Algebra 1 Common Core Student Edition, Grade 8-9

Esse n t i a l U n d e r st a n d i n g When simplifying an expression, you need to

perform operations in the correct order.

You might think about simplifying the expression 2 + 3 X 5 in two ways:

How do you simplify
an expression th at
contains a fraction?
You s ta rt by s im p lify in g
the num erator and
denominator. Then you
divide the num erator by
the denominator.

Add first.

2 + 3 X 5 = 5 X 5 = 2 5 X

i Multiply first, j

2 + 3 X 5 = 2+15 = 17

Both results may seem sensible, but only the second result is considered correct. This is

because the second way uses the order of operations that mathematicians have agreed

to follow. Always use the following order of operations:

Key Concept Order of Operations

1. Perform any operation(s) inside grouping symbols, such as parentheses ( ) and
   brackets [ ]. A fraction bar also acts as a grouping symbol.


2. Simplify powers.


3. Multiply and divide from left to right.


4. Add and subtract from left to right.

Si m p l i f y i n g a N u m e r i ca l Ex p r e ssi o n

What is the simplified form of each expression?

O (6 - 2)3 + 2

( 6 - 2 ) 3 + 2 = 4 : Subtract inside parentheses.

= 6 4 + 2 Simplify the power.

= 32 Divide.

1 16-1 Simplify the power.

; y Subtract.

= 3 Divide.

G o t It? 2. What is the simplified form of each expression?

a. 5 • 7 - 4 2 = 2

b. 12 - 25 + 5

C.4 + 3^4

7-2

d. Reasoning How does a fraction bar act as a grouping symbol? Explain.

PowerAlgebra.com | Lesson 1-2 Order of Op erat io ns and Evaluat ing Expressions 11