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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?
Warm-Up Exercises
Divide.
Evaluate power.27 32 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 left to right.STEP 3
Evaluate the expression 27 32 2 3.–
There are no grouping symbols, so go to Step 2.STEP 1
Evaluate powers.STEP 2
Warm-Up Exercises
STEP 4Add and subtract from left to right.
6 – 3 = 3
EXAMPLE 1
Subtract.
ANSWER
The value of the expression 27 32 2 – 3 is 3.
Evaluate expressions
Warm-Up ExercisesGUIDED 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
Warm-Up ExercisesGUIDED PRACTICE for Example 1
4. Evaluate the expression 15 + 62 – 4
ANSWER
4. 47
Warm-Up Exercises
24 – (9 + 1)
= 2[9]
EXAMPLE 2 Evaluate expressions with grouping symbols
Evaluate the expression.
a. 7(13 – 8) == 35
Subtract within parentheses.
Multiply.
b. 24 – (32 + 1) = Evaluate power.
= 24 – 10 Add within parentheses.
= 14 Subtract.
c. 2[30 – (8 + 13)] = Add within parentheses.
Subtract within brackets.
= 18 Multiply.
7(5)
2[30 – 21]
Warm-Up ExercisesEXAMPLE 3 Evaluate an algebraic expression
Evaluate the expression when x = 4.
9x3(x + 2)
Substitute 4 for x.
Add within parentheses.
1836= Multiply.
= 2 Divide.
= 3(4 + 2) 9 4
3 6 9 4
=
Warm-Up ExercisesGUIDED 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
Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3
Evaluate the expression when y = 8.
= 61y2 – 38.
= 312 – y – 19.
= 910y + 1 y + 1
10.
Warm-Up ExercisesStandardized Test PracticeEXAMPLE 4
Warm-Up ExercisesStandardized Test PracticeEXAMPLE 4
SOLUTION
Substitute 1.25 for j and 2 for s.
= 12(3.75 + 4) + 30 Multiply withinparentheses.
= 93 + 30 Multiply.
= 123 Add.
The sponsor’s cost is $123.The correct answer is B. .A B C D
ANSWER
= 12(7.75) + 30 Add within parentheses.
= 12(3 1.25 + 2 2) + 3012(3j +2s) + 30
Warm-Up ExercisesGUIDED 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 sandwicheswill double, but the cost of the trash bags will not.
ANSWER
Warm-Up ExercisesDaily Homework Quiz
3. 2(c2 + 4 ) when c = 4
ANSWER 16
ANSWER 40
2. 12 + (5 – 3)2
Evaluate the expression.
ANSWER 15
1. 33 9 + 4 3
Warm-Up ExercisesDaily Homework Quiz
The cost at the More Posters online store is less.
ANSWER
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?
4.
g2 – 8 2g – 5 when g = 6
• 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.
