<< 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 |
Notification Switch
Would you like to follow the 'Prealgebra' conversation and receive update notifications?