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ORDER OF OPERATIONS

Learn how to apply the order of operations to simplify expressions with multiple operations. Understand the vocabulary and follow the PEMDAS rule. Practice and master the properties of mathematics.

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ORDER OF OPERATIONS

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  1. ORDER OF OPERATIONS How to do a math problem with more than one operation in the correct order.

  2. Objective • I will be able to apply the order of operations to simplify expressions.

  3. VOCABULARY Numerical Expression A collection of numbers, operations, and grouping symbols Grouping Symbols Characters used to change the order of operations in an expression EX: ( ) Parenthesis [ ] Brackets Division Bar ----

  4. VOCABULARY Order of operations A procedure for evaluating an expression involving more than one operation PEMDAS ( ) 3² x/÷ (WHICHEVER COMES 1ST) +/- (WHICHEVER COMES 1ST)

  5. Simplify • To simplify an expression when there are more than two operations in the expression, you must use a set of rules called the order of operations.

  6. ORDER OF OPERATIONS • Simplify the terms within parentheses. • Simplify the terms with exponents. • Multiply and divide from left to right. • Add and subtract from left to right. PEMDAS

  7. PEMDAS • Remember the order by the phrase • Please • Excuse • My Dear • Aunt Sally

  8. The “P” and “E” • The “P” stands for items in parenthesis • Do all items in the parenthesis first (2 + 3) The “E” stands for Exponents Do anything that has a exponent (power) 82

  9. The “MD” • Represents Multiply and Divide • Do which ever one of these comes first in the problem Work these two operations from left to right

  10. The “AS” • Represents Add and Subtract • Do which ever one of these comes first • Work left to right 8 + 7 - 5 + 2

  11. Example Find 8 + (4 x 24) ÷ 32 Step 1: Simplify within the parentheses. 8 + (4 x 24)÷ 32 8 + (96) ÷ 32 Step 2: Divide 96 ÷ 32 8 + 3 Step 3: Add 8 +3 11 Solution:8 + (4 x 24) ÷ 32 = 11 24 X 4 32 96 8 + 3

  12. What happens if we don’t follow the order of operations? • If we just work the problem from left to right, we won’t get the correct answer! 8 + (4 x 24) ÷ 32 8+4 = 12 12 x24 = 288 288 ÷ 32 9 9 does not equal 11!

  13. Another Example Simplify: (20 – 2) ÷ 3 Step 1: Simplify within parentheses (20 -2) ÷ 3 Step 2: Divide (18) ÷ 3 Solution: (20 – 2) ÷ 3 = 6

  14. Janet 14 – (5+2) X 2 14 – 7 x 2 7 x 2 14 John 14 – (5+2) X 2 14 – 7 x 2 14 – 14 0 Look at the two students and decide which one correctly followed the order of operations!

  15. 3+23- (9+1) PEMDAS 3+23- 10 3+8-10 11-10 1

  16. 3 (9+1) + 62 PEMDAS 3(10)+62 3(10)+36 30+36 66

  17. Let’s practice!You have 5 seconds:take out your whiteboard, expo marker, and felt eraser.

  18. 4+5 x (6-2) PEMDAS 4+5 x 4 4+20 24

  19. 4+ 10 x 23 -16 PEMDAS 4+10 x 8 -16 4+ 80 -16 84-16 68

  20. 21 + 102 10 PEMDAS 21+10010 21 + 10 31

  21. 10+72-2 x 5 PEMDAS 10+49–2 x 5 10+49- 10 59 - 10 49

  22. 64  (9 x 3-19) PEMDAS 64(27 –19) 64 8 8

  23. PROPERTIES • COMMUTATIVE (+) 2 + 7 = 7 + 2 a + b = b + a • COMMUTATIVE (x) 4 x 9 = 9 x 4 ab = ba • ASSOCIATIVE (+) 3 + (5+1) = (3+5) + 1 a + (b+c) = (a+b) + c • ASSOCIATIVE (x) 8 x (2x9) = (8x2) x 9 a(bc) = (ab)c • DISTRIBUTIVE

  24. YOUR TURN … ON SLATES!!! YOU HAVE 5 SECONDS!!! 1) 5 + (12 – 3) 5 + 9 14 2) 8 – 3 • 2 + 7 8 - 6 + 7 2 + 7 9 3) 39 ÷ (9 + 4) 39 ÷ 13 3

  25. 15 • 103 15 • 1,000 15,000 • 10 + 8 ÷ 2 – 6 10 + 4 - 6 14 - 6 8 • 36 ÷ (1 + 2)2 36 ÷ 32 36 ÷ 9 4 7) 3 • 104 3 • 10,000 30,000

  26. 14 + 3(7 -2) – 2 • 5 14 + 3 • 5 - 2 • 5 14 + 15 - 2 • 5 14 + 15 – 10 29 – 10 19 • (5 – 1)3 ÷ 4 43 ÷ 4 64 ÷ 4 16

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