Rational Numbers Questions

Rational Numbers questions and answers may help students grasp the concept more quickly. Several questions on “Rational Numbers” appear in practically all board exams. Students can use these questions to acquire a quick overview of the topics and practise them in order to understand them better. Know the complete explanations for each question to double-check your answers. To learn more about rational numbers, click here.

Here are some rational numbers questions and answers for you to study and practice.

Rational Numbers Questions with Solutions

1. Is 58/0 a rational number?

Solution:

No, 58/0 is not a rational number. As we know, a rational number is a number which is of the form a/b, where b should not be equal to 0.

2. Find the reciprocal of the following rational numbers.

(a) 6/10

(b) 126/17

(c) 89/188

Solution:

(a) The reciprocal of 6/10 is 10/6.

(b) The reciprocal of 126/17 is 17/126.

(c) 188/89 is the reciprocal of 89/188.

3. Find the rational number that should be added to ⅜ to get the number -1/24.

Solution:

Let the unknown number be “x”.

Hence, from the given condition, we can write:

x + (⅜) = (-1/24)

Now, simplify the above equation, we get

8x + 3 = (-1/24) × 8

8x + 3 = -(⅓)

8x =( -⅓) – 3

8x = (-1-9)/3

8x = -10/3

x = -10/24

x = -5/12.

4. What is the additive inverse of 4/5?

Solution:

The additive inverse of 4/5 is -4/5.

Verification:

We know that the sum of the number and its additive inverse is equal to 0.

Hence, (4/5) + (-⅘) = (4-4)/5 = 0.

5. What is the sum of multiplicative inverse and the additive inverse of 2?

Solution:

Given number: 2

The additive inverse of 2 is -2

Multiplicative inverse of 2 is 1/2.

Thus, the sum of multiplicative inverse and additive inverse of 2 = (½) -2

Sum = (1-4)/2 = -3/2.

6. Multiply 6/7 by the reciprocal of 36/21.

Solution:

The reciprocal of 36/21 is 21/36.

Now, multiply 6/7 by 21/36

= (6/7) × (21/36)

= (1/1) × (3/6)

= ½

Hence, if 6/7 is multiplied by the reciprocal of 36/21, we get the rational number 1/2.

7. Solve the expression: [(1/2)×(3/2)] + [(4/6)×(2/3)]

Solution:

Given expression: [(1/2)×(3/2)] + [(4/6)×(2/3)]

First, simplify the expression inside the brackets.

[(1/2)×(3/2)] + [(4/6)×(2/3)] = (3/4) + (8/18)

[(1/2)×(3/2)] + [(4/6)×(2/3)] = (27+16)/36

[(1/2)×(3/2)] + [(4/6)×(2/3)] = 43/36

8. Verify x + y = y + x, if x = ½ and y = 3/4.

Solution:

Given: x = ½ and y = ¾.

L.H.S:

x + y = (½) + (¾)

x + y = (2+3)/4

x + y = 5/4

R.H.S:

y + x = (¾) + (½)

y + x = (3+2)/4

y + x = 5/4

Hence, L.H.S = R.H.S

Therefore, x + y = y + x is verified.

9. Subtract the rational number ⅔ from ⅞.

Solution:

To find: (7/8) – (2/3).

(7/8) – (2/3) = (21-16)/24

(7/8) – (2/3) = 5/24.

Hence, the rational number ⅔ subtracted from ⅞ is 5/24.

10. Find the number that should be multiplied with -3/5 to get 21?

Solution:

Let the unknown number be “p”.

Thus, (-⅗) × p = 21

The above equation can be written as:

-3p = 21×5

-3p = 105

p = -105/3

p = – 35

Therefore, -35 multiplied with -3/5 to get 21.

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Practice Questions

1. What is the sum of the additive inverse and multiplicative inverse of 7?

2. Simplify the expression: [(¾)×(7/2)] – [(4/7)×(5/6)].

3. Find the reciprocal of the rational numbers:

1. 12/57
2. -43/26
3. 97/-115

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