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Published byReynard Rice Modified over 6 years ago

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Order of Operations Also known to as PEMDAS

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EXAMPLE 1 Following Order of Operations Music You buy a used guitar for $50. You then pay $10 for each of five guitar lessons. The total cost can be found by evaluating the expression 50 + 10 x 5. Is the total cost $100 or $300 ?

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= 50 + 50 EXAMPLE 1 To find the guitar costs described, evaluate 50 + 10 5. 50 + 10 5 First multiply 10 and 5. = 100 Then add 50 and 50. ANSWER The total cost is $100. Following Order of Operations

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EXAMPLE 2 Evaluating a Variable Expression Substitute 25 for x and 2 for y. Evaluate the power. Multiply 8 and 3. = 1 Subtract 24 from 25. x 3y 3 – = 25 3(2 3 ) – = 25 3(8) – = 25 24 – Evaluate x 3y 3 when x = 25 and y = 2. –

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GUIDED PRACTICE for Examples 1 and 2 Evaluate the expression. 1. 5 + 6 x 5 35 ANSWER 2. 20 4 2 2 – 12 ANSWER 3. 10 3 + 3 3 57 ANSWER

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GUIDED PRACTICE 4. Evaluate a + 4b 2 when a = 6 and b = 5. 106 ANSWER for Examples 1 and 2

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EXAMPLE 3 Using the Left-to-Right Rule 5 + 3 - 6 a.a.12 7 + 3 - 6 = – Subtract 7 from 12. = 8 6 – Add 5 and 3. = 2 Subtract 6 from 8. 6 ) 3 = Divide 54 by 9. 6 3 = 18 Multiply 6 and 3. 54 9 (3+ b.b.

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EXAMPLE 4 Using Grouping Symbols Subtract inside parentheses. = 4(3) = 12 Multiply 4 and 3. = 20 10 Evaluate expressions grouped by fraction bar. = 2 Divide 20 by 10. Add inside parentheses. Evaluate the power. = 75 Multiply 25 and 3. = 5 2 3 = 25 3 b.b. 13 + 7 2 5 a.a.4(8 5) – c.c. (4 + 1) 2 3

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GUIDED PRACTICE for Examples 3 and 4 Evaluate the expression. 5. 18 10 + 5 - 1 – 12 ANSWER 6. (3 7) (6 - 3) 2 + 90 ANSWER 7. 8 3 4 + 2 4 ANSWER

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GUIDED PRACTICE Evaluate the expression. 8. 25 6 14 3 – + – 8 ANSWER 9. 16 2 11 88 ANSWER 10. 16(9 + 1) - 30 130 ANSWER for Examples 3 and 4

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EXAMPLE 5 Standardized Test Practice

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EXAMPLE 5 SOLUTION = 500 + 1200 + 600 Multiply first. = 1700 + 600 Add 500 and 1200. = 2300 Add 1700 and 600. ANSWER You score 2300 points. The correct answer is D. You need to evaluate the expression 1 500 + 3 400 + 4 150. 1 500 + 3 400 + 4 150 Standardized Test Practice

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GUIDED PRACTICE for Example 5 11. What If? In Example 5, suppose you complete two burntwists, two backflips, and one 360° flip. How many points do you score? 1950 points. ANSWER

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