<< 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:
ⓐ | |
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Are there any p arentheses? No. | |
Are there any e xponents? No. | |
Is there any m ultiplication or d ivision? Yes. | |
Multiply first. |
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Add. |
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ⓑ | |
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Are there any p arentheses? Yes. |
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Simplify inside the parentheses. |
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Are there any e xponents? No. | |
Is there any m ultiplication or d ivision? Yes. | |
Multiply. |
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Simplify:
ⓐ | |
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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. |
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Multiply. |
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ⓑ | |
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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. |
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Divide. |
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Simplify:
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Parentheses? Yes, subtract first. |
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Exponents? No. | |
Multiplication or division? Yes. | |
Divide first because we multiply and divide left to right. |
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Any other multiplication or division? Yes. | |
Multiply. |
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Any other multiplication or division? No. | |
Any addition or subtraction? Yes. |
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When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.
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Are there any parentheses (or other grouping symbol)? Yes. | |
Focus on the parentheses that are inside the brackets. |
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Subtract. |
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Continue inside the brackets and multiply. |
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Continue inside the brackets and subtract. |
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The expression inside the brackets requires no further simplification. | |
Are there any exponents? Yes. | |
Simplify exponents. |
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Is there any multiplication or division? Yes. | |
Multiply. |
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Is there any addition or subtraction? Yes. | |
Add. |
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Add. |
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Simplify:
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If an expression has several exponents, they may be simplified in the same step. | |
Simplify exponents. |
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Divide. |
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Add. |
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Subtract. |
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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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