Algebraic Expressions

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Algebraic Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course 3
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Warm Up Evaluate each expression for the given
values of the variables. Which operation
symbol goes with each word?
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1. 9y ? 13 for y 4
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2. 6n 2p for n 2 and p 3
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3. 3x ? y for x 1 and y 2

4. Sum
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5. Product
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6. Quotient
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7. Difference
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Problem of the Day Find a pair of numbers that
fits the description. Their product is 221 and
their sum is 30.
13, 17
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Learn to translate between algebraic expressions
and word phrases.
5

• a number plus 5

• add 5 to a number

n 5

• sum of a number and 5

• 5 more than a number

• a number increased by 5

• a number minus 11

• subtract 11 from a number

x ? 11

• difference of a number and 11

• 11 less than a number

• a number decreased by 11

• 3 times a number

• 3 multiplied by a number

3m

• product of 3 and a number

• a number divided by 7

• 7 divided into a number

• quotient of a number and 7

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Additional Examples 1 Translating Word Phrases
into Math Expressions
Write an algebraic expression for each word
phrase.
A. 9 less than a number w
9 less than a number w
w 9
w 9
B. 3 increased by the difference of p and 5
3 increased by the difference of p and 5
3 (p 5)
3 p 5
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Check It Out Example 1
Write an algebraic expression for each word
phrase.
A. the sum of a number h and 88 minus 4
the sum of h and 88 minus 4
h 88 4
h 88 4
B. the quotient of a number f and 6
quotient of f and 6
f ? 6
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Additional Example 2 Translating Math
Expressions into Word Phrases
Write a word phrase for the algebraic expression
9 3c.
9 3c
9 3 c
9 minus the product of 3 and c
9 minus the product of 3 and c.
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Check It Out Example 2
Write a word phrase for the algebraic expression
7 19b.
7 19b
7 19 b
7 plus the product of 19 and b
7 plus the product of 19 and b.
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To solve a word problem, you must first interpret
the action you need to perform and then choose
the correct operation for that action.
Combine
Add
How many all together?
Combine equal groups
How many all together?
Multiply
Separate
How many more? How many less?
Subtract
Separate into equal groups
How many equal groups?
Divide
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Additional Example 3 Writing and Evaluating
Expressions in Word Problems
A restaurant leased its banquet hall for a
function. The cost was 10 per person. Write an
algebraic expression to evaluate what the cost
would be if 20, 21, 22, or 23 people attended the
function
10 dollars n
Combine n equal amounts of 10.
10n
In dollars
Evaluate for n 20, 21, 22, and 23.
20 10 20 200
21 10 21 210
22 10 22 220
23 10 23 230
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Check It Out Example 3
Gasoline costs 1.99 per n gallons. What will the
cost be for 10, 12, 14, and 15 gallons?
1.99 n
Combine n equal amounts of 1.99.
1.99n
In dollars
10 1.99 10 19.90
Evaluate for n 10, 12, 14, and 15.
12 1.99 12 23.88
14 1.99 14 27.86
15 1.99 15 29.85
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Additional Example 4 Writing a Word Problem from
a Math Expression
Write a word problem that can be evaluated by the
algebraic expression 27 t, and evaluate the
expression for t 1.76.
Possible Answer Amed bought a new sweater for
27 plus sales tax t. If the tax was 1.76, what
was the total cost of the sweater?
27 t
27 1.76 28.76
Substitute 1.76 for t.
The total cost of the sweater was 28.76.
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Check It Out Example 4
Write a word problem that can be evaluated by the
algebraic expression 43 - d, and evaluate the
expression for d 10.24.
Possible Answer Tina bought a new jacket for
43 minus a store credit. If the store credit was
10.24 , what was the total cost of the jacket?
43 d
43 10.24 33.24
Substitute 10.24 for t.
The total cost of the jacket was 33.24.
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Lesson Quiz
Write an algebraic expression for each word
phrase. 1. 5 less than a number k 2. a number
x divided by 11 3. 4 times the sum of n and
5 Write an algebraic expression to evaluate the
word problem. 4. Karen buys n raffle tickets for
0.50 each. If she buys 13 of them, how much
will they cost?
k 5
4(n 5)
0.50n 6.50