## 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:

$$70+36÷(8−2)+1 = 70+36÷6+1=$$

$$ 70+6+1 = 77$$

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:

$${1+[4×(2+3)+1]}÷11=$$

$$={1+[4×5+1]}÷11=$$

$$={1+[20+1]}÷11=$$

$$={1+21}÷11=22÷11=2$$