Answer:
Why do we need an order of operations?
Example: In a room there are 2 teacher's chairs and 3 tables each with 4 chairs for the students. How many chairs are in the room?
We know there are 14, but how do we write this calculation? If we just write
2 + 3 x 4
how does a reader know whether the answer is
2 + 3 = 5, then multiply by 4 to get 20 or
3 x 4 = 12, then 2 + 12 to get 14?
There are two steps needed to find the answer; addition and multiplication. Without an agreed upon order of when we perform each of these operations to calculate a written expression, we could get two different answers. If we want to all get the same "correct" answer when we only have the written expression to guide us, it is important that we all interpret the expression the same way.
One way of explaining the order is to use brackets. This always works. To say that the 3 x 4 is done before the adding, we would use brackets like this:
2 + (3 x 4)
The brackets show us that 3 x 4 needs to be worked out first and then added to 2. However, we can also agree on an order of operations, which is explained below.
Another example: Calculate 15- 10 ÷ 5
If you do the subtraction first, you will get 1. If you do the division first, which is actually correct according to the rules explained below, you will get 13. We need an agreed order.