Class 7 Maths Working with Fractions Notes

Class 7 Maths Working with Fractions Notes

1. Introduction

Fractions are an essential part of mathematics. This chapter helps students:

  • Understand different types of fractions
  • Learn operations with fractions
  • Apply fractions in real-life situations

2. Key Concepts

2.1 Types of Fractions

  1. Proper Fraction – Numerator < Denominator (e.g., 3/4)
  2. Improper Fraction – Numerator ≥ Denominator (e.g., 7/5)
  3. Mixed Fraction – Whole number + Proper fraction (e.g., 2 1/3)
  4. Like Fractions – Fractions with same denominator (e.g., 3/7, 5/7)
  5. Unlike Fractions – Fractions with different denominators (e.g., 2/3, 3/4)

2.2 Conversion

  • Improper to Mixed Fraction: Divide numerator by denominator → quotient + remainder/denominator
  • Mixed to Improper Fraction: Multiply whole number by denominator + numerator → numerator of improper fraction

2.3 Operations with Fractions

2.3.1 Addition

  • Like Fractions: Add numerators, keep denominator same an+bn=a+bn\frac{a}{n} + \frac{b}{n} = \frac{a+b}{n}na​+nb​=na+b​
  • Unlike Fractions: Find LCM of denominators, convert to like fractions, then add

2.3.2 Subtraction

  • Same as addition, subtract numerators

2.3.3 Multiplication

ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}ba​×dc​=b×da×c​

2.3.4 Division

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}ba​÷dc​=ba​×cd​

2.4 Simplification

  • Always simplify fractions to their lowest terms by dividing numerator and denominator by HCF.

2.5 Word Problems

  • Fractions are used in real-life problems: recipes, distances, sharing, parts of shapes, etc.

Example:

  • A tank is 2/3 full. If 1/4 of its content is removed, what fraction remains? Remaining=23−23×14=23−212=8−212=612=12\text{Remaining} = \frac{2}{3} – \frac{2}{3} \times \frac{1}{4} = \frac{2}{3} – \frac{2}{12} = \frac{8-2}{12} = \frac{6}{12} = \frac{1}{2}Remaining=32​−32​×41​=32​−122​=128−2​=126​=21​

3. Tips for Working with Fractions

  1. Always convert mixed fractions to improper fractions before multiplication/division.
  2. Find LCM for adding or subtracting unlike fractions.
  3. Simplify at each step to avoid large numbers.
  4. Draw diagrams to visualize fractions when solving word problems.

4. Summary Table

OperationRule
Addition (like)Add numerators, keep denominator same
Addition (unlike)Convert to like fractions using LCM, then add
SubtractionSame as addition
MultiplicationMultiply numerators × numerators, denominators × denominators
DivisionMultiply by reciprocal of second fraction
SimplificationDivide numerator and denominator by HCF

Questions

Section A: Multiple Choice Questions (MCQs) – 10 Questions

  1. Which of the following is a proper fraction?
    a) 7/5
    b) 3/4
    c) 5/5
    d) 6/3
  2. Which fraction is an improper fraction?
    a) 2/7
    b) 5/3
    c) 1/2
    d) 3/8
  3. Convert 7/4 into a mixed fraction:
    a) 1 3/4
    b) 2 3/4
    c) 1 1/4
    d) 2 1/4
  4. Which of the following are like fractions?
    a) 2/5, 3/7
    b) 4/9, 7/9
    c) 1/2, 2/3
    d) 3/4, 5/6
  5. Add: 3/8 + 1/8 = ?
    a) 1/2
    b) 4/8
    c) 3/16
    d) 1/4
  6. Subtract: 7/10 − 2/5 = ?
    a) 1/10
    b) 3/10
    c) 1/2
    d) 5/10
  7. Multiply: 2/3 × 3/4 = ?
    a) 1/2
    b) 1/3
    c) 3/7
    d) 6/12
  8. Divide: 5/6 ÷ 2/3 = ?
    a) 5/4
    b) 2/5
    c) 3/4
    d) 4/5
  9. The sum of two like fractions 3/11 + 5/11 is:
    a) 8/11
    b) 15/22
    c) 1
    d) 1/2
  10. Which of the following fractions is in lowest terms?
    a) 6/9
    b) 15/20
    c) 8/12
    d) 7/9

Section B: Fill in the Blanks – 10 Questions

  1. 5/4 as a mixed fraction is _______.
  2. 3 2/5 as an improper fraction is _______.
  3. The LCM of denominators is used while adding _______ fractions.
  4. The HCF of numerator and denominator is used to _______ fractions.
  5. 7/8 + 1/8 = _______.
  6. 9/10 − 3/5 = _______.
  7. 4/7 × 2/3 = _______.
  8. 5/6 ÷ 5/12 = _______.
  9. Proper fractions have numerator _______ denominator.
  10. Improper fractions have numerator _______ denominator.

Section C: Short Answer Questions – 10 Questions

  1. Convert 11/6 into a mixed fraction.
  2. Convert 2 3/4 into an improper fraction.
  3. Add 2/5 + 3/10.
  4. Subtract 7/12 − 1/4.
  5. Multiply 3/8 × 4/5.
  6. Divide 7/9 ÷ 2/3.
  7. Simplify 12/18 to lowest terms.
  8. Write a word problem that can be solved using fraction addition.
  9. Write a word problem that can be solved using fraction multiplication.
  10. Draw a pie chart showing 3/8 of a cake eaten.

Section D: Long Answer / Problem-Solving – 10 Questions

  1. A tank is 3/4 full of water. If 1/3 of water is removed, what fraction remains?
  2. Ramesh ate 2/5 of a pizza, and Sita ate 1/4. What fraction of pizza was eaten in total?
  3. Divide 7/8 of chocolate equally among 4 friends. How much does each get?
  4. Multiply 5/6 by 3/7 and simplify the answer.
  5. A ribbon of 3 1/2 m is cut into pieces of 1/4 m. How many pieces are obtained?
  6. Add 3 2/3 + 2 3/4 and express as a mixed fraction.
  7. Subtract 5 5/6 − 3 7/12 and simplify the answer.
  8. The sum of two fractions is 7/10. If one fraction is 3/5, find the other fraction.
  9. A recipe needs 3/4 cup sugar and 1/3 cup oil. What is the total quantity of ingredients?
  10. A tank is 5/6 full. If 1/2 of it is used, how much remains?

Section E: Application / Higher-Order Thinking – 10 Questions

  1. A rope of 7 m is cut into 3 equal parts. What fraction of rope is each part?
  2. A garden has 2/5 rose plants and 1/3 tulip plants. What fraction of garden is covered by these plants?
  3. A jug contains 5/8 litre of juice. If 2/5 litre is poured out, how much remains?
  4. A student read 3/7 of a book on Monday and 2/7 on Tuesday. What fraction of the book is left?
  5. A container has 2/3 litre milk. How much milk will remain if 1/4 of it is used?
  6. A ribbon of 9 m is cut into pieces of 2/3 m. How many pieces can be made?
  7. A baker uses 1 1/2 kg flour and 2/3 kg sugar. Total weight used = ?
  8. A class completes 5/6 of a project on Monday and 1/12 on Tuesday. Fraction of project left = ?
  9. Two friends share 7/8 kg chocolates equally. How much does each get?
  10. A tank is 3/5 full of water. 2/3 of it is used for irrigation. Find remaining fraction.

Answers – Chapter 8: Working with Fractions

Section A: MCQs – Answers

  1. b) 3/4 – Numerator < Denominator → proper fraction.
  2. b) 5/3 – Numerator > Denominator → improper fraction.
  3. a) 1 3/4 – Divide 7 ÷ 4 → 1 remainder 3 → 1 3/4.
  4. b) 4/9, 7/9 – Same denominator → like fractions.
  5. b) 4/8 = 1/2 – Add numerators, keep denominator.
  6. b) 3/10 – Convert 2/5 = 4/10 → 7/10 − 4/10 = 3/10.
  7. a) 1/2 – (2×3)/(3×4) = 6/12 = 1/2.
  8. a) 5/4 – 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4.
  9. a) 8/11 – Same denominator → add numerators.
  10. d) 7/9 – Already in lowest terms.

Section B: Fill in the Blanks – Answers

  1. 1 1/4 – 5 ÷ 4 = 1 remainder 1.
  2. 13/5 – 2×5 + 3 = 13/5.
  3. Unlike fractions.
  4. Simplify fractions.
  5. 1 – 7/8 + 1/8 = 8/8 = 1.
  6. 3/10 – Convert 3/5 = 6/10 → 9/10 − 6/10 = 3/10.
  7. 8/21 – Multiply numerators and denominators: 4×2 / 7×3 = 8/21.
  8. 2 – 5/6 ÷ 5/12 = 5/6 × 12/5 = 2.
  9. Less than
  10. Greater than or equal to

Section C: Short Answer Questions – Answers

  1. 11/6 → 1 5/6
  2. 2 3/4 → 11/4
  3. 2/5 + 3/10 → LCM=10 → 4/10+3/10 = 7/10
  4. 7/12 − 1/4 → 1/4 = 3/12 → 7/12−3/12 = 4/12 = 1/3
  5. 3/8 × 4/5 = 12/40 = 3/10
  6. 7/9 ÷ 2/3 = 7/9 × 3/2 = 21/18 = 7/6 = 1 1/6
  7. 12/18 → divide numerator & denominator by 6 → 2/3
  8. Example: “Ramesh ate 2/5 of a cake and Sita ate 1/5. How much cake is eaten in total?” → 2/5+1/5=3/5
  9. Example: “A ribbon 3/4 m long is cut into 1/2 m pieces. How many pieces?” → 3/4 ÷ 1/2 = 3/2 = 1 1/2 pieces
  10. Pie chart: Shade 3/8 portion of circle → visualize remaining 5/8

Section D: Long Answer / Problem-Solving – Answers

  1. 3/4 − 1/3 of 3/4 → 1/3×3/4=1/4 → 3/4 − 1/4 = 2/4 = 1/2
  2. 2/5 + 1/4 → LCM=20 → 8/20+5/20=13/20 of pizza eaten
  3. 7/8 ÷ 4 = 7/32 each
  4. 5/6 × 3/7 = 15/42 = 5/14
  5. 3 1/2 = 7/2 → 7/2 ÷ 1/4 = 7/2 × 4/1 = 28/2 = 14 pieces
  6. 3 2/3 + 2 3/4 → 11/3 + 11/4 → LCM=12 → 44/12+33/12=77/12=6 5/12
  7. 5 5/6 − 3 7/12 → 35/6−43/12=70/12−43/12=27/12=2 3/12=2 1/4
  8. Total sum 7/10 − 3/5 → 3/5=6/10 → 7/10−6/10=1/10
  9. 3/4+1/3 → LCM=12 → 9/12+4/12=13/12=1 1/12 cup
  10. 5/6 × (1−1/2) = 5/6 × 1/2 = 5/12 remains

Section E: Application / Higher-Order Thinking – Answers

  1. 7 m ÷ 3 → each = 7/3 m = 2 1/3 m
  2. 2/5 + 1/3 → LCM=15 → 6/15 + 5/15 = 11/15 of garden
  3. 5/8 − 2/5 of 5/8 → 2/5×5/8=2/8=1/4 → 5/8−1/4=5/8−2/8=3/8 litre remains
  4. 3/7 + 2/7 = 5/7 read → remaining = 1−5/7=2/7
  5. 2/3 − 1/4 of 2/3 = 2/3 − 2/12=8/12−2/12=6/12=1/2 litre remains
  6. 9 ÷ 2/3 → 9 × 3/2 = 27/2 = 13 1/2 pieces
  7. 1 1/2 + 2/3 → 3/2 + 2/3 → LCM=6 → 9/6+4/6=13/6=2 1/6 kg
  8. 5/6 + 1/12 → LCM=12 → 10/12 +1/12=11/12 done → remaining 1−11/12=1/12
  9. 7/8 ÷ 2 = 7/16 kg each
  10. 3/5 − 2/3×3/5 = 3/5 − 6/15=9/15−6/15=3/15=1/5 remains