Order of Operations

Order of Operations

Think about the situation

Valli and her four friends went to a butter milk shop. Each had a cup of butter milk and paid ₹ 30, assuming that the cost of one cup of butter milk to be ₹ 6. But the shop keeper told that the cost of butter milk had increased by ₹ 2. Then, Valli decided to give ₹ 2 more and paid ₹ 32. But  the shop keeper claimed that she had to pay ₹ 40. Who is correct?

The amount ₹ 40 claimed by the Shop keeper is correct. This confusion can be avoided by using the brackets in the correct places like 5 × (6 + 2).

The rule of order of operations is called as BIDMAS.

Now, we try to solve 9 + 5 × 2 by using BIDMAS,

9 + (5 × 2) = 9 + 10

= 19

Example 1.9

Simplify: 24 + 2 × 8 ÷ 2 + 1

Solution

24 + 2 × 8 ÷ 2 − 1    (given question)

= 24 + 2 × 4 − 1 (÷ operation, completed first)

= 24 + 8 – 1        (× operation, completed second)

= 32 − 1             (+ operation, completed third)

= 31             (− operation , completed last)

Example 1.10

Simplify: 20 + [8 × 2 + {6 × 3 − 10 ÷ 5}]

Solution

20 + [8 × 2 + {   − 10 ÷ 5}]    (given question)

= 20 + [8 × 2 + {18 – 10 ÷ 5}]      (bar completed first)

= 20 + [8 × 2 + {18 − 2}]            ( ÷ completed second )

= 20 + [8 × 2 + 16]                    ({ } completed third)

= 20 + [16 + 16]                  (× completed fourth)

= 20 + 32                             ([ ] operation completed fifth)

= 52                                      ( + completed last)