In Class 8, rational numbers are where fractions and integers finally join into one number system. A rational number is any number that can be written as p/q with a whole-number top and a non-zero bottom — which quietly includes every integer, every fraction, and every terminating or repeating decimal. The chapter then asks your child to do things with them: add and subtract with negatives, multiply and divide, find an additive inverse or a reciprocal, use the commutative and distributive properties, place a number on the line, and tell a rational number apart from an irrational one like √2. It is a lot of connected ideas, and short regular practice is what makes them settle.

This free printable worksheet has 12 questions from Bmathpro’s own question bank of 10,500+ validated maths questions — the same bank our enrolled students practise from. Every answer comes with a one-line explanation, so you can check your child’s method, not just the final answer.

Set aside 15–20 minutes, keep the answers hidden until the end, and let your child attempt every question — a wrong attempt tells you more than a skipped one.

What this worksheet covers

• Recognising what makes a number rational (and spotting an irrational one)
• Adding, subtracting, multiplying and dividing rational numbers, including negatives
• Additive inverse and multiplicative inverse (reciprocal)
• Comparing two rational numbers
• Converting between fractions and decimals, including a recurring decimal
• Finding a rational number between two given rationals

Maps to the CBSE Class 8 Rational Numbers chapter (NCERT) and equivalent ICSE/State-board units.

Class 8 Rational Numbers Worksheet — 12 Questions

Warm-up

1. A rational number can be written as:
A. a square root of 2  B. p/q with q not zero  C. only a whole number  D. a never-ending non-repeating decimal

2. Which of these numbers is rational?
A. π  B. √3  C. 0.75  D. √2

3. Which of the following numbers is irrational?
A. √9  B. 0.25  C. 3/11  D. √7

4. What is the additive inverse of 3/7?
A. 7/3  B. −3/7  C. −7/3  D. 3/7

Building up

5. Add: 2/5 + 1/3. Give your answer as a fraction in lowest terms. (Write your answer.)

6. Subtract: 7/8 − 1/4. Give your answer as a fraction in lowest terms. (Write your answer.)

7. Multiply: (3/4) × (2/9). Give your answer as a fraction in lowest terms. (Write your answer.)

8. What is the multiplicative inverse (reciprocal) of 3/8? (Write your answer.)

9. Which statement correctly compares 3/5 and 4/7?
A. 3/5 < 4/7  B. 3/5 = 4/7  C. 3/5 > 4/7  D. They cannot be compared

Challenge

10. Evaluate: 2/3 + (−5/6). Give your answer as a fraction in lowest terms. (Write your answer.)

11. Find a rational number that lies exactly halfway between 1/4 and 1/2. (Write your answer.)

12. Convert the recurring decimal 0.272727… (the block 27 repeating) to a fraction in lowest terms. (Write your answer.)

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Answer key with explanations

Show answers and explanations (parents — open this after your child finishes)

1. B. p/q with q not zero — a rational number is a ratio of two integers with a non-zero denominator.
2. C. 0.75 — 0.75 = 3/4; π, √2 and √3 are irrational.
3. D. √7 — 7 is not a perfect square; √9 = 3, 0.25 and 3/11 are rational.
4. B. −3/7 — the additive inverse of x is −x, so 3/7 + (−3/7) = 0.
5. 11/15 — 6/15 + 5/15 = 11/15.
6. 5/8 — 7/8 − 2/8 = 5/8.
7. 1/6 — 6/36 = 1/6.
8. 8/3 — (3/8) × (8/3) = 1.
9. C. 3/5 > 4/7 — cross-multiply: 21 > 20.
10. −1/6 — 4/6 + (−5/6) = −1/6.
11. 3/8 — midpoint = (3/4) ÷ 2 = 3/8.
12. 3/11 — 99x = 27, so x = 27/99 = 3/11.

How to use this worksheet at home

• Keep it short and calm. 15–20 minutes beats an hour of pressure.
• Insist on lowest terms. Ask “can this fraction be reduced further?” every time.
• Praise the method, not the marks. (We deliberately don’t put marks on our worksheets.)

FAQs

Is this worksheet free to print?
Yes — free to use and print at home, no sign-up needed.

Which syllabus does it follow?
Standard Class 8 Rational Numbers chapter — CBSE (NCERT), ICSE and State boards.

What is the difference between a rational and an irrational number?
A rational number can be written as a fraction p/q (like 3/4 or 0.35); an irrational number cannot — its decimal never ends and never repeats, like √2 or π.

Where can my child get more practice like this?
Enrolled students get Math Gym, our paid practice app with 10,500+ questions — see our courses page.

Also practise: Class 8 Linear Equations · Class 8 Exponents & Powers · all Class 8 worksheets.

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