Rational Numbers Class 7 MCQ Questions

Answer: (a) Yes

Explanation: A Rational Number is defined as a number that can be expressed in form of, p/q where p and q are integers and q ≠ 0.

If we equate, and compare p/q = (-8)/5

we get

p = -8 which is an integer

q = 5 which is an integer and is not equal to 0

Since both the conditions are satisfied, we can say that (-8)/5 is a Rational Number.

Answer: (b) -29

Explanation: We know that a Rational Number is a number that can be expressed in form of, p/q where p and q are integers and q ≠ 0.

Denominator of a Rational Number is the number “q”, which is the bottom number in the Rational number.

So, Denominator of 23/(-29) is -29

Answer: (b) 18

Explanation: We know that a Rational Number is a number that can be expressed in form of, p/q where p and q are integers and q ≠ 0.

Numerator of a Rational Number is the number “p”, which is the upper number of the Rational number.

So, Numerator of 18/7 is 18.

Answer: (a) 3/2

Explanation: Step 1 : – To reduce a fraction into its standard form, we will first find the HCF of both Numerator and Denominator.

Step 2 : – Thereafter, we will divide both Numerator and Denominator by their HCF

The HCF of 45 and 30 is 15

(45÷15)/(30÷15) = 3/2

Hence, the standard form of 45/30 is 3/2.

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.

3/5 and 6/15

we get,

3 x 15 = 45

and 6 x 5 = 30

Since, 3 x 15 ≠ 6 x 5

So, (3/5) ≠ (6/15)

Hence, 3/5 and 6/15 are not equivalent Rational Number.

Answer: (a) 112/(-10)

Explanation: Numerator of −56/5 = -56

We need to change the Numerator of −56/5 to 112

We need to find a number, with which we should multiply -56 so it is equal to 112

To obtain that number, we would need to divide 112 by -56 i.e.,

112/(−56) = -2

So, we have to multiply both the Numerator and Denominator of given Rational Number by -2

(−56×−2)/(5×−2) = 112/(−10)

Hence, −56/5 can be expressed as 112/(−10).

Answer: (a) (-48)/(-80)

Explanation: Denominator of 12/20 = 12

We need to change the Denominator of 12/20 to -80

We need to find a number, with which we should multiply 20 so it is equal to -80

To obtain that number, we would need to divide -80 by 20 i.e.,

(−80)/20 = -4

So, we have to multiply both the Numerator and Denominator of given Rational Number by -4

(12×−4)/(20×−4) = (−48)/(−80)

Hence, 12/20 can be expressed as (−48)/(−80).

Answer: (a) -18

Explanation: Given:

(−6)/5 = x/15

If two Rational Numbers are equivalent, then the product obtained by cross Multiplying them would also be equal.

On Cross Multiplying the given Rational numbers

On Cross Multiplying,

x x 5 = -6 x 15

x = (−6×15)/5

x = (−90)/5

x = -18

Hence, x = -18.

Answer: (c) =

Explanation: If we express both the Rational numbers with positive Denominator, we would get

1st number = −7/16

2nd number = 7/(−16)

To express 7/(−16) with a positive Denominator we would multiply both its Numerator and Denominator by (-1).

i.e., (7×(−1))/(−16×(−1)) = −7/16

If two rational numbers have common denominators, the number with higher Numerator is greater

If we compare their Numerators, we notice that

-7 = -7

then,−7/16 = −7/16

Hence,−7/16 = 7/(−16)

Answer: (b) 23/21

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

Additive inverse of (−23)/21 = −(−23)/21 = 23/21

Alternative Method:

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

(−23/21) x (-1) = 23/21

Answer: (c) 8/19

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

= (15+(−7))/19

= 8/19

Hence, the sum of of 15/19 and -7/19 is 8/19.

Answer: (b) 13/20

Explanation: To add two Rational Numbers, first their Denominators should be positive

So, we would first express (3/−4) as a Rational Number with positive Denominator.

Multiplying both the Numerator and Denominator by (-1)

i.e., (3×(−1))/(−4×(−1)) = −3/4

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

LCM of 5 and 4 is 20

Divide LCM by the Denominator of first number

20 ÷ 5 = 4

We have to multiply , both the Numerator and Denominator of 7/5 by the quotient i.e., 4

(7×4)/(5×4) = 28/20

Divide LCM by the Denominator of second number

20 ÷ 4 = 5

We have to multiply , both the Numerator and Denominator of −3/4 by 5

(−3×5)/(4×5) = −15/20

Now (28/20) + (−15/20) = 13/20

Hence, the sum of 7/5 and (3/−4)= 13/20.

Answer: (c) 17/9

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

= (25−8)/9

= 17/9

So, the difference of (25/9) and (8/9) is 17/9.

Answer: (b) 11/12

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

LCM of 3 and 4 is 12

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

12 ÷ 3 = 4

We have to multiply , both the Numerator and Denominator of 5/3 by the quotient i.e., 4

(5×4)/(3×4) = 20/12

Divide LCM by the Denominator of second number

12 ÷ 4 = 3

We have to multiply , both the Numerator and Denominator of 3/4 by the quotient i.e., 3

(3×3)/(4×3) = 9/12

Now (20/12) – (9/12) = 11/12

Hence, (5/3) – (3/4) = 11/12.

Answer: (c) 45/12

Explanation: Let x be the number, which needs to be added to (−7/4) to get 12/6

(−7/4) + x = 12/6

x = (12/6) + (7/4)

LCM of 6 and 4 is 12

x = (24+21)/12

= 45/12

Hence, 45/12 is added to −7/4 to make it 12/6.

Answer: (a) 15/14

Explanation: Product of two rational Numbers = (Product of their Numerators Product of their Denominators)

= ((−9)/6) x ((−10)/14)

= (−9)×(−10)/(6×14)

( Product of two negative integers is always positive )

= 90/84

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

HCF of 90 and 84 is 6

Dividing both the Numerator and Denominator by their HCF

(90÷6)/(84÷6) = 15/14

Hence, product of ((−9)/6) x ((−10)/14) = 15/14.

Answer: (b) 7/(-9)

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 (−9/7), -9 is the Numerator and 7 is the Denominator

Hence, the Reciprocal of (−9/7) is (7/−9)

Answer: (c) -45/14

Explanation: We have, (−12)/7 ÷ (8/15)

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 8/15 is 15/8.

then, we can write the given problem as (−12/7) x (15/8).

(−12×15)/(7×8) = (−180)/56.

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

HCF of 180 and 56 is 4.

= (−180÷4)/(56÷4) = (−45)/14.

Hence, ((−12)/7) ÷ (8/15) is (−45)/14.