## Order of operations

When calculations have more than one operation, we have to follow rules for the order of operations:

**Step 1:**

From left to right, do all **multiplication and division**.

$$100−20×3+5 = 100−60+5$$

**Step 2:**

From left to right, do all

**addition and subtraction**.

$$100−60+5 = 45$$

However, if there are

**parentheses**or other types of brackets, do all operations that lie

**inside**them first:

$$ 70 + 36 ÷ (8 − 4) +1 =$$

$$= 70 + 36 ÷ 4 + 1 = $$

$$ =70 + 9 + 1 = 80 $$

The order of operations also applies while working inside parentheses:

$$8+(3+3×4) = 8+(3+12) $$

$$= 8+15 = 23$$

When you have parentheses inside brackets and braces (sometimes referred as

**nested parentheses**), always work from the inside out. There are multiple types of brackets. The innermost

**parentheses/round brackets ()**are calculated first, followed by the

**brackets/box brackets []**that normally form the next layer, followed by

**braces/curly brackets {}**that form a third layer outwards:

$$ {1 + [4 × (2 + 3) + 1]} ÷ 11 = $$

$$ = {1 + [4 × 5 + 1]} ÷ 11 = $$

$$ = {1 + [20 + 1]} ÷ 11 = $$

$$ = {1 + 21} ÷ 11 = 22 ÷ 11 = 2 $$