**High School Number Sense Lesson 7: Order of Operations**

When solving a mathematical expression, there are certain rules that dictate how we move through the process. The purpose of these rules is to ensure that everyone who evaluates the same expression comes up with the same answer. Otherwise, math would be subjective instead of objective. And for people like me, that would be a big problem--I want to know when I'm right! (Except now that I've been married 20 years as of tomorrow, I've learned that in terms of marital conflict,

**even when I'm right, I'm wrong!) :)**

This year on high school tests, problems involving basic order of operations (not including special variations--like estimates or fractions in disguise) showed up

**13 times**, usually around question # 8. For some reason, these questions rarely involved exponents this year, so I've decided to leave those out for this lesson and cover them next for middle school.

**Number Dojo Level: 63**

**The Order of PEMDAS**

**P**arentheses**E**xponents**M**ultiplication &**D**ivision**A**ddition &**S**ubtraction

**How to use PEMDAS**

- First, look for any parentheses and solve the expression inside first.
- Second, handle any exponents (and roots).
- Third, solve any multiplication and division operations, going left to right.
- Finally, solve the addition and subtraction parts, going left to right.

**Example 1 gone wrong (out of order): 8 + 6 ÷ 2 x 4 - 10**

- 8 + 6 = 14.
- 14 ÷ 2 = 7.
- 7 x 4 = 28.
- 28 - 10 =
**18**.

**Example 1 corrected: 8 + 6 ÷ 2 x 4 - 10**

- There are no parentheses or exponents (PE).
- So move on to multiplication and division (MD)--going left to right:
**6 ÷ 2 x 4**. 6 ÷ 2 = 3. 3 x 4 =**12**. - We are left with only addition and subtraction (AS):
**8 + 12 - 10**. Solve this left to right. 8 + 12 = 20. 20 - 10 =**10**.

**Example 2: 3 x 6 - 9 + 4 ÷ 2**

- There are no parentheses or exponents (PE).
- Move on to multiplication and division (MD). 3 x 6 =
**18**and 4 ÷ 2 =**2**. - We are left with only addition and subtraction (AS):
**18 - 9 + 2**. Solve this left to right. 18 - 9 = 9. 9 + 2 =**11**.

**Example 3: 1 + (2 - 3) x 4 ÷ 5**

- Solve inside the parentheses first. (2 - 3) =
**-1**. - There are no exponents.
- Move on to multiplication and division:
**-1 x 4 ÷ 5**. -1 x 4 = -4. -4 ÷ 5 =**-4/5**. - Finish up with addition and subtraction: 1 + -4/5 = 1 - 4/5 =
**1/5**.

**Example 4: 9 x (8 + 7 - 6) + 5 x 4 x (3 ÷ 2) - 1**

- Solve inside the parentheses first. 8 + 7 - 6 =
**9**. 3 ÷ 2 =**3/2**. - There are no exponents. We are left with
**9 x 9 + 5 x 4 x 3/2 - 1**. - Move on to multiplication and division: 9 x 9 =
**81**. 5 x 4 x 3/2 = 20 x 3/2 =**30**. - We are left with 81 + 30 - 1. Solve this left to right. The answer is
**110**.

**Here's a free worksheet to help you practice OrderOfOper:**

orderofoper.pdf |

**Up Next for High School: Square21-30**