📘 Class 8 Maths Worksheet

Topic: Rational Numbers

Name: ____________ Class: 8 Date: ____________

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✏️ Section A: Basic Level (Concepts & Identification)

1. Define a rational number.
2. Which of the following are rational numbers?
   a) $\frac{3}{5}$53​
   b) $\sqrt{2}$2​
   c) -7
   d) 0.25
3. Write two rational numbers between 0 and 1.
4. Write the additive inverse of $\frac{5}{6}$65​.
5. Write the multiplicative inverse of $-\frac{3}{4}$−43​.
6. Is 0 a rational number? Give reason.
7. Convert $\frac{7}{2}$27​ into decimal form.

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✏️ Section B: Medium Level (Operations)

8. Simplify: $\frac{2}{3} + \frac{1}{6}$32​+61​
9. Simplify: $\frac{5}{8} – \frac{1}{4}$85​−41​
10. Multiply: $\frac{3}{5} \times \frac{10}{9}$53​×910​
11. Divide: $\frac{7}{8} \div \frac{14}{16}$87​÷1614​
12. Simplify: $-\frac{2}{3} + \frac{5}{6}$−32​+65​
13. Arrange in ascending order: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$21​,32​,43​

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✏️ Section C: Advanced Level (Word Problems)

14. A rope of length $\frac{5}{6}$65​ m is cut into 2 equal parts. What is the length of each part?
15. A student scored $\frac{3}{5}$53​ of total marks in Maths and $\frac{4}{5}$54​ in Science. Find total fraction score.
16. If $x = \frac{2}{3}$x=32​, find $3x + \frac{1}{2}$3x+21​.
17. The sum of two rational numbers is $\frac{7}{4}$47​. One number is $\frac{3}{4}$43​. Find the other.
18. A tank is $\frac{3}{5}$53​ filled. If $\frac{2}{5}$52​ is added, what fraction is filled now?

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✏️ Section D: Higher Order Thinking (HOTS)

19. If $a = \frac{2}{3}$a=32​, find $a + \frac{1}{a}$a+a1​.
20. Prove that sum of two rational numbers is always rational (example based).
21. Find a rational number between $\frac{2}{5}$52​ and $\frac{3}{5}$53​.
22. If $x + \frac{1}{x} = 3$x+x1​=3, find possible value of $x$x (rational).
23. Write 3 rational numbers between $-1$−1 and $0$0.

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24. Without dividing, compare: $\frac{7}{9}$97​ and $\frac{5}{6}$65​.

✅ Answer Key

✏️ Section A: Basic Level

1. A rational number is a number that can be written in the form $\frac{p}{q}$qp​, where $q \ne 0$q=0.
2. Rational numbers: a, c, d
   ( $\frac{3}{5}$53​, -7, 0.25 )
3. Any two examples: 13,23\frac{1}{3}, \frac{2}{3}31​,32​ (or similar)
4. −56-\frac{5}{6}−65​
5. −43-\frac{4}{3}−34​
6. Yes, because 0 = $\frac{0}{1}$10​
7. 3.5

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✏️ Section B: Medium Level

8. $\frac{2}{3} + \frac{1}{6} = \frac{5}{6}$32​+61​=65​
9. $\frac{5}{8} – \frac{1}{4} = \frac{3}{8}$85​−41​=83​
10. $\frac{3}{5} \times \frac{10}{9} = \frac{2}{3}$53​×910​=32​
11. $\frac{7}{8} \div \frac{14}{16} = 1$87​÷1614​=1
12. $-\frac{2}{3} + \frac{5}{6} = \frac{1}{6}$−32​+65​=61​
13. Ascending order:
    12,23,34\frac{1}{2}, \frac{2}{3}, \frac{3}{4}21​,32​,43​

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✏️ Section C: Advanced Level

14. Each part = 512\frac{5}{12}125​ m
15. Total = 75\frac{7}{5}57​
16. $x = \frac{2}{3}$x=32​:
    $3x + \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2}$3x+21​=2+21​=25​
17. Other number = 111
18. Filled fraction = 1 (fully filled tank)

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✏️ Section D: HOTS

19. $a = \frac{2}{3}$a=32​:
    $a + \frac{1}{a} = \frac{2}{3} + \frac{3}{2} = \frac{13}{6}$a+a1​=32​+23​=613​
20. Example proof:
    Let $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$ba​+dc​=bdad+bc​, which is rational.
21. One example: 12\frac{1}{2}21​ (or any valid number between)
22. Possible values: x=3±52x = \frac{3 \pm \sqrt{5}}{2}x=23±5​​
    (Note: may not always be rational; depends on interpretation)
23. Any three rational numbers between -1 and 0:
    −14,−12,−34-\frac{1}{4}, -\frac{1}{2}, -\frac{3}{4}−41​,−21​,−43​

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24. Compare $\frac{7}{9}$97​ and $\frac{5}{6}$65​:
    Cross multiply:
    $7 \times 6 = 42$7×6=42, $5 \times 9 = 45$5×9=45
    👉 $\frac{5}{6}$65​ is greater

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