NCERT Solutions for Class 7th Maths Chapter 8 Working with Fractions
Updated on 2026-09-19
About this chapter
Multiplying by a fraction is done in two steps: divide the multiplicand by the multiplier's denominator, then multiply by its numerator. Drawing the two fractions as the sides of a rectangle inside a unit square shows why area = product of the sides . Brahmagupta's formula: a ⁄ b × c ⁄ d = a × c ⁄ b × d . Common factors may be cancelled before multiplying. The product is not always bigger: multiplying by a number between 0 and 1 makes it smaller; multiplying by a number greater than 1 makes it bigger. The reciprocal of a ⁄ b is b ⁄ a ; a fraction times its reciprocal is 1. To divide, multiply by the divisor's reciprocal. Dividing by a number between 0 and 1 makes the quotient larger than the dividend — which is why 6 ÷ 1 ⁄ 4 = 24.
- Multiplication of Fractions
- Worked Examples
- Multiplying Two Fractions
- Multiplying Fractional Units
- Division of Fractions
- Dividend, Divisor and the Quotient
- Some Problems Involving Fractions
- Fractional Relations
- A Dramma-tic Donation
- Chapter Exercises
Quick revision
| Idea | What it means | Example from the chapter | Key result |
|---|---|---|---|
| Whole number × fraction | Repeated addition of the fraction | 3 × 1/4 | 3/4 |
| Fraction × whole number | Divide by the denominator, multiply by the numerator | 2/5 × 3 | 6/5 |
| Unit square model | The whole is cut into rows × columns | 1/2 × 1/4 | 1/8 |
| Fractional units | 1 over the product of denominators | 1/b × 1/d | 1/(b × d) |
| Brahmagupta's product rule | Numerators × numerators, denominators × denominators | 5/12 × 7/18 | 35/216 |
| Cancelling (apavartana) | Divide out common factors first | 12/7 × 5/24 | 5/14 |
| Area of a rectangle | Fractional sides, area is their product | sides 3¾ ft and 9⅗ ft | 36 sq ft |
| Size of the product | Depends on whether the numbers are below or above 1 | 3/4 × 2/5 | 3/10, less than both |
| Reciprocal (व्युत्क्रम) | Turn the fraction upside down | 3/5 | 5/3, and 3/5 × 5/3 = 1 |
| Division rule | Multiply the dividend by the divisor's reciprocal | 2/3 ÷ 3/5 | 10/9 |
| Small divisor | Dividing by a fraction below 1 makes the answer bigger | 6 ÷ 1/4 | 24 |
| Order does not matter | The rectangle is the same if you swap its sides | 1/2 × 1/4 = 1/4 × 1/2 | 1/8 |
Exercises
- In-text Questions — Multiplication of Fractions Page 173–175
- In-text Questions — Worked Examples Page 176
- Figure it Out — Multiplication of Fractions Page 176–177
- Multiplying Two Fractions — In-text Questions Page 177–179
- Connection between the Area of a Rectangle and Fraction Multiplication — In-text Questions Page 180
- Multiplying Fractional Units — Figure it Out Page 180–181
- Multiplying Numerators and Denominators; Simplifying to Lowest Form — In-text Questions Page 181–182
- Figure it Out — Multiplication of Fractions Page 183–184
- Is the Product Always Greater than the Numbers Multiplied? / Order of Multiplication — In-text Questions Page 184–186
- In-text Questions — Division of Fractions Page 186–188
- Dividend, Divisor and the Quotient — In-text Questions Page 189
- In-text Questions — Some Problems Involving Fractions Page 190–191
- Fractional Relations — Math Talk Page 192–193
- A Dramma-tic Donation — In-text Questions Page 193–194
- Chapter Exercises — Figure it Out Page 196–198
- Chess Puzzles — Puzzle Time Page 199