Use the Language of Algebra

Read this text. Pay special attention to the Order of Operations portion that summarizes the rules for performing multi-step calculations.

Many students use a silly phrase to remember the order of operations: Please Excuse My Dear Aunt Sally, where the first letter of each word corresponds to a mathematical operation: parentheses, exponents, multiplication and division, addition and subtraction.

Do Examples 2.8 – 2.12, and check your answers. If you need more practice, you can try Try It 2.15 – 2.24.

Examples

Example 2.8

Simplify the expressions:
ⓐ 4+3⋅7
ⓑ (4+3)⋅7

Example 2.9

Simplify:
ⓐ 18÷9⋅2
ⓑ 18⋅9÷2

Example 2.10

Simplify: 18÷6+4(5−2).

Example 2.11

Simplify: 5+2^3+3[6−3(4−2)].

Example 2.12

Simplify: 2^3+3^4÷3−5^2.

Try It 2.15
Simplify the expressions:
ⓐ 12−5⋅2
ⓑ (12−5)⋅2

Try It 2.16
Simplify the expressions:
ⓐ 8+3⋅9
 ⓑ (8+3)⋅9

Try It 2.17
Simplify:
42÷7⋅3

Try It 2.18
Simplify:
12⋅3÷4

Try It 2.19
Simplify:
30÷5+10(3−2)

Try It 2.20
Simplify:
70÷10+4(6−2)

Try It 2.21
Simplify:
9+5^3−[4(9+3)]

Try It 2.22
Simplify:
7^2−2[4(5+1)]

Try It 2.23
Simplify:
3^2+2^4÷2+4^3

Try It 2.24
Simplify:
6^2−5^3÷5+8^2