NOTE Some students like to use the mnemonic “Please Excuse My Dear Aunt Sally”

to help remember the rules for order of operations.

Please Excuse My Dear Aunt Sally

Parentheses Exponents Multiply Divide Add Subtract

Be sure to multiply or divide in order from left to right. Then add or subtract in

order from left to right.

Using the Order of Operations

Simplify.

(a)

Multiply.

Add.

(b)

Divide.

Multiply.

= 22 Add.

= 16 + 6

= 8 # 2 + 6

24 , 3 # 2 + 6

= 11

= 5 + 6

5 + 2 # 3

EXAMPLE 4

SECTION 1.3 Exponents, Roots, and Order of Operations 27

NOW TRY
EXERCISE 4
Simplify.

15 - 3 # 4 + 2

NOW TRY
EXERCISE 5
Simplify.

• 52 + 10 , 5 - | 3 - 7 |

NOW TRY ANSWERS

4. 5 5. - 27

(c) Work inside the parentheses first.

Divide inside the parentheses.

Subtract inside the parentheses.

Multiply.

=- 3 Add. NOW TRY

= 2 + 1 - 52

=

1

2

4 + 1 - 52

=

1

2

4 + 12 - 72

1

2

4 + 16 , 3 - 72

NOW TRY

Using the Order of Operations

Simplify.

(a) Work inside the absolute value bars first.

Subtract inside the absolute value bars.

Take the absolute value.

Divide first, and then multiply.

Add.

(b) Work inside the parentheses first.

Add inside the parentheses.

Evaluate the power.

Multiply.

Add.

= 33 Subtract.

= 43 - 10

= 36 + 7 - 10

= 4 # 9 + 7 - 10

= 4 # 32 + 7 - 10

4 # 32 + 7 - 12 + 82

= 4

= 2 + 2

= 10 , 5 + 2 # 1

= 10 , 5 + 2 |- 1 |

10 , 5 + 2 | 3 - 4 |

EXAMPLE 5

NOT 3#2.

32 means 3#3,

Multiplications and divisions are done in the

order in which they appear from left to right.

So we divide first here.