Addition and Subtraction of Decimals

Class 7 Maths · Chapter 3: A Peek Beyond the Point · NCERT Ganita Prakash section 3.7

Learn

Zoya needs 2.7 m of cloth for a kurta and her sister 3.5 m for a skirt. Total: line up the points and add as usual: 7 tenths + 5 tenths = 12 tenths = 1 unit and 2 tenths, carry 1 → 6.2 m. The difference 3.5 − 2.7: exchange 1 unit for 10 tenths: 15 − 7 = 8 tenths → 0.8 m.

2.7 + 3.5 = 6.2 · 3.5 − 2.7 = 0.8

Longer numbers: 75.345 + 86.691 = 162.036. Thousandths: 5 + 1 = 6; hundredths: 4 + 9 = 13 → write 3, carry 1; tenths: 3 + 6 + 1 = 10 → write 0, carry 1; and so on. If the numbers have different lengths, add zeros: 0.934 + 0.6 = 0.934 + 0.600 = 1.534.

75.345 + 86.691 = 162.036

Decimal sequences: 4.4, 4.8, 5.2, 5.6, 6.0 … adds 0.4 each time; next come 6.4, 6.8, 7.2. And 5, 4.95, 4.90 … subtracts 0.05. Try them in your head!

4.4, 4.8, 5.2, 5.6, 6.0, 6.4 …

Estimate first: for 25.936 + 8.202, the sum is more than 25 + 8 = 33 (the whole parts) but less than 33 + 2 = 35, because each decimal part is less than 1. The exact sum is 34.138, which fits. A quick range like this catches mistakes such as misplaced points.

33 < 25.936 + 8.202 = 34.138 < 35

Explore: check the sums.

1. Match each sum or difference to its answer.

Remember

• Line up the decimal points (fill with zeros), then add or subtract as with whole numbers.
• Estimate with the whole parts: the sum lies between (sum of whole parts) and (that + 2).

Quick check

17 − 16.198 = ?

1. 0.802
2. 1.802
3. 0.198
4. 1.198

Think about it

Vegetables weigh 0.25 kg, 0.3 kg, 0.5 kg, 0.2 kg and 0.05 kg. What is the total?

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.