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Operation Verbal Expressions Algebraic Expressions


add 3 to a number
a number plus 3

n 3
the sum of a number and 3
3 more than a number
WRITE THESE IN THE BLANK SPACE
a number increased by 3
subtract 12 from a number
a number minus 12
the difference of a number and 12
-
x 12
12 less than a number
a number decreased by 12
take away 12 from a number
a number less than 12
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Operation Verbal Expressions Algebraic Expressions


2 times a number
2 multiplied by a number
2m or 2 m

WRITE THESE IN THE BLANK SPACE
the product of 2 and a number
6 divided into a number

a number divided by 6
the quotient of a number and 6
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Example 1 Translating Verbal Expressions into
Algebraic Expressions
Write each phrase as an algebraic expression.
A. the quotient of a number and 4
quotient means divide
B. w increased by 5
increased by means add
w 5
4
Example 1continued
C. the difference of 3 times a number and 7
difference of means subtract
times means multiply
3 x 7
3x 7
D. the quotient of 4 and a number, increased by
10
the quotient of 4 and a number, increased by 10
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Check It Out! Example 1
Write each phrase as an algebraic expression.
A. a number decreased by 10
decreased means subtract
n 10
B. r plus 20
plus means add
r 20
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When solving real-world problems, you may need to
determine the action to know which operation to
use.
Action Operation




WRITE THESE IN THE BLANK SPACE
Put parts together
Add
Put equal parts together
Multiply
Subtract
Find how much more
Separate into equal parts
Divide
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Example 2A Translating Real-World Problems into
Algebraic Expressions
Mr. Campbell drives at 55 mi/h. Write an
algebraic expression for how far he can drive in
h hours. Then evaluate the expression for h 3,
and tell what the value of the expression means.
You need to put equal parts together. This
involves multiplication.
55mi/h ? h hours
Write the expression.
55(h)
Substitute 3 for h.
55 ? 3
Multiply.
165
Mr. Campbell can drive 165 miles in 3 hours if he
drives at 55 miles per hour.
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Example 2B
On a test, multiple-choice questions are worth 1
point, short-answer questions are worth 2 points,
and essay questions are worth 10 points. Write an
algebraic expression for Maritzas total points
if she answers m multiple-choice, s short-answer,
and e essay questions correctly. Then evaluate
the expression for m 48, s 8, and e 3, and
tell what the value of the expression means.
Multiply to put equal parts together.
Points for multiple-choice questions 1m or m
Points for short-answer questions 2s
Points for essay questions 10e
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Example 2B Continued
Total points 1m 2s 10e
Write the expression.
Substitute 48 for m, 8 for s, and 3 for e.
1(48) 2(8) 10(3)
48 16 30
Multiply from left to right.
Add.
94
Maritza earned 94 points on the test.
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Check It Out! Example 1
1. Write each phrase as an algebraic expression.
4 times the difference of y and 8
4 times the difference of y and 8
y 8
4
4(y 8)
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Check It Out! Example 2
Julie Ann works on an assembly line building
computers. She can assemble 8 units an hour.
Write an expression for the number of units she
can produce in h hours. Then evaluate the
expression for h 5, and tell what the value of
the expression means.
You need to put equal parts together. This
involves multiplication.
8 units/h ? h hours 8h
8(h) units
Write the expression.
Substitute 5 for h.
8(5) units
Multiply.
40 units
Julie Ann can build 40 units in 5 hours.
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Check It Out! Example 2B
For lunch, students have 3 choices. A turkey
sandwich for 3, a bowl of soup for 2, and a
chicken salad for 4. Write an algebraic
expression to show how much it costs for s
sandwiches, b bowls of soup, and c chicken
salads. Then evaluate the expression for s 32,
b 20, and c 10, and tell what the value of
the expression means.
Multiply to put equal parts together.
turkey sandwich 3s
bowls of soup 2b
chicken salad 4c
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Check It Out! Example 2B Continued
Add to put equal parts together.
Total cost 3s 2b 4c
3s 2b 4c
Write the expression.
Substitute 32 for s, 20 for b, and 10 for c.
3(32) 2(20) 4(10)
Multiply from left to right.
96 40 40
176
Add.
The cost of 32 turkey sandwiches, 20 bowls of
soup, and 10 chicken salads is 176.