NCERT Class 6 Mathematics Textbook for Blind and Visually Impaired Students made Screen Readable by Professor T K Bansal.

Meera bought 6 notebooks from the market and the cost was Rs.10 per notebook. Her sister Seema also bought 7 notebooks of the same type. Find the total money they paid.

Seema calculated the amount like this
6 × 10 + 7 × 10
= 60 + 70
= 130
Answer. Rs.130

Meera calculated the amount like this
6 + 7 =13
and 13 × 10 = 130
Answer. Rs.130

You can see that Seema’s and Meera’s ways to get the answer are a bit different.
But both give the correct result. Why?

Seema says, what Meera has done is 7 + 6 × 10.

Appu points out that 7 + 6 × 10 = 7 + 60 = 67. Thus, this is not what Meera had done. All the three students are confused.

To avoid confusion in such cases we may use brackets. We can pack the numbers 6 and 7 together using a bracket, indicating that the pack is to be treated as a single number. Thus, the answer is found by (6 + 7) × 10 = 13 × 10.

This is what Meera did. She first added 6 and 7 and then multiplied the sum by 10.

This clearly tells us : First, turn everything inside the brackets ( ) into a single number and then do the operation outside which in this case is to multiply by 10.

Try These 1.18

Q1. Write the expressions for each of the following using brackets.
(a) Four multiplied by the sum of nine and two.
(b) Divide the difference of eighteen and six by four.
(c) Forty five divided by three times the sum of three and two.

Q2. Write three different situations for (5 + 8) × 6.
(One such situation is : Sohani and Reeta work for 6 days; Sohani works 5 hours a day and Reeta 8 hours a day. How many hours do both of them work in a week?)

Q3. Write five situations for the following where brackets would be necessary.
(a) 7(8 − 3)
(b) (7 + 2) (10 − 3)

1.4.1 Expanding brackets

Now, observe how use of brackets allows us to follow our procedure systematically. Do you think that it will be easy to keep a track of what steps we have to follow without using brackets?

(i) 7 × 109 = 7 × (100 + 9) = 7 × 100 + 7 × 9 = 700 + 63 = 763

(ii)102 × 103 = (100 + 2) × (100 + 3) = (100 + 2) × 100 + (100 + 2) × 3
= 100 × 100 + 2 × 100 + 100 × 3 + 2 × 3
= 10,000 + 200 + 300 + 6 = 10,000 + 500 + 6
= 10,506

(iii) 17 × 109 = (10 + 7) × 109 = 10 × 109 + 7 × 109
= 10 × (100 + 9) + 7 × (100 + 9)
= 10 × 100 + 10 × 9 + 7 × 100 + 7 × 9
= 1000 + 90 + 700 + 63 = 1,790 + 63
= 1,853