Page 83 - Ganit Kaushal

But if you change the position of the brackets:

(12 + 8) ÷ 2 × 3 = 20 ÷ 2 × 3 = 10 × 3 = 30
3 × (3 – 3) ÷ 3 + 3 = 3 × 0 ÷ 3 + 3 = 3 × 0 + 3 = 0 + 3 = 3
The result is different based on where the brackets are placed.
4. Complex Example:
When dealing with multiple brackets and operations, always solve the innermost bracket first.

For example: 10 + {12 ÷ (3 × 2)} = 10 + {12 ÷ 6} = 10 + 2 = 12
Having learnt the BODMAS rule, let us do some examples on BODMAS and the addition of
number patterns.
Ex 1. Write the expression 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.
Sol. (a) Sum of nine and two = 9 + 2

So, four multiplied by the sum of nine and two = 4 × (9 + 2).
(b) Difference of eighteen and six = 18 – 6
So, division of 18 – 6 by 4 = (18 – 6) ÷ 4.
(c) The required expression is 45 ÷ {3(3 + 2)}.

Ex 2. Simplify the following using the BODMAS rule.
(a) 16 + 3(91 ÷ 7) (b) {5(8 + 2) – 5} × 2 (c) 80 + [190 – {8 × 9 + (110 – 50)}]
Sol: (a) 16 + 3(91 ÷ 7) = 16 + 3 × 13 [ 91 ÷ 7 = 13]
= 16 + 39 = 55
(b) {5(8 + 2) – 5} × 2 = {5 × 10 – 5} × 2 [ 8 + 2 = 10]

= {50 – 5} × 2 [ 5 × 10 = 50]
= 45 × 2 = 90
(c) 80 + [190 – {8 × 9 + (110 – 50)}] = 80 + [190 – {8 × 9 + 60}] [ 110 – 50 = 60]

= 80 + [190 – {72 + 60}] = 80 + [190 – 132]
= 80 + 58 = 138
Ex 3. Evaluate 104 × 105 using brackets.
Sol. 104 × 105 = (100 + 4) × (100 + 5) = (100 + 4) × 100 + (100 + 4) × 5
= 100 × 100 + 4 × 100 + 100 × 5 + 4 × 5
= 10,000 + 400 + 500 + 20 = 10,000 + 900 + 20 = 10,920

Ex 4. In the figure (a), some numbers are placed in a pattern. Find out 40 40 40 40
the sum of the numbers in the pattern. Should we add them one 50 50 50 50 50
by one, or can we use a quicker way? (NCERT)

Sol. Obviously, we can add these numbers in Figure (a), one by one, 40 40 40 40
but that won’t be an intelligent way of doing it. It will also make 50 50 50 50 50
our calculations lengthy and boring.
40 40 40 40
Figure (a)

Number Play 81