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About Rational Numbers — Class 8 CBSE

Study properties of rational numbers: closure, commutativity, distributivity. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 3). 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 Number Operations
  • The Distributive Property
  • Rational Numbers Between Two Rational Numbers
  • Operations on Rational Numbers

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

Rational Numbers — solved examples for Class 8 CBSE

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 p/q form with p = 3 and q = 7.
  3. √2, √5, and π are irrational numbers.

Answer: 3/7

Example 2medium

Simplify: 3/5 + (-2/3)
  1. A)-1/15
  2. B)1/15
  3. C)11/15
  4. D)-11/15

Step-by-step solution

  1. LCM of 5 and 3 is 15.
  2. Convert:
    3/5=9/15,−2/3=−10/153/5 = 9/15, -2/3 = -10/15
  3. Add:
    9/15+(−10/15)=−1/159/15 + (-10/15) = -1/15

Answer: -1/15

Example 3hard

Simplify: (3/4 × 8/9) - (2/3 × 9/16)
  1. A)7/24
  2. B)5/24
  3. C)1/4
  4. D)1/8

Step-by-step solution

  1. First product:
    3/4×8/9=24/36=2/33/4 × 8/9 = 24/36 = 2/3
  2. Second product:
    2/3×9/16=18/48=3/82/3 × 9/16 = 18/48 = 3/8
  3. Subtract (LCM = 24):
    2/3−3/8=16/24−9/24=7/242/3 - 3/8 = 16/24 - 9/24 = 7/24

Answer: 7/24

Practice questions on Rational Numbers

  1. Q1.easy

    What is the additive identity for rational numbers?
    1. A)1
    2. B)0
    3. C)-1
    4. D)1/2
    Show answer

    Answer: 0

    Hint: Adding this number to any rational number gives the same number back.

  2. Q2.easy

    What is the multiplicative identity for rational numbers?
    1. A)0
    2. B)1
    3. C)-1
    4. D)1/2
    Show answer

    Answer: 1

    Hint: Multiplying any rational number by this number gives the same number.

  3. Q3.easy

    Find the additive inverse of 3/5.
    1. A)5/3
    2. B)-3/5
    3. C)3/5
    4. D)-5/3
    Show answer

    Answer: -3/5

    Hint: The additive inverse of a number is the number that gives 0 when added to it.

  4. Q4.medium

    Find the product: (-3/7) × (14/9)
    1. A)-2/3
    2. B)2/3
    3. C)-6/7
    4. D)6/7
    Show answer

    Answer: -2/3

    Hint: Multiply numerators together and denominators together, then simplify.

  5. Q5.medium

    Verify: -3/5 × (2/7 + 4/7) = (-3/5 × 2/7) + (-3/5 × 4/7). Which property does this demonstrate?
    1. A)Commutative
    2. B)Associative
    3. C)Distributive
    4. D)Closure
    Show answer

    Answer: Distributive

    Hint: One operation is being 'spread' over another.

  6. Q6.medium

    Find five rational numbers between 1/3 and 1/2.
    1. A)5/12, 6/12, 7/12, 8/12, 9/12
    2. B)3/8, 4/9, 5/12, 7/18, 11/24
    3. C)9/24, 10/24, 11/24, 12/24, 13/24
    4. D)1/4, 2/5, 3/6, 4/7, 5/8
    Show answer

    Answer: 9/24, 10/24, 11/24, 12/24, 13/24

    Hint: Convert to fractions with a large common denominator to find numbers in between.

  7. Q7.hard

    Find the value of: (-2/3) ÷ (4/5) + (1/6) × (-3/2)
    1. A)-13/12
    2. B)-5/6
    3. C)-1/12
    4. D)-7/6
    Show answer

    Answer: -13/12

    Hint: Follow BODMAS: do division and multiplication first, then addition.

  8. Q8.hard

    If 2/3 of a number is -8, what is the number?
    1. A)-12
    2. B)12
    3. C)-16/3
    4. D)16/3
    Show answer

    Answer: -12

    Hint: Set up the equation: (2/3) × x = -8 and solve for x.

  9. Q9.hard

    Insert 4 rational numbers between -1/2 and 1/2.
    1. A)-3/10, -1/10, 1/10, 3/10
    2. B)-1/4, 0, 1/4, 1/3
    3. C)-1/3, -1/6, 1/6, 1/3
    4. D)0, 1/4, 1/3, 2/5
    Show answer

    Answer: -3/10, -1/10, 1/10, 3/10

    Hint: Multiply numerator and denominator by 5 to get -5/10 and 5/10, then pick 4 numbers in between.

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.