# 3. Order of Operations

Problem: There are 2 ways to answer this question:

2 + 3 × 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, 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 × 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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