Luttrell 2012
59
Name: ______________________
Date: _____
4c- Order of Operations
In English, there is a standard way of writing; there is an order of words that belie the meaning.
The subject is first, followed by verb, and then the direct object. The sentence, “the dog chased
the cat” has a different meaning from “the cat chased the dog”. The same can be said about
mathematical operations. There is a prescribed order of simplifying expressions. This order can
be remembered by the mnemonic “Please excuse my dear aunt Sally” or “Please eat Ms. Daisy’s
apple sauce.” The first letter of each word represents the mathematical operations:
Parentheses,
Exponents, Multiplication, Division, Addition
, and
Subtraction
.
Actually division and subtraction are a special type of multiplication and addition. So whenever
you have multiplication and division (addition and subtraction) together, they are treated equally.
That means you do the operations as they present themselves from
left to right
.
Example A: 2×3÷2 + 1 - 2
Example B: -(-3) - [-(- 4) + 2] + 7
6 ÷2 + 1 - 2
3 - [4+2] + 7
3 + 1 - 2
3 - 6 + 7
4 - 2 -3 + 7
2 4
Simplify the following expressions:
1. (2×3×4 - 1×3)
2
2. 3(2 - 3)
2
×3 - 1
3. (2+2
2
) ÷ 3 - 6 ÷ 3
4. 1 + 4
2
÷ (5-3)
5. 2 - 2 ×3
2
+ 1
6. (2÷2)×[3
2
-1]
7. 2
x
- 3
x
(5
x
) + 3
x
8. 2
x
- 2
x
(5
x
+ 3)
9. (2-3)
x
+ 4
x
+ 3
