LESSON: Order of Operations

Order of Operations

READ: Evaluating Expressions with Grouping Symbols

Evaluating Numerical Expressions Using Powers and Grouping Symbols

We can also use the order of operations when we have exponent powers and grouping symbols like parentheses. Let’s review where exponents and parentheses fall in the order of operations.


Order of Operations

P - parentheses

E - exponents

MD - multiplication or division in order from left to right

AS - addition or subtraction in order from left to right


According to the order of operations parentheses comes first. We always do the work in parentheses first. Then we evaluate exponents.


Example

2 + (3 - 1) \times 2

In this example, we can see that we have four things to look at. We have 1 set of parentheses, addition, subtraction in the parentheses and multiplication. We can evaluate this expression using the order of operations.

& 2 + (3 - 1) \times 2\ & 2 + 2 \times 2\ & 2 + 4\ & = 6

Our answer is 6.


What about when we have parentheses and exponents?

Example

35 + 3^2 - (3 \times 2) \times 7

We start by using the order of operations. It says we evaluate parentheses first.

$$(3)( 2) = 6$$

$$35 + 3^2 -6(7)$$

Next, we evaluate exponents.

$$3^2=9$$

$$35+9-6(7)$$

Next, we complete multiplication or division in order from left to right. We have multiplication.

& 6 \times 7 = 42\ & 35 + 9 - 42

Next, we complete addition and/or subtraction in order from left to right.

35 + 9 & = 44\ 44 - 42 & = 2

Our answer is 2.