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About Fractions Operations — Class 7 CBSE

Multiply and divide fractions and mixed numbers; solve word problems. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 8). On this page you can practice 61 questions across three difficulty levels — 20 easy, 21 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 36-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Fractions Operations

  • Understanding Fractions: The Building Blocks
  • Adding and Subtracting Fractions
  • Multiplying Fractions: Finding 'Parts Of'
  • Dividing Fractions: Sharing and Grouping
  • Mastering Fraction Operations: Putting It All Together

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

Fractions Operations — solved examples for Class 7 CBSE

Example 1easy

Which statement correctly describes a proper fraction?
  1. A)Its numerator is greater than its denominator.
  2. B)Its numerator is equal to its denominator.
  3. C)Its numerator is less than its denominator.
  4. D)Its denominator is zero.

Step-by-step solution

  1. A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).
  2. For example, 1/2, 3/4, and 5/7 are all proper fractions because their numerators are less than their denominators.
  3. Options A describes an improper fraction, B describes a fraction equal to 1, and D describes an undefined expression.

Answer: Its numerator is less than its denominator.

Example 2medium

What is the sum of 3 1/4 and 2 5/6?
  1. A)5 3/12
  2. B)6 1/12
  3. C)5 6/10
  4. D)6 3/12

Step-by-step solution

  1. Convert mixed fractions to improper fractions: 3 1/4 = (3×4+1)/4 = 13/4 and 2 5/6 = (2×6+5)/6 = 17/6.
  2. Find the LCM of the denominators (4 and 6), which is 12.
  3. Convert fractions to equivalent fractions with denominator 12: 13/4 = (13×3)/(4×3) = 39/12 and 17/6 = (17×2)/(6×2) = 34/12.
  4. Add the equivalent fractions: 39/12 + 34/12 = 73/12. Convert back to mixed fraction: 73 ÷ 12 = 6 with a remainder of 1. So, 6 1/12.

Answer: 6 1/12

Example 3hard

A large tank was 5/6 full of water. A family used 1/3 of the total water for their daily needs. Later, a delivery added 1/4 of the tank's capacity to it. Finally, another 1/2 of the *current* amount of water was used for gardening. What fraction of the tank is now filled with water?
  1. A)7/12
  2. B)1/4
  3. C)5/8
  4. D)3/8

Step-by-step solution

  1. Initial water in tank: 5/6 of the total capacity.
  2. Water remaining after daily use (1/3 of total): 5/6 - 1/3 = 5/6 - 2/6 = 3/6 = 1/2 of the total capacity.
  3. Water after delivery added (1/4 of total): 1/2 + 1/4 = 2/4 + 1/4 = 3/4 of the total capacity.
  4. Water remaining after gardening (1/2 of the *current* amount): 3/4 - (1/2 × 3/4) = 3/4 - 3/8 = 6/8 - 3/8 = 3/8 of the total capacity.
  5. So, 3/8 of the tank is now filled with water.

Answer: 3/8

Practice questions on Fractions Operations

  1. Q1.easy

    Ravi attempted to add 1/3 and 1/2 as follows: 1/3 + 1/2 = (1+1)/(3+2) = 2/5. What was Ravi's mistake?
    1. A)He did not find a common denominator before adding.
    2. B)He added the numerators incorrectly.
    3. C)He added the denominators incorrectly.
    4. D)He subtracted the fractions instead of adding them.
    Show answer

    Answer: He did not find a common denominator before adding.

    Hint: Remember that fractions can only be added or subtracted directly if they have the same denominator.

  2. Q2.easy

    Rohan had 5/6 of a pizza. He ate 1/3 of the pizza. How much pizza is left?
    1. A)2/3
    2. B)1/6
    3. C)1/2
    4. D)5/18
    Show answer

    Answer: 1/2

    Hint: To find out how much is left, you need to subtract the amount eaten from the initial amount. Remember to find a common denominator.

  3. Q3.easy

    Imagine a rectangular chocolate bar divided into 3 equal rows and 4 equal columns. If you shade 2 rows and then shade 3 columns, the region that is double-shaded represents the product of which two fractions?
    1. A)2/3 × 3/4
    2. B)3/2 × 4/3
    3. C)1/3 × 1/4
    4. D)2/4 × 3/3
    Show answer

    Answer: 2/3 × 3/4

    Hint: Think about what fraction of the whole the '2 rows' represent and what fraction the '3 columns' represent.

  4. Q4.medium

    Subtract 2 1/4 from 5 1/2.
    1. A)2 1/4
    2. B)3 1/2
    3. C)2 3/4
    4. D)3 1/4
    Show answer

    Answer: 3 1/4

    Hint: Start by converting the mixed numbers to improper fractions, then find a common denominator before subtracting.

  5. Q5.medium

    Find the product of 2/3 and 6/7.
    1. A)1/7
    2. B)2/7
    3. C)4/7
    4. D)12/21
    Show answer

    Answer: 4/7

    Hint: Multiply the numerators and the denominators. Look for opportunities to simplify by cancelling common factors.

  6. Q6.medium

    Divide 5/6 by 2 1/2.
    1. A)1/2
    2. B)2/3
    3. C)1/6
    4. D)1/3
    Show answer

    Answer: 1/3

    Hint: When dividing fractions, remember to multiply the first fraction by the reciprocal of the second fraction. Don't forget to convert mixed numbers first.

  7. Q7.hard

    Evaluate the expression: (3 1/2 + 2/3) × 1 1/5 - 1/6
    1. A)4 1/2
    2. B)3 5/6
    3. C)4 5/6
    4. D)5 1/6
    Show answer

    Answer: 4 5/6

    Hint: Remember the order of operations (BODMAS/PEMDAS). Convert all mixed numbers to improper fractions before performing calculations.

  8. Q8.hard

    A painter used 2/5 of his paint supply on Monday. On Tuesday, he used 1/3 of the *remaining* paint. If he had 12 litres of paint left, how many litres did he have initially?
    1. A)30 litres
    2. B)25 litres
    3. C)36 litres
    4. D)20 litres
    Show answer

    Answer: 30 litres

    Hint: Work backwards from the final remaining amount. First, figure out what fraction of the paint was left after Tuesday's use, then after Monday's use, relative to the original amount.

  9. Q9.hard

    Let A = 7/8 and B be a proper fraction (i.e., 0 < B < 1). Which of the following statements is always true?
    1. A)A × B > A
    2. B)A × B < A
    3. C)A × B = A
    4. D)A × B = 1
    Show answer

    Answer: A × B < A

    Hint: Consider what happens when you multiply a number by a fraction that is less than 1. Does the number increase or decrease?

These are 9 of the 61 questions available for Fractions Operations. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.