Swapping and Grouping

Class 7 Maths · Chapter 2: Arithmetic Expressions · NCERT Ganita Prakash section 2.2

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A drone goes up 6 m and then down 4 m: its height is 6 − 4 = 6 + (−4) = 2 m. Swap the terms: (−4) + 6 = 2, the same. Swapping two terms never changes the sum, even with negative numbers. This is the commutative property of addition.

6 + (−4) = (−4) + 6 = 2

Grouping: in (−7) + 10 + (−11), add the first two first: 3 + (−11) = −8. Or the last two first: (−7) + (−1) = −8. Same answer! Grouping does not change the sum: the associative property. Putting both together, terms can be added in any order.

(−7) + 10 + (−11) = −8 in any order

Why it helps: you added a long list and got 11,749, but forgot the number 9,055. No need to start again: just add it to your total, 11,749 + 9,055 = 20,804, because the order of adding does not matter. Also, add easy pairs first: 37 + 48 + 63 = (37 + 63) + 48 = 148.

37 + 48 + 63 = (37 + 63) + 48 = 148

Order in everyday life: "Wear your cap and your shoes": either order, you look the same. "Wear your socks and your shoes": the order matters! In maths, adding is like the cap and shoes, but subtracting is not: 10 − 3 is 7, while 3 − 10 is −7.

10 − 3 = 7 but 3 − 10 = −7

Explore: does the order matter?

1. Sort each action.

Remember

• Swapping terms or grouping them differently never changes the sum.
• Change subtractions to added negative terms first; then add in any order.

Quick check

Which has the same value as 87 + 46 − 109?

1. 46 − 109 + 87
2. 87 − 46 + 109
3. 87 − (46 + 109)
4. 109 − 87 + 46

Think about it

Add 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + 9 − 10 in a clever way.

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.