# The Calculations' Order (PEMDAS)

PEMDAS is an acronym for the words:

**P**arentheses**E**xponents**M**ultiplication**D**ivision**A**ddition**S**ubtraction

It refers to the order in which these calculations need to be performed.

### Info

**Parentheses**need to be calculated before**Exponents**.**Exponents**need to be calculated before**Multiplication**and**Division**.**Multiplication**and**Division**need to be calculated in the order they occur from left to right.**Multiplication**and**Division**need to be calculated before**Addition**and**Subtraction**.**Addition**and**Subtraction**need to be calculated in the order they occur from left to right.

### Examples 1

$4\cdot5+2=?$

calculations' order:

- Multiplication before Addition

$4\cdot5+2$ $=20+2$ $=22$

$14-9+6=?$

calculations' order:

- Addition and Subtraction in the order they occur

$14-9+6$ $=5+6$ $=11$

$9\div3\cdot2=?$

calculations' order:

- Multiplication and Division in the order they occur

$9\div3\cdot2$ $=3\cdot2$ $=6$

$12-8\cdot5\div4+7=?$

calculations' order:

- Multiplication and Division before Addition and Subtraction
- Multiplication and Division in the order they occur
- Addition and Subtraction in the order they occur

$12-8\cdot5\div4+7$ $=12-40\div4+7$ $=12-10+7$ $=2+7$ $=9$

### Remember

If there are parentheses in the calculation, the same PEMDAS rule applies to the calculation inside these parentheses.

### Examples 2

$(24\div4-8)\cdot7=?$

calculations' order:

- Parentheses before Multiplication and Division
- Multiplication and Division before Subtraction

$(24\div4-8)\cdot7$ $=(6-8)\cdot7$ $=-2\cdot7$ $=-14$

$(5+4)\cdot2^{3}=?$

calculations' order:

- Parentheses before Exponents
- Exponents before Multiplication

$(5+4)\cdot2^{3}$ $=9\cdot2^{3}$ $=9\cdot8$ $=72$

$14-(3+16\div4)\cdot2=?$

calculations' order:

- Parentheses before Multiplication and Division
- Multiplication and Division before Addition and Subtraction

$14-(3+16\div4)\cdot2$ $=14-(3+4)\cdot2$ $=14-7\cdot2$ $=14-14$ $=0$

$6\cdot(20\div2-7)+4^{2}=?$

calculations' order:

- Parentheses before Exponents
- Exponents before Multiplication and Division
- Multiplication and Division before Addition and Subtraction

$6\cdot(20\div2-7)+4^{2}$ $=6\cdot(10-7)+4^{2}$ $=6\cdot3+4^{2}$ $=6\cdot3+16$ $=18+16$ $=34$

### Hint

The acronym PEMDAS can be memorized through the phrase:

**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally.

### Info

In the UK they use the acronym BODMAS, which stands for:

**B**rackets**O**rders**D**ivide**M**ultiply**A**dd**S**ubtract

and in Canada they use the acronym BEDMAS, which stands for:

**B**rackets**E**xponents**D**ivide**M**ultiply**A**dd**S**ubtract

However, they all mean the same thing.