| << Chapter < Page | Chapter >> Page > |
| Order of Operations | |
|---|---|
| P lease | P arentheses |
| E xcuse | E xponents |
| M y D ear | M ultiplication and D ivision |
| A unt S ally | A ddition and S ubtraction |
It’s good that ‘ M y D ear’ goes together, as this reminds us that m ultiplication and d ivision have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.
Similarly, ‘ A unt S ally’ goes together and so reminds us that a ddition and s ubtraction also have equal priority and we do them in order from left to right.
Simplify the expressions:
| ⓐ | |
 | |
| Are there any p arentheses? No. | |
| Are there any e xponents? No. | |
| Is there any m ultiplication or d ivision? Yes. | |
| Multiply first. |
 |
| Add. |
 |
 |
| ⓑ | |
 | |
| Are there any p arentheses? Yes. |
 |
| Simplify inside the parentheses. |
 |
| Are there any e xponents? No. | |
| Is there any m ultiplication or d ivision? Yes. | |
| Multiply. |
 |
Simplify:
| ⓐ | |
 | |
| Are there any p arentheses? No. | |
| Are there any e xponents? No. | |
| Is there any m ultiplication or d ivision? Yes. | |
| Multiply and divide from left to right. Divide. |
 |
| Multiply. |
 |
| ⓑ | |
 | |
| Are there any p arentheses? No. | |
| Are there any e xponents? No. | |
| Is there any m ultiplication or d ivision? Yes. | |
| Multiply and divide from left to right. | |
| Multiply. |
 |
| Divide. |
 |
Simplify:
 | |
| Parentheses? Yes, subtract first. |
 |
| Exponents? No. | |
| Multiplication or division? Yes. | |
| Divide first because we multiply and divide left to right. |
 |
| Any other multiplication or division? Yes. | |
| Multiply. |
 |
| Any other multiplication or division? No. | |
| Any addition or subtraction? Yes. |
 |
When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.
 | |
| Are there any parentheses (or other grouping symbol)? Yes. | |
| Focus on the parentheses that are inside the brackets. |
 |
| Subtract. |
 |
| Continue inside the brackets and multiply. |
 |
| Continue inside the brackets and subtract. |
 |
| The expression inside the brackets requires no further simplification. | |
| Are there any exponents? Yes. | |
| Simplify exponents. |
 |
| Is there any multiplication or division? Yes. | |
| Multiply. |
 |
| Is there any addition or subtraction? Yes. | |
| Add. |
 |
| Add. |
 |
 |
Simplify:
 | |
| If an expression has several exponents, they may be simplified in the same step. | |
| Simplify exponents. |
 |
| Divide. |
 |
| Add. |
 |
| Subtract. |
 |
 |
| Operation | Notation | Say: | The result is… |
|---|---|---|---|
| Addition | the sum of and | ||
| Multiplication | The product of and | ||
| Subtraction | the difference of and | ||
| Division | divided by | The quotient of and |
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