1)

i.e., 36×(−1)−108×(−1) = −36108

The HCF of 36 and 108 is 36

Dividing both the Numerator and Denominator by their HCF i.e., 36 we would get

(−36÷36)/(108÷36) = −1/3

Hence, standard form of 36/(−108) is −1/3

Answer: (b) No

Explanation: If two Rational Numbers are equivalent, the product obtained by Cross Multiplying them would also be equal

On Cross Multiplying the given Rational numbers

(4/5) and (16/15)

we get,

4 x 15 = 60

and 16 x 5 = 80

Since, 4 x 15 ≠ 16 x 5

So, (4/5) ≠ (16/15)

Hence, (4/5) and (16/15) are not equivalent Rational Number.

Answer: (a) 65/(-80)

Explanation: Numerator of (−13)/16 = -13

We need to change the Numerator of (−13)/16 to 65

We need to find a number, with which we should multiply -13 so it is equal to 65

To obtain that number, we would need to divide 65 by -13 i.e.,

65/(−13) = -5

So, we have to multiply both the Numerator and Denominator of given Rational Number by -5

(−13×−5)/(16×−5) = 65/(-80)

Hence, −13/16 can be expressed as 65/(-80)

Answer: (a) (-45)/(-75)

Explanation: Denominator of 15/25 = 15

We need to change the Denominator of 15/25 to -75

We need to find a number, with which we should multiply 25 so it is equal to -75

To obtain that number, we would need to divide -75 by 25 i.e.,

−75/25 = -3

So, we have to multiply both the Numerator and Denominator of given Rational Number by -3

(15×−3)/(25×−3) = (−45)/(−75)

Hence, 15/25 can be expressed as (−45)/(−75).

Answer: (b) =

Explanation: Express both the Rational numbers with positive Denominator.

1st number = −12/13

2nd number = 12/(−13)

To express 12/(−13) with positive Denominator we would multiply both its Numerator and Denominator by (-1).

i.e., (12×(−1))/(−13×(−1)) = −12/13

Since both the numbers are equal, we can say −12/13 = 12/(−13)

Answer: (b) 8/11

Explanation: (Sum of Rational Numbers whose Denominators are equal) = (Sum of their Numerators / Common Denominator)

= (13+(−5))/11

= 8/11

Hence, the sum of of 13/11 and 5/11 is 8/11.

Answer: (a) 27/16

Explanation: To add two Rational Numbers with different Denominator, we will first find the LCM of both the Denominators.

LCM of 4 and 16 is 16

Now we would divide such LCM by Denominator of first number and the result would be multiplied with both the numerator and denominator of such number

Dividing LCM by the Denominator of first number

16 ÷ 4 = 4

Multiplying both the Numerator and Denominator of 54 by the quotient i.e., 4

(5×4)/(4×4) = 20/16

Dividing LCM by the Denominator of Second number

16 ÷ 16 = 1

Multiplying both the Numerator and Denominator of 7/16 by 1

(7×1)/(16×1) = 7/16

Now (20/16) + (7/16) = 27/16

Hence, the sum of 5/4 and 7/16 = 27/16

Answer: (a) -12/23

Explanation: Additive inverse of any number is that number with minus (negative) sign before it.

Additive inverse of 12/23 is −12/23

Alternative Method:

We can also find the additive inverse of a Number by multiplying it with -1

(12/23) x (-1) = −12/23

Answer: (a) 15/7

Explanation: Difference of Rational Numbers when Denominators are equal = (Difference of their Numerators / Common Denominator)

= (28−13)/7

= 15/7

So, the difference of 28/7 and 13/7 is 15/7.

Answer: (c) 23/20

Explanation: To subtract two Rational Numbers with different Denominators, first we will find the LCM of both the Denominators.

LCM of 4 and 5 is 20

Now we would divide such LCM by Denominator of first number and the result would be multiplied with both the numerator and denominator of such number

Divide LCM by the Denominator of first number

20 ÷ 4 = 5

We have to multiply , both the Numerator and Denominator of 74 by the quotient i.e., 5

7×54×5 = 3520

Divide LCM by the Denominator of second number

20 ÷ 5 = 4

We have to multiply , both the Numerator and Denominator of 35 by the quotient i.e., 4

(3×4)/(5×4) = 12/20

Now (35/20) – (12/20) = 23/20

Hence, (7/4) – (3/5) = 23/20

Answer: (a) 59/12

Explanation: Let x be the number, which needs to be added to −2312 to get 93

(−23/12) + x = 9/3

x = (9/3) + (23/12)

LCM of 3 and 12 is 12

x = (36+23)/12

= 59/12

Hence, 59/12 is added to −23/12 to make it 9/3

Answer: (b) 9/2

Explanation: Let, the other Rational Number be x

We are given that the sum of the two Rational Numbers is = 7

(5/2) + x = 7

x = 7 – (5/2)

x = (7/1)- (5/2)

LCM of denominator in the two numbers , 1 and 2 is 2

x = (14−5)/2

x = 9/2

Hence, the other Rational Number is 9/2

Answer: (a) 6/5

Explanation: Let, the other Rational Number be x

We are given that the Product of the two Rational Numbers is 97

(15/14) x x = 97

x = (9/7)x (14/15)

x = (3/1)x (2/5)

x = 6/5

Hence, the other Rational Number is 6/5

Answer: (a) 9/20

Explanation: Product of two rational Numbers=Product of their Numerators /Product of their Denominators

(3/5) x (3/4) = (3×3)/(5×4) = 9/20

To further simplify the given numbers into their lowest form, we would divide both the Numerator and Denominator by their HCF

HCF of 9 and 20 is 1

Dividing both the Numerator and Denominator by their HCF

(9÷1)/(20÷1) = 9/20

Hence, the product of 3/5 and 3/4 = 9/20

Answer: (b) 5/(-7)

Explanation: In order to find Reciprocal or Multiplicative Inverse of any Rational Number, we simply reverse the Fraction i.e., the Numerator becomes Denominator , and the Denominator becomes Numerator.

In −7/5, -7 is the Numerator and 5 is the Denominator

Hence, the Reciprocal of −7/5 is 5/(−7)

Answer: (b) -8/5

Explanation: We have, (4/5) ÷ (−6)/12

In order to divide a Rational Number by another Rational Number

We have to multiply first Rational Number with Reciprocal of the second Rational Number

Since, Reciprocal of −6/12 is 12/−6)

We can write the given equation as 4/5 ÷ (−6)/12

= (4/5) x (12/−6)

To make the Denominator positive, we would multiply 12 and -6 by -1

Given equation would now be (4/5) x (−12/6)

(4×(−12))/(5×6) = −48/30

To further simply the given numbers into their lowest form, we would divide both the Numerator and Denominator by their HCF

HCF of 48 and 30 is 6

= (−48÷6)/(30÷6) = −8/5

Hence, (4/5) ÷ (−6)/12 is −8/5

Answer: (b) 11/15

Explanation: Let x be the number, from which we divide 2411 to obtain 58

we are given that

(24/11) ÷ x = 5/8

(24/11) ÷ 1x = 5/8

1/x = (5/8) x (24/11)

x = (8/5) x (11/24)

x = (1/5) x (11/3)

x = 11/15

Hence, other Rational Number is 11/15