Rational Number Questions

Rational number questions with solutions are provided here for students to practice and prepare for their upcoming examinations. These questions are based on the Class 8 syllabus. They are prepared as per the NCERT (CBSE) guidelines. Solving these questions will help students understand the concept well, and improve their skills.

Also, check:

• Important 2 Marks Questions for Class 8 Maths
• Important 3 Marks Questions for Class 8 Maths
• Important 4 Marks Questions for Class 8 Maths

Rational numbers are the numbers which are represented in the form of p/q, where

(i) p and q are integers

(ii) q ≠ 0

(iii) p and q are co-prime numbers, that is, HCF(p, q) = 1.

Learn more about Rational Numbers.

Rational Number Class 8 Questions with Solution

Let us practice some important rational numbers questions for class 8 to prepare for examinations.

Question 1: Find the additive inverse of the following:

(i) 22/4 (ii) ⅜ (iii) – 24/–5 (iv) 17/(– 6)

Solution:

(i) 22/4

The additive inverse of 22/4 is – 22/4 or – 11/2.

(ii) ⅜

The additive inverse of ⅜ is – ⅜.

(iii) – 24/–5

The additive inverse of –24/–5 or 24/5 is – 24/5.

(iv) 17/(– 6)

The additive inverse of 17/(–6) or – 17/6 is 17/6.

Question 2: Find the multiplicative inverse of the following:

(i) 18/7 (ii) 34/6 (iii) 29/3 (iv) –6/7

Solution:

(i) 18/7

The multiplicative inverse of 18/7 is 7/18.

(ii) 34/6

The multiplicative inverse of 34/6 is 6/34 or 3/17.

(iii) 29/3

The multiplicative inverse of 29/3 is 3/29.

(iv) –6/7

The multiplicative inverse of –6/7 is –7/6.

Question 3: Evaluate:

Solution:

Question 4: State true or false for the following:

(i) Rational numbers are closed with respect to division.

(ii) Every whole number is a rational number.

(iii) Every integer is a rational number.

(iv) There are infinitely many rational numbers between any two rational numbers.

(v) 1 and –1 are the only rational numbers which are equal to their reciprocal.

Solution:

(i) Rational numbers are closed with respect to division. (False)

(ii) Every whole number is a rational number. (True)

(iii) Every integer is a rational number. (False)

(iv) There are infinitely many rational numbers between any two rational numbers. (True)

(v) 1 and –1 are the only rational numbers which are equal to their reciprocal. (True)

Question 5: Find five rational numbers between ⅔ and ⅘ .

Solution:

We have the equivalent fractions,

⅔ = (2 × 5)/(3 × 5) = 10/15 and ⅘ = (4 × 3)/(5 × 3) = 12/15

To find five rational numbers lets multiply both numerator and denominator of the equivalent fractions by 5, we get

(10 × 5)/(15 × 5) = 50/75 and (12 × 5)/(15 × 5) = 60/75

Therefore, five rational numbers between ⅔ = 50/75 and ⅘ = 60/75 are

51/75, 52/75, 53/75, 54/75, 55/75.

Also Read:

• Exponents and Powers
• Algebraic expressions
• Surface Area and Volume
• Ratio and Proportion

Question 6: State which property is in the following:

(i) ⅖ + ( –⅚ + ½) = {⅖ + ( –⅚)} + ½

(ii) 3 – 45/7 + 3/2 = (3 + 3/2) – 45/7

(iii) 300 × 45 = (300 × 40) + (300 × 5)

(iv) 2/19 × 19/2 = 1

(v) 3/7 + (–3/7) = 0

Solution:

Question 7: Find ten rational numbers between 2 and 3.

Solution:

Multiply and divide both the numbers by 11, we get

(2 × 11)/11 = 22/11 and (3 × 11)/11 = 33/11

Rational numbers between 2 = 22/11 and 3 = 33/11 are:

23/11, 24/11, 25/11, 26/11, 27/11, 28/11, 29/11, 30/11, 31/11, 32/11.

Question 8: From a 50 m cloth, 7/3 m cloth cut out to make a shirt and 14/5 is cut out to make a curtain. Find the remaining length of the cloth?

Solution:

Total length of the cloth = 50 m

Cloth used for making shirt = 7/3 m

Cloth used for making curtain = 14/5 m

Remaining cloth = 50 – 7/3 – 14/5 = 50 – {7/3 + 14/5}

= 50 – {77/15} = (750 – 77)/15 = 673/15 m

Question 9: A train covers 256 km in an hour. How much distance it would cover in 35/8 hours?

Solution:

Distance covered by the train in one hour = 256 km

Distance covered in 35/8 hours = 256 × 35/8 = 1120 km

Question 10: The monthly salary of a man is ₹ 65000, one-fifth of his salary is spend paying the rent, 5/26th of his remaining salary is spent in buying groceries, and half of the rest salary is spent miscellaneous expenses. How much his monthly saving?

Solution:

Total salary = ₹ 65000

Amount spend in paying the rent = ⅕ × 65000 = ₹ 13000

Remaining amount = 65000 – 13000 = ₹ 52000

Amount spend in groceries = 5/26 × 52000 = ₹ 10000

Remaining amount = 52000 – 10000 ₹ 42000

Miscellaneous expenses = ½ × 42000 = ₹ 21000

∴ his monthly savings = ₹ 21000.

Video Lesson on Rational Numbers Class 8

Practice Questions on Rational Numbers Class 8

1. State true or false for the following:

(i) All integers are rational number.

(ii) Multiplicative inverse does not exist for rational numbers.

(iii) 1 is the additive identity for rational numbers.

(iv) ⅔ lies in between the rational numbers ⅛ and 7/9.

2. Find rational numbers between ⅖ and 9/5.

3. Represent the following rational numbers on the number line

(i) ⅔ (ii) ⅗ (iii) –9/4

4. A rational number x is equal to ⅖ times the sum of 34/7 and 1/14. Find the rational number.

5. Reena could run 21/5 m in an hour. How much she can run in 34/7 hours?

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