3. Order of Operations

Problem: There are 2 ways to answer this question involving numbers:

`2 + 3 xx 7`

We can either

  • Add the 2 and 3 first and then multiply the result by 7 (we would get 35), OR
  • We could multiply the 3 and 7 then add the 2 (giving us 23).

Which is correct?

To reduce confusion and so that we all get the same answer when combining numbers using the operations of adding, subtracting, multiplying or dividing, the following convention is used.

BODMAS

BODMAS is the agreed convention for answering problems that are a mixture of adding, subtracting, multiplying and dividing. It stands for:

B: Do what is inside brackets first
O: Order is important in mathematics!
DM: Do divisions and multiplications as you come to them, from left to right
AS: Finally, do additions and subtractions as you come to them, from left to right.

So for our problem above, the correct answer would be:

`2 + 3 xx 7`

`= 2 + 21`

`= 23`

Continues below

Example 1

Evaluate 10 − 2 × 3

Example 2

Evaluate (10 − 2) × 3

Example 3

Simplify −4 + 5 × (7 + 3)

Example 4

Simplify 12(5 + 6 × 3) ÷ (4 + 2)

Example 5

Simplify −2(x + 5 × 7 + 3)

[Note the difference between the letter "x" and the multiplication operator "×".]

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