Math Elementary arithmetic The Calculations' Order

# The Calculations' Order (PEMDAS)

PEMDAS is an acronym for the words:

1. Parentheses
2. Exponents
3. Multiplication

Division

Subtraction

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

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### 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

1. $4\cdot5+2=?$

calculations' order:

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

2. $14-9+6=?$

calculations' order:

• Addition and Subtraction in the order they occur

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

3. $9\div3\cdot2=?$

calculations' order:

• Multiplication and Division in the order they occur

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

4. $12-8\cdot5\div4+7=?$

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

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

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### Remember

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

### Examples 2

1. $(24\div4-8)\cdot7=?$

calculations' order:

• Parentheses before Multiplication and Division
• Multiplication and Division before Subtraction

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

2. $(5+4)\cdot2^{3}=?$

calculations' order:

• Parentheses before Exponents
• Exponents before Multiplication

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

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

calculations' order:

• Parentheses before Multiplication and Division
• Multiplication and Division before Addition and Subtraction

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

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

calculations' order:

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

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

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### Hint

The acronym PEMDAS can be memorized through the phrase:

Please Excuse My Dear Aunt Sally.

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### Info

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

1. Brackets
2. Orders
3. Divide

Multiply

Subtract

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

1. Brackets
2. Exponents
3. Divide

Multiply