1. Course 2 1-5 Order of Operations 1-5 Order of Operations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 2 1-5 Order of Operations Warm Up Evaluate in order from left to right. 1. 18 ÷ 3 + 7 2. 10 2 ÷ 4 – 8 3. 10 + 23 – 8 + 7 4. 8  2 – 3 + 24 5. 81 ÷ 9  3 + 15 13 17 32 37 42

3. Course 2 1-5 Order of Operations Problem of the Day Classify each statement as true or false. If the statement is false, insert parentheses to make it true. false 1. 4  5 + 6 = 44 () 2. 24 – 4  2 = 40 () false 3. 25 ÷ 5 + 6  3 = 23 4. 14 – 2 2 ÷ 2 = 12 true

4. Course 2 1-5 Order of Operations Learn to use the order of operations to simplify numerical expressions.

5. Course 2 1-5 Order of Operations Vocabulary numerical expression order of operations

6. Course 2 1-5 Order of Operations When you get ready for school, you put on your socks before you put on your shoes. In mathematics, as in life, some tasks must be done in a certain order. A numerical expression is made up of numbers and operations. When simplifying a numerical expression, rules must be followed so that everyone gets the same answer. That is why mathematicians have agreed upon the order of operations.

7. Course 2 1-5 Order of Operations ORDER OF OPERATIONS 1. Perform operations within grouping symbols. 2. Evaluate powers. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.

8. Course 2 1-5 Order of Operations Simplify the expression. Additional Example 1A: Using the Order of Operations 3 + 15 ÷ 5 3 + 3 6 Divide. Add.

9. Course 2 1-5 Order of Operations Simplify the expression. Additional Example 1B: Using the Order of Operations 44 – 14 ÷ 2 · 4 + 6 44 – 7 · 4 + 6 44 – 28 + 6 16 + 6 22 Divide and multiply from left to right. Subtract and add from left to right.

10. Course 2 1-5 Order of Operations Simplify the expression. Additional Example 1C: Using the Order of Operations 3 + 2 3 · 5 3 + 8 · 5 3 + 40 43 Evaluate the power. Multiply. Add.

11. Course 2 1-5 Order of Operations Check It Out: Example 1A Simplify the expression. 2 + 24 ÷ 6 2 + 4 6 Divide. Add.

12. Course 2 1-5 Order of Operations Check It Out: Example 1B Simplify the expression. 28 – 21 ÷ 3 · 4 + 5 28 – 7 · 4 + 5 28 – 28 + 5 0 + 5 5 Divide and multiply from left to right. Subtract and add from left to right.

13. Course 2 1-5 Order of Operations Check It Out: Example 1C Simplify the expression. 2 + 3 2 · 4 2 + 9 · 4 2 + 36 38 Evaluate the power. Multiply. Add.

14. Course 2 1-5 Order of Operations Simplify the expression. Additional Example 2A: Using the Order of Operations with Grouping Symbols 42 – (3 · 4) ÷ 6 42 – 12 ÷ 6 42 – 2 40 Perform the operation inside the parentheses. Divide. Subtract.

15. Course 2 1-5 Order of Operations When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set. Helpful Hint

16. Course 2 1-5 Order of Operations Additional Example 2B: Using the Order of Operations with Grouping Symbols [(26 – 4 · 5) + 6] 2 [(26 – 20) + 6] 2 [6 + 6] 2 12 2 144 The parentheses are inside the brackets, so perform the operations inside the parentheses first. Simplify the expression.

17. Course 2 1-5 Order of Operations Check It Out: Example 2A Simplify the expression. A. 24 – (4 · 5) ÷ 4 24 – (4 · 5) ÷ 4 24 – 20 ÷ 4 24 – 5 19 Perform the operation inside the parentheses. Divide. Subtract.

18. Course 2 1-5 Order of Operations Check It Out: Example 2B Simplify the expression. [(32 – 4 · 4) + 2] 2 [(32 – 16) + 2] 2 [16 + 2] 2 18 2 324 The parentheses are inside the brackets, so perform the operations inside the parentheses first.

19. Course 2 1-5 Order of Operations Additional Example 3: Application Sandy runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks. Simplify the expression (5 + 3 · 3) · 4 to find how many miles she ran last month. WeekDays Week 15 Week 23 Week 33 Week 43 (5 + 3 · 3) · 4 (5 + 9) · 4 14 · 4 56Sandy ran 56 miles last month. Perform the operations in parentheses first. Add. Multiply.

20. Course 2 1-5 Order of Operations Check It Out: Example 3 Jill is learning vocabulary words for a test. From the list, she already knew 30 words. She is learning 4 new words a day for 3 days each week. Evaluate the expression 3 · 4 · 7 + 30 to find out how many words will she know at the end of seven weeks. DayWords Initially30 Day 14 Day 24 Day 34 (3 · 4 · 7) + 30 (12 · 7) + 30 84 + 30 114 Perform the operations in parentheses first. Jill will know 114 words at the end of 7 weeks. Multiply. Add.

21. Course 2 1-5 Order of Operations Lesson Quiz: Part I Simplify each expression. 1. 27 + 56 ÷ 7 2. 9 · 7 – 5 3. (28 – 8) ÷ 4 4. 136 – 10 2 ÷ 5 5. (9 – 5) 3 · (7 + 1) 2 ÷ 4 58 35 5 116 1,024

22. Course 2 1-5 Order of Operations Lesson Quiz: Part II Evaluate. 6. Denzel paid a basic fee of $35 per month plus $2 for each phone call beyond his basic plan. Simplify the expression 35 + 8(2) to find how much Denzel paid for a month with 8 calls beyond the basic plan. $51

23. Course 2 1-5 Order of Operations 1-6 Properties Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

24. Course 2 1-5 Order of Operations Warm Up Evaluate. 1. 2 + 5  3 – 7 2. 5(3 – 1) ÷ (3 + 2) 3. (4 + 1) 2 – 8 ÷ 2 4. 12 ÷ 3  6 – 20 10 2 21 4

25. Course 2 1-5 Order of Operations Problem of the Day Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy? 27

26. Course 2 1-5 Order of Operations Learn how to identify properties of rational numbers and use them to simplify numerical expressions.

27. Course 2 1-5 Order of Operations Vocabulary Commutative Property Associative Property Identity Property Distributive Property

28. Course 2 1-5 Order of Operations

29. Course 2 1-5 Order of Operations

30. Course 2 1-5 Order of Operations

31. Course 2 1-5 Order of Operations Additional Example 1: Identifying Properties of Addition and Multiplication Tell which property is represented. A. (2  6)  1 = 2  (6  1) B. 3 + 0 = 3 C. 7 + 9 = 9 + 7 (2  6)  1 = 2  (6  1) The numbers are regrouped. Associative Property 3 + 0 = 3 One of the factors is 0. Identity Property 7 + 9 = 9 + 7 The order of the variables is switched. Commutative Property

32. Course 2 1-5 Order of Operations Check It Out: Example 1 Tell which property is represented. A. 7  1 = 7 B. 3 + 4 = 4 + 3 C. (5  1)  2 = 5  (1  2) 7  1 = 7 One of the factors is 1. Identity Property 3 + 4 = 4 + 3 The order of the numbers is switched. Commutative Property (5  1)  2 = 5  ( 1  2) The numbers are regrouped. Associative Property

33. Course 2 1-5 Order of Operations Additional Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 B. 20  9  5 21 + 16 + 9 = 16 + 9 + 21 Commutative Property. = 16 + (9 + 21) = 16 + 30 Associative Property. = 46 Add. 20  9  5 = 20  5  9 Commutative Property. = 20  (5  9) = 20  45 Associative Property. = 900 Multiply.

34. Course 2 1-5 Order of Operations Check It Out: Example 2A & B Simplify each expression. Justify each step. A. 17 + 14 + 3 B. 12  3  5 17 + 14 + 3 = 14 + 17 + 3 Commutative Property. = 14 + (17 + 3) = 14 + 20 Associative Property. = 34 Add. 12  3  5 = 3  5  12 Commutative Property. = 3  (5  12) = 3  60 Associative Property. = 180 Multiply.

35. Course 2 1-5 Order of Operations You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

36. Course 2 1-5 Order of Operations Additional Example 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: Method 2: = (6  50) + (6  4) Rewrite 54 as 50 + 4. = 300 + 24 = 324 Use the Distributive Property. Multiply. 6(54) = 6(60 – 6) Rewrite 54 as 60 – 6. = (6  60) – (6  6) = 360 - 36 Use the Distributive Property. Multiply. = 324 Subtract. Add. 6(54) = 6(50 + 4)

37. Course 2 1-5 Order of Operations Check It Out: Example 3 Use the Distributive Property to find 8(19). Method 1: Method 2: = (8  10) + (8  9) Rewrite 19 as 10 + 9. = 80 + 72 = 152 Use the Distributive Property. Multiply. 8(19) = 8(20 – 1) Rewrite 19 as 20 – 1. = (8  20) – (8  1) = 160 – 8 Use the Distributive Property. Multiply. = 152 Subtract. Add. 8(19) = 8(10 + 9)

38. Course 2 1-5 Order of Operations Lesson Quiz Tell which property is represented. 1. 17  1 = 17 2. (12 + 14) + 5 = 12 + (14 + 5) 3. 2  16 = 16  2 Simplify each expression. Justify each step. 4. 4  12  25 5. 48 + (15 + 2) Use the Distributive Property to find each product. 6. 6  (12 + 5) 7. (20 – 7)  9 Identity Property Associative Property Commutative Property 1,200 65 102 117