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About Rational Numbers — Class 8 ICSE

Study properties of rational numbers including closure, commutativity, and distributivity. This topic is part of the ICSE Class 8 mathematics syllabus (chapter: Chapter 1). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Rational Numbers

  • What are Rational Numbers?
  • Properties of Rational Numbers
  • Operations with Unlike Denominators
  • Finding Rational Numbers Between Two Numbers
  • Representation and Summary

Interactive lesson · about 20 minutes · checkpoint question after every unit

Rational Numbers — solved examples for Class 8 ICSE

Example 1easy

Which of the following is a rational number?
  1. A)√2
  2. B)π
  3. C)3/7
  4. D)√5

Step-by-step solution

  1. A rational number is any number that can be written as a fraction p/q, where p and q are integers and q ≠ 0.
  2. 3/7 is already in the form p/q with p = 3, q = 7.
  3. √2, √5, and π are irrational numbers — they cannot be expressed as fractions.

Answer: 3/7

Example 2medium

Verify the distributive property: 2/3 × (4/5 + 1/5)
  1. A)2/3
  2. B)2/5
  3. C)1
  4. D)10/15

Step-by-step solution

  1. LHS:
    2/3×(4/5+1/5)=2/3×5/5=2/3×1=2/32/3 × (4/5 + 1/5) = 2/3 × 5/5 = 2/3 × 1 = 2/3
  2. RHS:
    2/3×4/5+2/3×1/5=8/15+2/15=10/15=2/32/3 × 4/5 + 2/3 × 1/5 = 8/15 + 2/15 = 10/15 = 2/3
  3. LHS = RHS = 2/3. Distributive property verified!

Answer: 2/3

Example 3hard

If (a/b) + (b/a) = 25/12, find the value of a/b given that a/b > 1.
  1. A)4/3
  2. B)3/4
  3. C)5/3
  4. D)3/5

Step-by-step solution

  1. Let x = a/b. Then:
    x+1/x=25/12x + 1/x = 25/12
  2. Multiply by 12x:
    12x2+12=25x12x² + 12 = 25x
  3. Rearrange:
    12x2−25x+12=012x² - 25x + 12 = 0
  4. Factor:
    (3x−4)(4x−3)=0,sox=4/3orx=3/4(3x - 4)(4x - 3) = 0, so x = 4/3 or x = 3/4
  5. Since a/b > 1:
    a/b=4/3a/b = 4/3

Answer: 4/3

Practice questions on Rational Numbers

  1. Q1.easy

    What is the additive inverse of -5/8?
    1. A)-5/8
    2. B)5/8
    3. C)8/5
    4. D)-8/5
    Show answer

    Answer: 5/8

    Hint: The additive inverse of a number is what you add to it to get 0.

  2. Q2.easy

    What is the multiplicative inverse (reciprocal) of 3/4?
    1. A)-3/4
    2. B)4/3
    3. C)-4/3
    4. D)3/4
    Show answer

    Answer: 4/3

    Hint: The multiplicative inverse of a/b is b/a.

  3. Q3.easy

    Simplify: 2/5 + 3/5
    1. A)5/5
    2. B)1
    3. C)5/10
    4. D)6/10
    Show answer

    Answer: 1

    Hint: When denominators are the same, just add the numerators.

  4. Q4.medium

    Find the sum: 3/4 + (-5/6)
    1. A)-1/12
    2. B)1/12
    3. C)-8/10
    4. D)8/10
    Show answer

    Answer: -1/12

    Hint: Find the LCM of 4 and 6 to get a common denominator.

  5. Q5.medium

    Simplify: (-3/7) × (14/9)
    1. A)-2/3
    2. B)2/3
    3. C)-42/63
    4. D)6/7
    Show answer

    Answer: -2/3

    Hint: Multiply and then simplify. You can cancel common factors first.

  6. Q6.medium

    Find 5 rational numbers between -1/2 and 1/2.
    1. A)-2/5, -1/5, 0, 1/5, 2/5
    2. B)1, 2, 3, 4, 5
    3. C)-3, -2, -1, 0, 1
    4. D)-1/3, 0, 1/3, 2/3, 1
    Show answer

    Answer: -2/5, -1/5, 0, 1/5, 2/5

    Hint: Convert to an equivalent fraction with a larger denominator, then pick numbers in between.

  7. Q7.hard

    Find the value of: (1/2)(1 - 1/3)(1 - 1/4)(1 - 1/5)...(1 - 1/10)
    1. A)1/10
    2. B)1/5
    3. C)1/9
    4. D)1/20
    Show answer

    Answer: 1/10

    Hint: Simplify each bracket: (1 - 1/n) = (n-1)/n. Look for a telescoping pattern.

  8. Q8.hard

    The product of two rational numbers is -28/81. If one of them is 14/27, find the other.
    1. A)-2/3
    2. B)2/3
    3. C)-6/7
    4. D)6/7
    Show answer

    Answer: -2/3

    Hint: If a × b = product, then b = product ÷ a.

  9. Q9.hard

    Simplify: [(−3/5) × (10/9)] ÷ [(−15/8) × (4/25)]
    1. A)20/9
    2. B)-20/9
    3. C)9/20
    4. D)-9/20
    Show answer

    Answer: 20/9

    Hint: Compute numerator and denominator products separately, then divide.

These are 9 of the 60 questions available for Rational Numbers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.