# Order of operations

All operations 1-20

## 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 \$\$

All operations 1-100

## 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 \$\$

Translating verbal expressions into equations

## Basic arithmetic operations

Sum - outcome of adding two or more numbers

summand + summand =sum

Example: Calculate the sum of 12 and 3.

### Subtraction

Difference - outcome of subtracting two numbers

minuend – subtrahend = difference

Example: Calculate the difference of 12 and 3.

The parts you subtract or add are also called terms.

### Multiplication

Product - outcome of multiplying two or more numbers.

factor × factor = product

Example: Calculate the product of 12 and 3.
Answer: 12 × 3 = 36

### Division

Quotient - outcome of division of two numbers

dividend ÷ divisor = quotient

Example: Calculate the quotient of 12 and 3.
Answer: 12 ÷ 3 = 4