# 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 bracketsfirstO:Order is important in mathematics!DM:Do divisionsandmultiplicationsas you come to them, fromleft to rightAS:Finally, do additionsandsubtractionsas you come to them, fromleft to right.

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

`2 + 3 xx 7`

`= 2 + 21`

`= 23`

### 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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