1. Order of Operations
Animated PowerPoint
©Amy Harrison, 2014

2. 1. Parentheses (Grouping Symbols)
Order of Operations P. E.
1. Parentheses (Grouping Symbols)
2. Exponents
3. Multiplication and Division from LEFT to RIGHT M. D.
4. Addition and Subtraction from LEFT to RIGHT
“Please excuse my dear aunt Sally’s loud radio” A. S.
©Amy Harrison, 2014

3. Warm-Up Complete the operations in the order listed.
What number is 2 times 3 minus 4?
What number is 54 divided by nine plus 2?
Add 5 and 7. Then multiply by 9. What is your answer?
Subtract 16 and 5. Then multiply by 3. Finally, divide by 11. What is your answer?
©Amy Harrison, 2014

4. Warm-Up Answers 1. What number is 2 times 3 minus 4?
2 x 3 – 4 = 6 – 4 = 2
2. What number is 54 divided by nine plus 2?
54 ÷ 9 = = 8
3. Add 5 and 7. Then multiply by 9. What is your answer?
5 + 7 = 12 x 9 = 108
4. Subtract 16 and 5. Then multiply by 3. Finally, divide by 11. What is your answer?
= 11 x 3 = 33 ÷ 11= 3
©Amy Harrison, 2014

5. Let’s Discuss: GIVE EXAMPLES!
DOES
ORDER MATTER?
ATTENTION:
©Amy Harrison, 2014
In Math?
In Life?
Let’s Discuss: GIVE EXAMPLES!

6. Sign the check vs. Check the sign
In most languages, the meaning of the word depends on the order that you say it. For example,
Sign the check vs. Check the sign
Can you think of any examples like this?
©Amy Harrison, 2014

7. I understand “order”, but what is an operation?
𝑶𝒌…
I understand “order”, but what is an operation?
𝐁𝐚𝐬𝐢𝐜 𝐎𝐩𝐞𝐫𝐚𝐭𝐢𝐨𝐧𝐬 𝐢𝐧𝐜𝐥𝐮𝐝𝐞…
Addition
Subtraction
Multiplication
Division
©Amy Harrison, 2014

8. 𝟏𝟔−𝟓 •𝟐 𝟏𝟏 •𝟐 𝟐𝟐 𝟏𝟔−𝟓 •𝟐 𝟏𝟔−𝟏𝟎 𝟔 I 𝒈𝒐𝒕 𝒕𝒘𝒐 𝒂𝒏𝒔𝒘𝒆𝒓𝒔! 𝑾𝒉𝒐 𝒊𝒔 𝒓𝒊𝒈𝒉𝒕?
𝑰𝒏 𝒘𝒉𝒂𝒕 𝒐𝒓𝒅𝒆𝒓 𝒘𝒐𝒖𝒍𝒅 𝒚𝒐𝒖 𝒔𝒐𝒍𝒗𝒆 𝒕𝒉𝒊𝒔 𝒑𝒓𝒐𝒃𝒍𝒆𝒎?
𝟏𝟔−𝟓 •𝟐
𝟏𝟏 •𝟐 𝟐𝟐
Mr. Blue thinks you need to subtract before you multiply because you read a book from left to right.
𝟏𝟔−𝟓 •𝟐
𝟏𝟔−𝟏𝟎 𝟔
Mrs. Purple thinks you need to multiply before you subtract because multiplying is harder.
I 𝒈𝒐𝒕 𝒕𝒘𝒐 𝒂𝒏𝒔𝒘𝒆𝒓𝒔! 𝑾𝒉𝒐 𝒊𝒔 𝒓𝒊𝒈𝒉𝒕?
Do you agree with either way of thinking?
©Amy Harrison, 2014

9. Mathematicians created a special order that is used to solve ALL problems. This way, Mr. Blue, Mrs. Purple, and EVERYONE ELSE will never be confused about which operation to do first! This is called “The Order of Operations”.
©Amy Harrison, 2014

10. 𝑺𝒕𝒊𝒍𝒍 𝒏𝒐𝒕 𝒔𝒖𝒓𝒆?
𝑯𝑨𝑽𝑬 𝑵𝑶 𝑭𝑬𝑨𝑹…
𝑷𝑬𝑴𝑫𝑨𝑺
𝑰𝑺 𝑯𝑬𝑹𝑬‼!
©Amy Harrison, 2014

11. Order of Operations
1. Parentheses or 2. Exponents Multiplication & Division from left to right • ÷ 4. Addition & Subtraction from left to right + −
©Amy Harrison, 2014

12. Order of Operations
Example 1:
𝟓−𝟑 +𝟑•𝟖÷𝟒
Steps:
©Amy Harrison, 2014

13. Order of Operations 𝟓−𝟑 +𝟑•𝟖÷𝟒 𝟐+𝟑•𝟖÷𝟒 𝟐+𝟐𝟒÷𝟒 𝟐+𝟔 𝟖 Example: 1 Steps:
Perform operations in parentheses (5-3)
𝟐+𝟐𝟒÷𝟒
Multiply/Divide from left to right (3•8)
𝟐+𝟔
Add/ Subtract from left to right (2 + 6) 𝟖
©Amy Harrison, 2014

14. Order of Operations
Example 2:
𝟐𝟏÷𝟑 𝟏𝟔−𝟗 •𝟏𝟔− 𝟐 𝟒
©Amy Harrison, 2014

15. Order of Operations 𝟐𝟏÷𝟑 𝟏𝟔−𝟗 •𝟏𝟔− 𝟐 𝟒 𝟐𝟏÷𝟑 𝟕 •𝟏𝟔−𝟐(𝟐)(𝟐)(𝟐)
Example 2:
𝟐𝟏÷𝟑 𝟏𝟔−𝟗 •𝟏𝟔− 𝟐 𝟒
𝟐𝟏÷𝟑 𝟕 •𝟏𝟔−𝟐(𝟐)(𝟐)(𝟐)
𝟐𝟏÷𝟐𝟏•𝟏𝟔−𝟏𝟔
𝟏•𝟏𝟔−𝟏𝟔
𝟏𝟔−𝟏𝟔 𝟎
©Amy Harrison, 2014

16. 𝟏𝟐÷𝟒•𝟗−𝟏𝟕 𝟐𝟖÷𝟐−𝟑•𝟒 Example 3: Example 4: ©Amy Harrison, 2014

17. 𝟏𝟐÷𝟒•𝟗−𝟏𝟕 𝟐𝟖÷𝟐−𝟑•𝟒 𝟑•𝟗−𝟏𝟕 𝟏𝟒−𝟏𝟐 𝟐𝟏−𝟏𝟕 𝟐 𝟒 Example 3: Example 4:
©Amy Harrison, 2014
©Amy Harrison, 2014

18. 𝟐𝟎•𝟐−𝟔•𝟒 𝟒𝟎÷𝟒−𝟐•𝟓 Example 5: Example 6: ©Amy Harrison, 2014

19. 𝟐𝟎•𝟐−𝟔•𝟒 𝟒𝟎÷𝟒−𝟐•𝟓 𝟒𝟎−𝟐𝟒 𝟏𝟎−𝟏𝟎 𝟏𝟔 𝟎 Example 5: Example 6:
©Amy Harrison, 2014
©Amy Harrison, 2014

20. 𝟐𝟎÷(𝟏𝟐÷𝟑)•𝟔 𝟗−𝟔 •(𝟕+𝟑) Example 7: Example 8: ©Amy Harrison, 2014

21. 𝟐𝟎÷(𝟏𝟐÷𝟑)•𝟔 𝟗−𝟔 •(𝟕+𝟑) 𝟑•𝟏𝟎 𝟐𝟎÷𝟒•𝟔 𝟑𝟎 𝟓•𝟔 Example 7: Example 8:
©Amy Harrison, 2014
©Amy Harrison, 2014

22. 𝟓+ 𝟗•𝟓 𝟑 𝟏𝟎−𝟕 𝟑 ÷(𝟗−𝟔) Example 9: Example 10: ©Amy Harrison, 2014
𝟏𝟎−𝟕 𝟑 ÷(𝟗−𝟔)
©Amy Harrison, 2014
©Amy Harrison, 2014

23. 𝟓+ 𝟗•𝟓 𝟑 𝟏𝟎−𝟕 𝟑 ÷(𝟗−𝟔) 𝟑 𝟑 ÷𝟑 𝟓+ 𝟒𝟓 𝟑 𝟗 𝟓+𝟏𝟓 𝟐𝟎 Example 9: Example 10:
𝟏𝟎−𝟕 𝟑 ÷(𝟗−𝟔)
𝟑 𝟑 ÷𝟑
𝟓+ 𝟒𝟓 𝟑 𝟗
𝟓+𝟏𝟓 𝟐𝟎
©Amy Harrison, 2014
©Amy Harrison, 2014

24. ORDER OF OPERATIONS RULES
1. Parentheses 𝒐𝒓 E.
2. Exponents 𝟑 𝟐
3. Multiplication and Division from LEFT to RIGHT
• ÷ M. D.
4. Addition and Subtraction from LEFT to RIGHT
+ −
“Please excuse my dear aunt Sally’s loud radio” A. S.
©Amy Harrison, 2014

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