Removing Brackets

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

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Brackets after a minus sign: 200 − (40 + 3). It is easier to take away 40, then take away 3: 200 − 40 − 3 = 157. Both numbers inside are taken away, so 200 − (40 + 3) = 200 − 40 − 3. When a minus sign stands before brackets, every term inside changes sign as the brackets go.

200 − (40 + 3) = 200 − 40 − 3 = 157

Taking away a difference: 500 − (250 − 100) = 500 − 150 = 350. If we took away the whole 250, we would have taken away 100 too many, so we add it back: 500 − 250 + 100. Again the signs inside changed: +250 became −250, and −100 became +100.

500 − (250 − 100) = 500 − 250 + 100 = 350

Brackets after a plus sign: Zoya has 28 shells in one box and 35 in another, then gives away 10 from the second: 28 + (35 − 10) = 28 + 35 − 10 = 53. When brackets follow a plus sign, the terms keep their signs. Don't just memorise: think what the expression means!

28 + (35 − 10) = 28 + 35 − 10 = 53

Tinker the terms: if 53 + (−16) = 37, then 54 + (−16) is 1 more = 38, and 53 + (−15) is also 1 more = 38, because −15 is one more than −16. Change a term by some amount and the sum changes by the same amount. So 207 − 68 = 210 − 71: both numbers went up by 3.

207 − 68 = 210 − 71 = 139

Explore: remove the brackets.

1. Match each expression to the same one without brackets.

Remember

• Minus before brackets: signs inside change (a − (b + c) = a − b − c; a − (b − c) = a − b + c).
• Plus before brackets: signs stay. Changing a term changes the sum by the same amount.

Quick check

Remove the brackets: 27 − (8 + 3) = ?

1. 27 − 8 − 3
2. 27 − 8 + 3
3. 27 + 8 − 3
4. 27 + 8 + 3

Think about it

To subtract 9, a friend always subtracts 10 and adds 1 (36 − 9 = 26 + 1). Does this always work? Why?

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.