Some Problems Involving Fractions

Class 7 Maths · Chapter 8: Working with Fractions · NCERT Ganita Prakash section 8.3

Learn

Meher makes 5 cups of tea with 1/4 litre of milk. Each cup gets 1/4 ÷ 5 = 1/4 × 1/5 = 1/20 litre. A tank fills 7/10 in an hour; in 3/4 hour it fills 3/4 × 7/10 = 21/40. Write the situation as a multiplication or division, then use the rules.

1/4 ÷ 5 = 1/20

From the Śulbasūtra (around 800 BCE): how many square bricks of side 1/5 unit cover 7 1/2 square units? Each brick has area 1/5 × 1/5 = 1/25. So we need 15/2 ÷ 1/25 = 15/2 × 25 = 375/2 bricks, that is 187 1/2. These ancient Indian geometry texts used fractions freely.

15/2 ÷ 1/25 = 375/2

Fountains (from Pṛthūdakasvāmī, around 860 CE): four fountains fill a tank in 1, 1/2, 1/4 and 1/5 of a day. In one day they fill it 1, 2, 4 and 5 times: together 12 times a day. So together they need 1/12 day.

1 + 2 + 4 + 5 = 12 → 1/12 day

A joke from Līlāvatī (Bhāskara II, 1150 CE): a miser gave a beggar 1/4 of 1/16 of 1/5 of 1/2 of 2/3 of 3/4 of a dramma (a silver coin worth 1280 cowrie shells). Multiply: the product is 6/7680 = 1/1280 dramma, exactly one cowrie! "Of" always means multiply.

1/4 × 1/16 × 1/5 × 1/2 × 2/3 × 3/4 = 1/1280

Explore: multiply or divide?

1. Sort each problem by the operation it needs.

Remember

• "Of" means multiply; sharing equally means divide.
• Rates: something done in 1/k of a day is done k times in a day.

Quick check

Four saplings stand in a row, 3/4 m apart. How far is the first from the last?

1. 9/4 m
2. 3 m
3. 3/4 m
4. 12/4 m

Think about it

A road takes 1/6 of a farm. The owner gives half of the rest to her daughter and 1/3 of the rest to her son. What part does she keep?

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.