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**1.2 Apply order of operations**

You will use the order of operations to evaluate expressions. Essential Question: How do you use the order of operations to evaluate an expression?

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**Evaluate the expression 27 32 2 3. –**

EXAMPLE 1 Evaluate expressions Evaluate the expression – STEP 1 There are no grouping symbols, so go to Step 2. STEP 2 Evaluate powers. – 3 = – 3 Evaluate power. STEP 3 Multiply and divide from left to right. – 3 = – 3 Divide. – 3 = 6 – 3 Multiply.

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**Add and subtract from left to right.**

EXAMPLE 1 Evaluate expressions STEP 4 Add and subtract from left to right. 6 – 3 = 3 Subtract. ANSWER The value of the expression – 3 is 3.

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GUIDED PRACTICE for Example 1 1. Evaluate the expression 20 – 42 ANSWER 2. Evaluate the expression ANSWER 3. Evaluate the expression ANSWER

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GUIDED PRACTICE for Example 1 4. Evaluate the expression – 4 ANSWER

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**Evaluate expressions with grouping symbols**

EXAMPLE 2 Evaluate expressions with grouping symbols Evaluate the expression. a. 7(13 – 8) = 7(5) Subtract within parentheses. = 35 Multiply. b. 24 – (32 + 1) = 24 – (9 + 1) Evaluate power. = 24 – 10 Add within parentheses. = 14 Subtract. c. 2[30 – (8 + 13)] = 2[30 – 21] Add within parentheses. c. = 2[9] Subtract within brackets. = 18 Multiply.

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**Evaluate an algebraic expression**

EXAMPLE 3 Evaluate an algebraic expression Evaluate the expression when x = 4. 9x 3(x + 2) = 3(4 + 2) 9 4 Substitute 4 for x. 3 6 9 4 = Add within parentheses. 18 36 = Multiply. = 2 Divide.

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GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression. (3 + 9) = 48 6. 3(8 – 22) = 12 7. 2[( 9 + 3) ] = 6

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GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression when y = 8. y2 – 3 8. = 61 12 – y – 1 9. = 3 10y + 1 y + 1 10. = 9

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EXAMPLE 4 Standardized Test Practice

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**Standardized Test Practice**

EXAMPLE 4 Standardized Test Practice SOLUTION 12(3j +2s) + 30 = 12( ) + 30 Substitute 1.25 for j and 2 for s. = 12( ) + 30 Multiply within parentheses. = 12(7.75) + 30 Add within parentheses. = Multiply. = 123 Add. Multiply. The sponsor’s cost is $123.The correct answer is B A B C D ANSWER

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GUIDED PRACTICE for Example 4 11. WHAT IF? In Example 4, suppose the number of volunteers doubles. Does the sponsor’s cost double as well? Explain. The sponsor’s cost is $216. No; the total cost of the juice drinks and sandwiches will double, but the cost of the trash bags will not. ANSWER

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Daily Homework Quiz Evaluate the expression. ANSWER 15 (5 – 3)2 ANSWER 16 3. 2(c ) when c = 4 ANSWER 40

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Daily Homework Quiz 4. g2 – 8 2g – 5 when g = 6 ANSWER 4 5. The cost (in dollars) to buy p posters at the Posters Plus online store is given by the expression 3.5p At the More Posters online store, the cost is given by 4.25p Which store has the lower cost for 5 posters? The cost at the More Posters online store is less. ANSWER

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**You will use the order of operations to evaluate expressions. **

Essential Question: How do you use the order of operations to evaluate an expression? The order of operations is a series of steps to use when evaluating expressions. Parentheses, brackets, and fraction bars act as grouping symbols. Always evaluate expressions using the following order: evaluate expressions inside grouping symbols, evaluate powers, multiply and divide from left to right, and then add and subtract from left to right.

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Divide. Evaluate power. 27 3 2 2 – 3 = 27 9 2 – 3 EXAMPLE 1 27 9 2 – 3 = 3 2 – 3 3 2 – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

Divide. Evaluate power. 27 3 2 2 – 3 = 27 9 2 – 3 EXAMPLE 1 27 9 2 – 3 = 3 2 – 3 3 2 – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

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