Order of Operations

1. Order of Operations Click the arrow to begin learning about orders of operations.

2. Objectives • Students will learn how to determine which operations should be carried out first, in math problems involving several operations. These will include addition, subtraction, multiplication, division, and parentheses. • Students will learn how to solve a variety of math problems containing various operations.

3. Common Core Standards • Operations and algebraic thinking (5.OA) • Write and interpret numerical expressions. • Use parentheses, brackets, and braces in numerical expressions and evaluate expressions with these symbols.

4. Introduction • During this tutorial, you will be learning about the correct order of operations for solving math problems. • Click on the arrow buttons to go through the tutorial. • If you get stuck, you can always click on the button to come back to this slide and start over. Good luck and have fun! Home

5. Home Getting started… • To get started, let’s solve some math problems. Use a paper and pencil to help you solve these. • Click on the correct answer for each problem. Complete the problems in order. • 3+5x6=? • 4+(3-2)x2=? 90 33 6 10

6. Home 90 is incorrect. Don’t worry! For now, that is OK. Click the arrow and try the next problem.

7. Home 33 is correct! Great job! You will learn why this is the correct answer soon. Click the arrow and try the second problem.

8. Home 10 is incorrect. Don’t worry! For now, that is OK. Click the arrow to learn more about how to solve these problems.

9. Home 6 is correct! Great job! You will learn why this is the correct answer soon. Click the arrow to learn more about how to solve these problems.

10. Home Order of OperationsWhat is an operation? • Let’s start out with reviewing what an operation is. In math, operations are the things we do with numbers (adding, subtracting, multiplying, dividing). These are represented using symbols: × ÷ - +

11. Home Order of OperationsWhat does that mean? • When you are solving a math problem, you have to do each operation in a specific order. • This might seem like a silly rule, but if you do not follow it you will not get the correct answer.

12. Home How does it work? Now that you know what Order of Operations means, you are going to learn some rules about solving problems. Then, you are going to practice solving some math problems.

13. Home Rule 1 • You must always solve a math problem from left to right, just like when you are reading a word. • Go to the next page to see an example.

14. Home 12-5+6=? • Look at the problem above. If I added 5 and 6 first, this is what I would get: 12-5+6=? • I would add the 5 and 6, which equals 11. I would put the 11 in place of the 5+6. Now I have this problem: 12-11= ? • The answer is 1. I did not solve the problem from left to right. Let’s see what happens if I do.

15. Home 12-5+6=? • If I start from the left, and do the subtraction first, this is what I would get: 12-5+6=1 • I would subtract 5 from 12 first, which equals 7. I would put the 7 in place of the 12-5. 7+6= ? • The answer is 13 this time. This is the correct answer, because I followed the rule and solved the problem from left to right. • Click “Try it!” to try a problem on your own. Try it!

16. Home Now you try! • Solve this problem from left to right. Use scratch paper if you need to. 15-3+2=? • Which answer is correct? 10 14 12

17. Home Great job! You are correct. You solved the problem from left to right. You are ready for the next rule for order of operations. • Click on the arrow to continue.

18. Home Sorry, that is not correct. Remember that you need to solve the problem from left to right. 15-3+2=? • Click the arrow to go back and try the problem again.

19. Home Multiplication and Division • Rule 1 is easy when we only have addition and subtraction operations. • What about when we have multiplication and division operations? Click the question mark to find out.

20. Home Rule 2 • Multiplication and division always have to be done before subtraction and addition. • You still need to remember to solve the problem from left to right too! • Multiplication and division are solved from left to right first. • Addition and subtraction are solved from left to right next. • Go to the next slide to see an example.

21. Home 9-4×2+2=? • If I solve the problem from left to right without doing the multiplication first, this is what happens: 9-4×2+2=? • I subtract 4 from 9 first and get 5. I put the 5 in place of the 9-4. 5×2+2=? • Then, I multiply 5 and 2 to get 10. I put the 10 in place of the 5×2, and now I need to finish up my problem. 10+2=12 • My answer is 12. Let’s see what happens when we do the multiplication first. Click the arrow to find out.

22. Home 9-4×2+2=? • If I solve the multiplication part of the problem first, this is what happens: 9-4×2+2=? • I multiply 4 and 2 first and get 8. I put the 8 in place of the 4×2. 9-8+2=? • Now, since I only have addition and subtraction left, I do those operations from left to right. I subtract 8 from 9, and get 1. I put the 1 in the place of 9-8. 1+2=3 • My answer is 3. This is the correct answer, because I followed the order of operations. • Click “Try it!” to try some problems on your own. Try it!

23. Home 15-5×2+6=? • Solve the problem above. Use a paper and pencil if needed. • Click on the correct answer below. 11 26 25

24. Home You are Correct! • You solved the problem correctly. Great job! • If you guessed the answer, this is how the problem should be solved. Check your work, or try this. • 15-5×2+6=? The multiplication should be done first. • 15-10+6=? Next, complete the addition and subtraction from left to right. • 5+6=? 5+6=11

25. Home Sorry, that answer is incorrect. Remember that you must do the multiplication and division operations first (from left to right). Then you can complete the addition and subtraction from left to right. • Click the arrow to go back and try the problem again.

26. Home 20÷4+5×3=? • Solve the problem above. Use a paper and pencil if needed. • Click on the correct answer below. 30 20

27. Sorry, that answer is incorrect. Remember that you must do the multiplication and division operations first (from left to right). Then you can complete the addition and subtraction from left to right. Home • Click the arrow to go back and try the problem again.

28. Home You are Correct! • You solved the problem correctly. Great job! • If you guessed the answer, this is how the problem should be solved. Check your work or try this. • 20÷4+5×3=? Multiplication and division comes first, but you must solve the from left to right. So, the division should be done first. • 5+5×3=? The multiplication is next. • 5+15=? Now, do the addition. 5+15=20

29. Home Parenthesis () • So far, you have learned: • Solve problems from left to right. • Division and multiplication must be done first (from left to right). • Addition and subtraction is done next (from left to right). • What about when there are parentheses? • Push the question mark to find out.

30. Home Rule 3 • Operations in parentheses always have to be done first. • You still need to remember to solve the problem from left to right too! • All operations in parentheses are done from left to right first. • Multiplication and division are solved from left to right next. • Addition and subtraction are solved from left to right last. • Go to the next slide to see an example.

31. Home 5×(4+3)-2=? • The operations in parentheses must be done first. 5×(4+3)-2=? • (4+3) is 7, so put 7 in place of it. 5×7-2=? • Since there are no more parentheses, I can do all of the multiplication and division next. 5×7 is 35, so I put 35 in place of that. 35-2=? • I finish the problem by doing the addition and subtraction. 35-2=33

32. Home • To see another example, click the orange arrow. • To practice some problems on your own, click the green arrow.

33. Home 2×5+(6÷3)=? • First, you need to complete the operations in the parentheses. 2×5+(6÷3)=? • (6÷3) is 2, so put the 2 in place of it. 2×5+2=? • Multiplication and division are next, so solve 2×5. This equals 10, so put 10 in the problem. 10+2=? • Last, you can do the addition and subtraction. 10+2=12

34. Now, Practice the Rules on Your Own! • Use a pencil and paper. Click on the correct answer for each problem. Make sure you complete the problems in order. This time, show your work on your paper. • 7-5+(8÷2)×9=? • (10-4)×6+12=? • 8+12×2-(16÷2)=? 54 38 45 108 62 48 24 32 12 Home

35. Home You are Correct! • If you guessed the correct answer, click the arrow to go back and try to get the correct answer on your own. • If you successfully solved the problem, click the arrow to go back and try the next one.

36. Sorry, you are Incorrect • Sorry, you got the incorrect answer for this problem. Remember the rules: • You must complete the operations in parentheses first. • You must complete all division and multiplication next, moving from left to right. • You must complete all addition and subtraction last, moving left to right. • Go back and try the problem again. Home

37. Home You are Correct! • If you guessed the correct answer, click the back arrow to go back and try to get the correct answer on your own. • If you successfully solved the problem, click the forward arrow to continue.

38. Congratulations! • You have just completed the “Order of Operations” lesson! • Give your work from the last 3 problems to your teacher.