Algebraic Expressions Essential Question

1
Algebraic Expressions Essential Question
How do verbal expressions translate to algebraic
expressions?
2
Warm Up Evaluate each expression for the given
values of the variables. Which operation
symbol goes with each word?
23
1. 9y 13 for y 4
18
2. 6n 2p for n 2 and p 3
1
3. 3x y for x 1 and y 2
?

4. Sum
5. Product
?
?
6. Quotient
7. Difference
3
Word Phrases Expression


?
?

• a number plus 5

• sum of a number and 5

n 5

• 5 more than a number

• subtract 11 from a number

x 11

• difference of a number and 11

• 11 less than a number

• 3 multiplied by a number

3 ? m or 3m

• product of 3 and a number

• 7 divided into a number

• quotient of a number and 7

4
Additional Example 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)
5
Check It Out! Example 1
Write an algebraic expression for each word
phrase.
A. 88 times the difference of h and 4
88 times the difference of h and 4
88 (h 4)
88(h 4)
B. the quotient of a number f and 6
quotient of f and 6
f ? 6
6
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
7
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
8
To solve a word problem, first interpret the
action you need to perform and then choose the
correct operation for that action.
9
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 determine what the cost
would be if n people attended the function. Then
evaluate the expression for 20, 21, 22, or 23
people.
10 n
Combine n equal amounts of 10.
10n
Cost in dollars
n 10n Cost




20 10(20) 200
Evaluate for n 20, 21, 22, and 23.
21 10(21) 210
22 10(22) 220
23 10(23) 230
10
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
Cost in dollars
n 1.99n Cost




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
11
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.
12
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 did Tina pay for the jacket?
43 d
43 10.24 32.76
Substitute 10.24 for d.
Tina paid 32.76 for the jacket.