1.2 Apply order of operations

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Presentation transcript:

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?

Evaluate the expression 27 32 2 3. – EXAMPLE 1 Evaluate expressions Evaluate the expression 27 32 2 3. – STEP 1 There are no grouping symbols, so go to Step 2. STEP 2 Evaluate powers. 27 32 2 – 3 = 27 9 2 – 3 Evaluate power. STEP 3 Multiply and divide from left to right. 27 9 2 – 3 = 3 2 – 3 Divide. 3 2 – 3 = 6 – 3 Multiply.

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 27 32 2 – 3 is 3.

GUIDED PRACTICE for Example 1 1. Evaluate the expression 20 – 42 ANSWER 1. 4 2. Evaluate the expression 2 32 + 4 ANSWER 2. 22 3. Evaluate the expression 32 23 + 6 ANSWER 3. 10

GUIDED PRACTICE for Example 1 4. Evaluate the expression 15 + 62 – 4 ANSWER 4. 47

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.

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.

GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression. 5. 4(3 + 9) = 48 6. 3(8 – 22) = 12 7. 2[( 9 + 3) 4 ] = 6

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

EXAMPLE 4 Standardized Test Practice

Standardized Test Practice EXAMPLE 4 Standardized Test Practice SOLUTION 12(3j +2s) + 30 = 12(3 1.25 + 2 2) + 30 Substitute 1.25 for j and 2 for s. = 12(3.75 + 4) + 30 Multiply within parentheses. = 12(7.75) + 30 Add within parentheses. = 93 + 30 Multiply. = 123 Add. Multiply. The sponsor’s cost is $123.The correct answer is B. . A B C D ANSWER

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

Daily Homework Quiz Evaluate the expression. 1. 33  9 + 4 3 ANSWER 15 2. 12 + (5 – 3)2 ANSWER 16 3. 2(c2 + 4 ) when c = 4 ANSWER 40

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 + 6.75. At the More Posters online store, the cost is given by 4.25p + 2.55. Which store has the lower cost for 5 posters? The cost at the More Posters online store is less. ANSWER

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.