Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Evaluate each algebraic expression for
the given values of the variables. 1. 7x 4
for x 6 2. 8y 22 for y 9 3. 12x
for x 7 and y 4 4. y 3z for y 5 and z
6
46
50
8 y
86
23
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(No Transcript)
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Objective You will learn how to translate words
into numbers, variables, and operations.
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A Great Dane weighs about 40 times as much as a
Chihuahua. An expression for the weight of the
Great Dane could be 40c, where c is the weight of
the Chihuahua.
When solving real-world problems, you will need
to translate words, or verbal expressions, into
algebraic expressions.
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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
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
2m or 2 m
2 multiplied by a number

the product of 2 and a number
6 divided into a number
6
a

a number divided by 6
or
a 6
the quotient of a number and 6
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Translating Verbal Expressions into Algebraic
Expressions
Write each phrase as an algebraic expression.
Example 1 the quotient of a number and 4
quotient means divide
Example 2 w increased by 5
increased by means add
w 5
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Translating Verbal Expressions into Algebraic
Expressions
Write each phrase as an algebraic expression.
Example 3 the difference of 3 times a number
and 7
the difference of 3 times a number and 7
3 x 7
3x 7
Example 4 the quotient of 4 and a number,
increased by 10
the quotient of 4 and a number, increased by 10
10
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Check It Out!
Write each phrase as an algebraic expression.
Example 5 a number decreased by 10
decreased means subtract
n 10
Example 6 r plus 20
plus means add
r 20
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Check It Out!
Write each phrase as an algebraic expression.
Example 7 the product of a number and 5
the product of a number and 5
n 5
5n
Example 8 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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When solving real-world problems, you may need to
determine the action to know which operation to
use.
Action Operation




Put parts together
Add
Put equal parts together
Multiply
Subtract
Find how much more
Divide
Separate into equal parts
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Additional Example 9 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 55(h) miles
55(h) miles
Write the expression.
Substitute 3 for h.
55(3) miles
Multiply.
165
Mr. Campbell can drive 165 miles in 3 hours.
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Additional Example 10 Translating Real- World
Problems into Algebraic Expressions
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.
multiple-choice questions 1m or m
short-answer questions 2s
essay questions 10e
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Additional Example 10 Continued
Add to put the parts together.
Total points 1m 2s 10e
1m 2s 10e
Write the expression.
Substitute 48 for m, 8 for s, and 3 for e.
1(48) 2(8) 10(3)
Multiply from left to right.
48 16 30
94
Add.
Maritza earned 94 points on the test.
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Check It Out! Example 11
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
Julie Ann can build 40 units in 5 hours.
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Check It Out! Example 12
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 12 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.
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Home Learning
On-Line Tutoring
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Lesson Quiz
Write each phrase as an algebraic expression. 1.
18 less than a number 2. the quotient of a
number and 21 3. 8 times the sum of x and 15 4. 7
less than the product of a number and 5
x 18
8(x 15)
5n 7
5. The county fair charges an admission of 6 and
then charges 2 for each ride. Write an algebraic
expression to represent the total cost after r
rides at the fair.
6 2r