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About Rational Numbers — Class 7 IB

Extend number understanding to rational numbers, their ordering, and operations. This topic is part of the IB Class 7 mathematics syllabus (chapter: Unit 1). On this page you can practice 41 questions across three difficulty levels — 1 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

  • Introduction to Rational Numbers
  • Equivalent Rational Numbers and Simplification
  • Adding and Subtracting Rational Numbers
  • Multiplying and Dividing Rational Numbers
  • Converting, Ordering, and Density Property

Interactive lesson · about 90 minutes · checkpoint question after every unit

Rational Numbers — solved examples for Class 7 IB

Example 1easy

The number line below shows points P, Q, R, and S. Which point correctly represents the fraction 3/4?
  1. A)P
  2. B)Q
  3. C)R
  4. D)S

Step-by-step solution

  1. Identify the total number of equal segments between 0 and 1. There are 4 segments.
    Segments=4Segments = 4
  2. Each segment represents 1/4 of the whole. Count 3 segments from 0.
    PointRisatthe3rdmarkoutof4,representing3/4.Point R is at the 3rd mark out of 4, representing 3/4.
  3. Therefore, point R correctly represents 3/4.

Answer: R

Example 2medium

A point P is located on a number line between 0 and 1. If the line segment from 0 to 1 is divided into 8 equal parts, and P is at the 5th mark from 0, what rational number does point P represent?
  1. A)3/8
  2. B)4/8
  3. C)5/8
  4. D)7/8

Step-by-step solution

  1. The entire segment from 0 to 1 is divided into 8 equal parts, so each part represents 1/8 of the whole.
  2. Point P is at the 5th mark from 0. This means it represents 5 of these 8 equal parts.
    5×(1/8)=5/85 × (1/8) = 5/8
  3. Therefore, the rational number represented by point P is 5/8.

Answer: 5/8

Example 3hard

Points A, B, C, and D are placed on a number line such that the distance between A and B is 2/3 of the distance between C and D. If A is at 1/6, B is at 5/6, and D is at 3, and C is to the left of D, what is the coordinate of C?
  1. A)A. 11/6
  2. B)B. 2
  3. C)C. 5/3
  4. D)D. 13/6

Step-by-step solution

  1. Calculate distance AB: d(A,B) = 5/6 - 1/6 = 4/6 = 2/3.
  2. Use the ratio to find distance CD: d(A,B) = (2/3) × d(C,D) => 2/3 = (2/3) × d(C,D) => d(C,D) = 1.
  3. Since D is at 3 and C is to the left of D, C = D - d(C,D) = 3 - 1 = 2.

Answer: B. 2

Practice questions on Rational Numbers

  1. Q1.medium

    A chef is scaling a recipe. If 3/4 cup of flour is needed for a small batch, which of the following represents an equivalent amount for a larger batch?
    1. A)6/8 cups
    2. B)5/6 cups
    3. C)9/10 cups
    4. D)12/15 cups
    Show answer

    Answer: 6/8 cups

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

  2. Q2.medium

    Elena spent 1/3 of an hour travelling to school and then 1/4 of an hour travelling to her sports practice in Berlin. What is the total fraction of an hour she spent travelling?
    1. A)2/7
    2. B)5/12
    3. C)1/7
    4. D)7/12
    Show answer

    Answer: 7/12

    Hint: Remember to find a common denominator before adding fractions with different denominators.

  3. Q3.medium

    Calculate the value of 7/8 - 1/2.
    1. A)5/8
    2. B)3/8
    3. C)6/6
    4. D)1/4
    Show answer

    Answer: 3/8

    Hint: To subtract fractions with different denominators, first find a common denominator.

  4. Q4.hard

    If the fraction (3x - 1) / (x + 2) is equivalent to 5/3, what is the value of x?
    1. A)A. 11/4
    2. B)B. 13/4
    3. C)C. 13/8
    4. D)D. 11/8
    Show answer

    Answer: B. 13/4

    Hint: Set up a proportion and use cross-multiplication to solve for x.

  5. Q5.hard

    A baker in Paris used 3/8 of a bag of flour on Monday and 1/6 of the same bag on Tuesday. On Wednesday, they used an additional 1/3 of the *remaining* flour. What fraction of the original bag of flour is left?
    1. A)A. 5/12
    2. B)B. 11/36
    3. C)C. 7/24
    4. D)D. 1/3
    Show answer

    Answer: B. 11/36

    Hint: First, find the total flour used on Monday and Tuesday. Then calculate the remaining flour before Wednesday's use.

  6. Q6.hard

    A rectangular plot of land in rural Germany has its length reduced by 1/4 and its width by 1/5. What fraction of the original area remains?
    1. A)A. 1/20
    2. B)B. 3/5
    3. C)C. 3/4
    4. D)D. 9/20
    Show answer

    Answer: B. 3/5

    Hint: If the length is reduced by 1/4, what fraction of the original length remains? Do the same for the width.

These are 6 of the 41 questions available for Rational Numbers. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.