Multiplication of Fractions

Class 7 Maths · Chapter 8: Working with Fractions · NCERT Ganita Prakash section 8.1

Learn

Ishaan walks 3 km in an hour, so in 5 hours he walks 5 × 3 = 15 km. His pet tortoise walks only 1/4 km an hour; in 3 hours it walks 3 × 1/4 = 1/4 + 1/4 + 1/4 = 3/4 km. A fraction times a whole number works just like repeated adding.

3 × 1/4 = 3/4

A fraction of an hour: in 1/5 hour Ishaan walks 3 km split into 5 equal parts: 3/5 km. In 2/5 hour, twice that: 6/5 km. So for 2/5 × 3, first divide by the denominator 5, then multiply by the numerator 2. And 1/4 × 1/2: half of a quarter is 1/8.

2/5 × 3 = 6/5

The area picture: take a unit square as the whole. For 3/4 × 2/5, shade 2/5 of it in rows (5 rows), then take 3 of 4 columns of that. The square has 5 × 4 = 20 small parts and 6 are dark: 3/4 × 2/5 = 6/20 = 3/10. A rectangle with fraction sides has area = their product.

3/4 × 2/5 = 6/20 = 3/10

Brahmagupta's rule (628 CE): a/b × c/d = (a × c)/(b × d). Cancel first to keep numbers small: 12/7 × 5/24, divide 12 and 24 by 12 to get 1/7 × 5/2 = 5/14. When both numbers are above 1, the product is bigger than both; when both are between 0 and 1, it is smaller than both; one of each, it lands in between. Order does not matter: a/b × c/d = c/d × a/b.

a/b × c/d = (a × c)/(b × d)

Explore: shade the product.

1. 1/2 × 1/4: half of a quarter. Cut the whole into 8 equal parts and shade the product.
2. 2/3 × 3/4 = 6/12. Cut the whole into 12 parts and shade 6/12.

Remember

• a/b × c/d = (a × c)/(b × d); cancel common factors first.
• Multiplying by a number between 0 and 1 makes a number smaller; by more than 1, bigger.

Quick check

What is 3/4 × 2/5 in lowest form?

1. 3/10
2. 5/9
3. 6/9
4. 8/15

Think about it

Which is heavier: 12/15 of 500 g, or 3/20 of 4 kg?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.