The order of operations is the order to be respected when performing calculations in a chain of operations.
When several operations are present in a calculation, it is called a chain of operations. To perform the calculation, a precise sequence indicated by the order of operations must be followed.
Here is the order (or chain) of operations that must be respected. If one of these operations is not present, we go to the next operation on the list.
- Brackets
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
To remember the order, think of the following acronym: BEMDAS.
A sentence can also be made up with words beginning with the letters BEMDAS.
Example: “Bill Excuses My Dear Aunt Sally”
11 × 2 + 5³ ÷ 5 - (10 + 12) = ?
1. Brackets |
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The equation in the brackets is 10 + 12. |
11 × 2 + 5³ ÷ 5 - (10 + 12) = ? |
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I rewrite the expression using the answer. |
11 × 2 + 5³ ÷ 5 - 22 = ? |
2. Exponents |
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5³ = 125 |
11 × 2 + 5³ ÷ 5 - 22 = ? |
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I rewrite the expression using the answer. |
11 × 2 + 125 ÷ 5 - 22 = ? |
3. Multiplication and Division (from left to right) |
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The first multiplication or division in the chain is 11 × 2. |
11 × 2 + 125 ÷ 5 - 22 = ? |
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I rewrite the expression using the answer. |
22 + 125 ÷ 5 - 22 = ? |
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The second multiplication or division in the chain is 125 ÷ 5. 125 ÷ 5 = 25 |
22 + 125 ÷ 5 - 22 = ? |
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I rewrite the expression using the answer. |
22 + 25 - 22 = ? |
4. Addition and Subtraction (from left to right) |
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The first addition or subtraction in the chain is 22 + 25. |
22 + 25 - 22 = ? |
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I rewrite the expression using the answer. |
47 - 22 = ? |
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The second addition or subtraction in the chain is 47 - 22. 47 - 22 = 25 |
47 - 22 = ? |
11 × 2 + 5³ ÷ 5 - (10 + 12) = 25
When all the operations have been completed, the calculations should look like a funnel.
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