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.
$$10−4×0.5+5 =$$
$$= 10−2+5$$
Step 2:
From left to right, do all addition and subtraction.
$$10−2+5 = 13$$
However, if there are parentheses or other types of brackets, do all operations that lie inside them first:
$$ 7 + 6 ÷ (1.5 + 1.5) + 1 =$$
$$= 7 + 6 ÷ 3 + 1 = $$
$$= 7 + 2 + 1 = 10 $$
The order of operations also applies while working inside parentheses:
$$0.8+(0.3+0.3×4) =$$
$$=0.8+(0.3+1.2) =$$
$$= 0.8+1.5 = 2.3$$
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:
$$ {1 + [4 × (2 + 3) + 1]} ÷ 11 = $$
$$ = {1 + [4 × 5 + 1]} ÷ 11 = $$
$$ = {1 + [20 + 1]} ÷ 11 = $$
$$ = {1 + 21} ÷ 11 = 22 ÷ 11 = 2 $$
