Loading...

About Rational Numbers — Class 7 ICSE

Explore the set of rational numbers, their properties, and representation on the number line. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 3). On this page you can practice 58 questions across three difficulty levels — 19 easy, 20 medium, and 19 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
  • Properties of Rational Numbers
  • Operations on Rational Numbers
  • Representation and Comparison of Rational Numbers
  • Equivalent, Standard Form, and Density of Rational Numbers

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

Rational Numbers — solved examples for Class 7 ICSE

Example 1easy

Which of the following statements about rational numbers is TRUE?
  1. A)A. All integers are rational numbers, but not all rational numbers are integers.
  2. B)B. All rational numbers are integers, but not all integers are rational numbers.
  3. C)C. All fractions are rational numbers, but not all rational numbers are fractions.
  4. D)D. The denominator of a rational number can be zero.

Step-by-step solution

  1. A rational number is defined as a number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.
  2. Every integer 'n' can be written as n/1, making it a rational number. However, rational numbers like 1/2 are not integers.
  3. While many fractions are rational numbers, some rational numbers (like 5/1) are integers and not typically called fractions. Also, the definition of a fraction usually implies a positive numerator and denominator, which is not always true for rational numbers.
  4. The denominator of a rational number cannot be zero, as division by zero is undefined.

Answer: A. All integers are rational numbers, but not all rational numbers are integers.

Example 2medium

Which of the following numbers is NOT a rational number?
  1. A)A) 0/5
  2. B)B) -3/7
  3. C)C) 9/0
  4. D)D) 4

Step-by-step solution

  1. A rational number is defined as a number that can be expressed in the form p/q, where p and q are integers and q is not equal to zero.
  2. Options A (0/5), B (-3/7), and D (4, which can be written as 4/1) all satisfy the condition q ≠ 0, making them rational numbers.
  3. In option C (9/0), the denominator q is 0. Division by zero is undefined, therefore 9/0 is not a rational number.

Answer: C) 9/0

Example 3hard

For what integer value of 'k' is the expression (5k - 10) / (2k + 6) NOT a rational number?
  1. A)2
  2. B)-3
  3. C)0
  4. D)5

Step-by-step solution

  1. A rational number is defined as a number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.
  2. For the given expression (5k - 10) / (2k + 6) to NOT be a rational number, its denominator must be zero.
  3. Set the denominator to zero and solve for k: 2k + 6 = 0.
  4. 2k = -6, which implies k = -3. If k = -3, the denominator becomes 0, making the expression undefined and thus not a rational number.

Answer: -3

Practice questions on Rational Numbers

  1. Q1.easy

    Rohan was asked to find an equivalent rational number for -3/7 with a denominator of 28. His solution was -12/28. Is his solution correct, and if so, why?
    1. A)A. Yes, because he multiplied both the numerator and the denominator by 4.
    2. B)B. No, because he should have multiplied the numerator by -4.
    3. C)C. Yes, because he divided both the numerator and the denominator by -4.
    4. D)D. No, because the denominator should have been -28.
    Show answer

    Answer: A. Yes, because he multiplied both the numerator and the denominator by 4.

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

  2. Q2.easy

    Which of the following rational numbers is in its standard (simplest) form?
    1. A)A. -8/12
    2. B)B. 15/-25
    3. C)C. -7/13
    4. D)D. 18/27
    Show answer

    Answer: C. -7/13

    Hint: A rational number is in its standard form if its denominator is positive and the only common factor between its numerator and denominator is 1.

  3. Q3.easy

    On a number line, point P represents the rational number -5/4. Which of the following statements correctly describes the position of P?
    1. A)A. P is to the right of 0 and between 1 and 2.
    2. B)B. P is to the left of 0 and between -1 and -2.
    3. C)C. P is to the right of 0 and between 0 and 1.
    4. D)D. P is to the left of 0 and between 0 and -1.
    Show answer

    Answer: B. P is to the left of 0 and between -1 and -2.

    Hint: First, determine if the number is positive or negative. Then, convert the improper fraction to a mixed fraction to easily identify its location between two integers.

  4. Q4.medium

    Which of the following rational numbers is equivalent to -4/9?
    1. A)A) -8/18
    2. B)B) 4/-9
    3. C)C) -12/27
    4. D)D) All of the above
    Show answer

    Answer: D) All of the above

    Hint: Equivalent rational numbers are formed by multiplying or dividing both the numerator and the denominator by the same non-zero integer.

  5. Q5.medium

    Reduce the rational number -45/75 to its standard form.
    1. A)A) -3/5
    2. B)B) -9/15
    3. C)C) 3/-5
    4. D)D) -5/3
    Show answer

    Answer: A) -3/5

    Hint: To reduce a rational number to its standard form, divide both the numerator and the denominator by their highest common factor (HCF).

  6. Q6.medium

    Arrange the following rational numbers in ascending order: 2/3, -1/2, 5/6, -3/4.
    1. A)A) -3/4, -1/2, 2/3, 5/6
    2. B)B) -1/2, -3/4, 2/3, 5/6
    3. C)C) -3/4, -1/2, 5/6, 2/3
    4. D)D) 5/6, 2/3, -1/2, -3/4
    Show answer

    Answer: A) -3/4, -1/2, 2/3, 5/6

    Hint: To compare rational numbers, find the Least Common Multiple (LCM) of their denominators and convert them to equivalent fractions with this common denominator.

  7. Q7.hard

    If x/(-9) is an equivalent rational number to (-24)/27, and y/(-12) is equivalent to 7/3, find the value of (x - y).
    1. A)-20
    2. B)20
    3. C)-36
    4. D)36
    Show answer

    Answer: 36

    Hint: Remember that equivalent rational numbers have the same value. Use cross-multiplication or simplification to find the values of x and y separately.

  8. Q8.hard

    Which of the following rational numbers is the smallest: -7/9, -5/6, -11/12, -2/3?
    1. A)-7/9
    2. B)-5/6
    3. C)-11/12
    4. D)-2/3
    Show answer

    Answer: -11/12

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

  9. Q9.hard

    A rational number 'P' is represented by a point on the number line that is exactly equidistant from -5/8 and 3/4. What is the value of P?
    1. A)1/16
    2. B)-1/16
    3. C)1/8
    4. D)-1/8
    Show answer

    Answer: 1/16

    Hint: A point equidistant from two other points on a number line is their midpoint. The midpoint of two numbers 'a' and 'b' is given by (a + b) / 2.

These are 9 of the 58 questions available for Rational Numbers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.