Warm Up

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Warm Up
Lesson Presentation
Lesson Quiz
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Warm Up Simplify. 1. 42 2. 5 16
3. 23 4. 3 7
16
8
4
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Translate each word phrase into a numerical or
algebraic expression.
5. the product of 8 and 6
8 ? 6
6. the difference of 10y and 4
10y 4
Simplify each fraction.
7.
8.
8
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Objective
Use the order of operations to simplify
expressions.
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Vocabulary
order of operations
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When a numerical or algebraic expression
contains more than one operation symbol, the
order of operations tells which operation to
perform first.
Order of Operations
Perform operations inside grouping symbols.
First
Second
Evaluate powers.
Perform multiplication and division from left to
right.
Third
Perform addition and subtraction from left to
right.
Fourth
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Grouping symbols include parentheses ( ),
brackets , and braces . If an expression
contains more than one set of grouping symbols,
evaluate the expression from the innermost set
first.
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Helpful Hint
The first letter of these words can help you
remember the order of operations.
Parentheses Exponents Multiply Divide Add Subtract
Please Excuse My Dear Aunt Sally
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Example 1 Translating from Algebra to Words
Simplify each expression.
A. 15 2 3 1
15 2 3 1
There are no grouping symbols.
15 6 1
Multiply.
Subtract and add from left to right.
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B. 12 32 10 2
12 32 10 2
There are no grouping symbols.
Evaluate powers. The exponent applies only to the
3.
12 9 10 2
12 9 5
Divide.
Subtract and add from left to right.
8
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Check It Out! Example 1a
Simplify the expression.
8 3
There are no grouping symbols.
Divide.
16 3
48
Multiply.
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Check It Out! Example 1b
Simplify the expression.
5.4 32 6.2
There are no grouping symbols.
5.4 32 6.2
5.4 9 6.2
Simplify powers.
3.6 6.2
Subtract
2.6
Add.
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Check It Out! Example 1c
Simplify the expression.
20 2(4 1)
There are two sets of grouping symbols.
20 2(4 1)
Perform the operations in the innermost set.
20 2(5)
Perform the operation inside the brackets.
20 10
2
Divide.
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Example 2A Evaluating Algebraic Expressions
Evaluate the expression for the given value of x.
10 x 6 for x 3
First substitute 3 for x.
10 x 6
10 3 6
Multiply.
Subtract.
10 18
8
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Example 2B Evaluating Algebraic Expressions
Evaluate the expression for the given value of x.
42(x 3) for x 2
42(x 3)
First substitute 2 for x.
42(2 3)
Perform the operation inside the parentheses.
42(1)
16(1)
Evaluate powers.
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Multiply.
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Check It Out! Example 2a
Evaluate the expression for the given value of x.
14 x2 4 for x 2
14 x2 4
14 22 4
First substitute 2 for x.
14 4 4
Square 2.
14 1
Divide.
Add.
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Check It Out! Example 2b
Evaluate the expression for the given value of x.
(x 22) (2 6) for x 6
(x 22) (2 6)
(6 22) (2 6)
First substitute 6 for x.
(6 4) (2 6)
Square two.
Perform the operations inside the parentheses.
(24) (8)
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Divide.
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Fraction bars, radical symbols, and
absolute-value symbols can also be used as
grouping symbols. Remember that a fraction bar
indicates division.
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Example 3A Simplifying Expressions with
Other Grouping
Symbols
Simplify.
2(4) 22 42 9
The fraction bar acts as a grouping symbol.
Simplify the numerator and the denominator before
dividing.
Multiply to simplify the numerator.
8 22 16 9
Evaluate the power in the denominator.
Add to simplify the numerator. Subtract to
simplify the denominator.
14 7
2
Divide.
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Example 3B Simplifying Expressions with
Other Grouping
Symbols
Simplify.
342 8 2
The absolute-value symbols act as grouping
symbols.
342 8 2
Evaluate the power.
316 8 2
Divide within the absolute-value symbols.
316 4
Add within the absolute-symbols.
320
3 20
Write the absolute value of 20.
60
Multiply.
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Check It Out! Example 3a
Simplify.
5 2(8) (2) 3
The fraction bar acts as a grouping symbol.
Simplify the numerator and the denominator before
dividing.
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Evaluate the power in the denominator.
Multiply to simplify the numerator.
Add.
Divide.
1
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Check It Out! Example 3b
Simplify.
4 72 3
The absolute-value symbols act as grouping
symbols.
4 72 3
Subtract within the absolute-value symbols.
32 3
32 3
Write the absolute value of 3.
9 3
Square 3.
3
Divide.
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Check It Out! Example 3c
Simplify.
The radical symbol acts as a grouping symbol.
Subtract.
3 7
Take the square root of 49.
Multiply.
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You may need grouping symbols when translating
from words to numerical expressions.
Remember!
Look for words that imply mathematical operations.
difference subtract
sum add
product multiply
quotient divide
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Example 4 Translating from Words to Math
Translate each word phrase into a numerical or
algebraic expression.
A. the sum of the quotient of 12 and 3 and
the square root of 25
Show the quotient being added to .
B. the difference of y and the product of 4
and
Use parentheses so that the product is evaluated
first.
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Check It Out! Example 4
Translate the word phrase into a numerical or
algebraic expression the product of 6.2 and the
sum of 9.4 and 8.
Use parentheses to show that the sum of 9.4 and 8
is evaluated first.
6.2(9.4 8)
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Example 5 Retail Application
A shop offers gift-wrapping services at three
price levels. The amount of money collected for
wrapping gifts on a given day can be found by
using the expression 2B 4S 7D. On Friday the
shop wrapped 10 Basic packages B, 6 Super
packages S, and 5 Deluxe packages D. Use the
expression to find the amount of money collected
for gift wrapping on Friday.
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Example 5 Continued
2B 4S 7D
First substitute the value for each variable.
2(10) 4(6) 7(5)
20 24 35
Multiply.
44 35
Add from left to right.
79
Add.
The shop collected 79 for gift wrapping on
Friday.
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Check It Out! Example 5
Another formula for a player's total number of
bases is Hits D 2T 3H. Use this expression
to find Hank Aaron's total bases for 1959, when
he had 223 hits, 46 doubles, 7 triples, and 39
home runs.
Hits D 2T 3H total number of bases
First substitute values for each variable.
223 46 2(7) 3(39)
223 46 14 117
Multiply.
400
Add.
Hank Aarons total number of bases for 1959 was
400.
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Lesson Quiz
Simply each expression.
1. 25 (6 4)
1
4
3. 5 ? 8 4 16 22
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Translate each word phrase into a numerical or
algebraic expression.
4. 3 three times the sum of 5 and n
3(5 n)
5. the quotient of the difference of 34 and 9 and
the square root of 25
6. the volume of a storage box can be found
using the expression l w(w 2). Find the
volume of the box if l 3 feet and w 2 feet.
24 cubic feet