Brackets and Terms

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

Learn

One expression, two answers? Ishaan brings 30 marbles; Neel brings 5 bags with 4 marbles each. Ishaan writes 30 + 5 × 4. Someone adds first: 35 × 4 = 140. Someone multiplies first: 30 + 20 = 50. From the story, 50 is right. Just like commas in a sentence, maths needs rules so an expression means only one thing.

30 + (5 × 4) = 30 + 20 = 50

Brackets say "do this first". You buy a pen for ₹15 and a notebook for ₹56 and pay with ₹100. The change is 100 − (15 + 56) = 100 − 71 = ₹29. Without brackets, 100 − 15 + 56 would give 141, more than you paid, which makes no sense!

100 − (15 + 56) = 29

Terms are the parts of an expression joined by +. To find them, change every subtraction into adding the inverse: 83 − 14 = 83 + (−14), so the terms are 83 and −14. A product or division with no + inside is one term: in 2 − 10 + 4 × 6 the terms are 2, −10 and 4×6.

2 − 10 + 4 × 6 = 2 + (−10) + 24 = 16

The rule for evaluating: first work out anything in brackets, then work out each term (multiplications and divisions), then add all the terms. So 30 + 5 × 4 = 30 + 20 = 50, and 5 × (3 + 2) + 7 × 8 + 3 = 25 + 56 + 3 = 84.

5 × (3 + 2) + 7 × 8 + 3 = 84

Explore: one term or more?

1. Sort each expression.

Remember

• Brackets first; then work out each term; then add the terms.
• Terms are the parts joined by +; subtracting = adding the inverse: 83 − 14 = 83 + (−14).

Quick check

What is the value of 39 − 2 × 6 + 11?

1. 38
2. 232
3. 62
4. 16

Think about it

33 children play a game; the teacher calls "groups of 5". Write an expression for the children, using groups and those left over.

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.