Question

Order of Operations

If the Order of Operations did not exist, how many

possible solutions can you find for this expression?

4 + 9 + 16 : 4 - 8 – 3 x 5

Answer 1

Given:

`4 + 9 + 16 / 4 - 8 -3 * 5`

To find:

The number of possible solutions, if the Order of Operations did not exist.

Solution:

We have,

`4 + 9 + 16 / 4 - 8 -3 *  5`

Now,

Case 1:

`[4 + 9 + 16] / [4 - 8 -(3 *  5)]=29/ (4 - 8 -15)`

`4 + 9 + 16 /  4 - 8 -(3 *  5)=-(29)/(19)`

Case 2:

`[4 + 9 + 16] /  (4 - 8 -3) *  5=29/  (-7* 5)`

`4 + 9 + 16 /  (4 - 8 -3) *  5=-(29)/(35)`

Case 3:

`4 + 9 + (16 / 4) - 8 -(3 *  5)=4+9+4-8-15`

`4 + 9 + (16 / 4) - 8 -(3 *  5)=-6`

Many more possibilities are there.

Therefore, there are more than 3 possible solutions.