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About Rational Numbers — Class 7 CBSE

Explore rational numbers, equivalence, and place on the number line. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 12). On this page you can practice 49 questions across three difficulty levels — 10 easy, 19 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 34-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Rational Numbers

  • Introduction to Rational Numbers
  • Equivalent Rational Numbers
  • Rational Numbers on the Number Line
  • Comparing Rational Numbers
  • Operations with Rational Numbers & Summary

Interactive lesson · about 15 minutes · checkpoint question after every unit

Rational Numbers — solved examples for Class 7 CBSE

Example 1easy

Which of the following statements correctly describes how to find an equivalent rational number to p/q (where q ≠ 0)?
  1. A)Multiply only the numerator by a non-zero integer.
  2. B)Add the same non-zero integer to both the numerator and the denominator.
  3. C)Multiply both the numerator and the denominator by the same non-zero integer.
  4. D)Divide the numerator by any non-zero integer and the denominator by a different non-zero integer.

Step-by-step solution

  1. An equivalent rational number is obtained by multiplying or dividing both the numerator and the denominator by the same non-zero integer.
  2. This ensures that the value of the rational number remains the same, only its representation changes.
    (p×k)/(q×k)=p/q,wherek≠0(p × k) / (q × k) = p/q, where k ≠ 0

Answer: Multiply both the numerator and the denominator by the same non-zero integer.

Example 2medium

Which of the following numbers is a rational number?
  1. A)√3
  2. B)1/0
  3. C)-5/2
  4. D)π

Step-by-step solution

  1. A rational number can be written as p/q, where p and q are integers and q ≠ 0.
  2. Option A (√3) is an irrational number, it cannot be expressed as a simple fraction of integers.
  3. Option B (1/0) is undefined because the denominator is zero. It is not a rational number.
  4. Option C (-5/2) is in the form p/q, where -5 and 2 are integers and 2 ≠ 0. So, it is a rational number.
  5. Option D (π) is an irrational number.

Answer: -5/2

Example 3hard

Which of the following statements about rational numbers is ALWAYS true?
  1. A)A) Every rational number is an integer.
  2. B)B) Every integer is a rational number.
  3. C)C) Every fraction is a rational number, but not every rational number is a fraction.
  4. D)D) The product of two rational numbers is always an integer.

Step-by-step solution

  1. A rational number is any number that can be expressed as p/q, where p and q are integers and q ≠ 0. Fractions are typically defined as a/b where a and b are positive integers, representing parts of a whole.
  2. Statement A is false (e.g., 1/2 is rational but not an integer). Statement B is true (any integer 'n' can be written as n/1). Statement D is false (e.g., 1/2 × 1/3 = 1/6, which is not an integer).
  3. Statement C is true. All fractions (e.g., 3/4, 7/2) fit the definition of a rational number. However, rational numbers like -2/3 or -5 are not typically referred to as 'factions' because fractions usually imply positive values and a 'part of a whole' concept.

Answer: C) Every fraction is a rational number, but not every rational number is a fraction.

Practice questions on Rational Numbers

  1. Q1.easy

    Identify the smallest rational number among -3/4, -2/3, 1/2, and 0.
    1. A)0
    2. B)1/2
    3. C)-2/3
    4. D)-3/4
    Show answer

    Answer: -3/4

    Hint: To compare negative rational numbers with different denominators, it's helpful to convert them to equivalent fractions with a common denominator or visualize them on a number line.

  2. Q2.easy

    Anil tried to add 2/5 and 1/3. He wrote: (2+1)/(5+3) = 3/8. What was his mistake?
    1. A)He should have multiplied the numerators instead of adding them.
    2. B)He forgot to simplify the fraction 3/8.
    3. C)He incorrectly added the denominators directly without finding a common denominator.
    4. D)He should have subtracted the fractions instead of adding them.
    Show answer

    Answer: He incorrectly added the denominators directly without finding a common denominator.

    Hint: Recall the rule for adding rational numbers with different denominators. You can't simply add the top and bottom numbers.

  3. Q3.easy

    What is the result of -5/7 - (-2/7)?
    1. A)-3/7
    2. B)3/7
    3. C)-7/7
    4. D)7/7
    Show answer

    Answer: -3/7

    Hint: Remember that subtracting a negative number is the same as adding its positive counterpart. The denominators are already the same.

  4. Q4.medium

    Which of the following rational numbers is a negative rational number?
    1. A)3/5
    2. B)-(-2/7)
    3. C)0
    4. D)-4/9
    Show answer

    Answer: -4/9

    Hint: A negative rational number has either a negative numerator or a negative denominator, but not both, when expressed in its simplest form.

  5. Q5.medium

    Which of the following rational numbers is equivalent to 2/3?
    1. A)4/9
    2. B)6/8
    3. C)10/15
    4. D)12/16
    Show answer

    Answer: 10/15

    Hint: To find an equivalent rational number, multiply or divide both the numerator and the denominator by the same non-zero integer.

  6. Q6.medium

    The standard form of the rational number -45/75 is:
    1. A)-3/5
    2. B)-9/15
    3. C)3/5
    4. D)-15/25
    Show answer

    Answer: -3/5

    Hint: To reduce a rational number to its standard form, divide both the numerator and denominator by their HCF (Highest Common Factor) and ensure the denominator is positive.

  7. Q7.hard

    If the rational number (2x - 1) / (x + 3) is equivalent to -5, what is the value of x?
    1. A)A) 2
    2. B)B) -2
    3. C)C) 1
    4. D)D) -1
    Show answer

    Answer: B) -2

    Hint: Remember that -5 can be written as -5/1. For equivalent rational numbers, their cross-products are equal.

  8. Q8.hard

    A rational number is given as (-48) / (-72). What is its standard form, and what is the sum of its numerator and denominator in standard form?
    1. A)A) 2/3, sum = 5
    2. B)B) -2/3, sum = 1
    3. C)C) 2/3, sum = 1
    4. D)D) -2/3, sum = -5
    Show answer

    Answer: A) 2/3, sum = 5

    Hint: First, simplify the rational number by finding the greatest common divisor (GCD) of the absolute values of the numerator and denominator. Also, remember that the denominator in standard form must be positive.

  9. Q9.hard

    Arrange the following rational numbers in ascending order: -5/7, -1/2, -3/4, -13/14.
    1. A)A) -13/14, -5/7, -3/4, -1/2
    2. B)B) -1/2, -3/4, -5/7, -13/14
    3. C)C) -13/14, -3/4, -5/7, -1/2
    4. D)D) -1/2, -5/7, -3/4, -13/14
    Show answer

    Answer: C) -13/14, -3/4, -5/7, -1/2

    Hint: To compare negative rational numbers, first convert them to equivalent fractions with a common positive denominator. Remember that for negative numbers, the one with a larger absolute value is smaller.

These are 9 of the 49 questions available for Rational Numbers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.