Page 108 - Algebra 1

L E S S O N Translating Between Words and
17
Algebraic Expressions
Warm Up
1. Vocabulary An expression that has only numbers and operations is a
(9)
(numeric, variable) expression. Simplify each expression.
2. 5 - 7 + 5 - (-3) 3. (5 + 7)4 + 7(5 - 3) (6) (15)
4. (x3 + m5)x2m2 (15)
5. Which value is equivalent to −(−6)3?
(11)
A -216 B 216 C 18 D -18
New Concepts Algebraic expressions, or variable expressions, are expressions that contain at least one variable. A numeric expression contains only numbers and
operations.
Translating Word and Phrases into Algebraic Expressions
Words
Phrases
Expressions
Addition
sum, total, more than, added, increased, plus
4 added to a number
7 increased by a number
x+4 7+x
Subtraction
less, minus, decreased by, difference, less than
the difference of 5 and a number 8 less than a number
5-x x-8
Multiplication
product, times, multiplied
the product of a number and 12 a number times 3
12(x) 3x
Division
quotient, divided by, divided into
the quotient of a number and 6 10 divided by a number
x÷6
_10 x
Hint
Remember that in multiplication, the coefficient is usually written before the variable.
Example
1
Translating Words into Algebraic Expressions
Write an algebraic expression for each phrase.
a. y increased by 12 SOLUTION y + 12
c. 8 less than the quotient of m and 15
SOLUTION _m - 8 15
b. the product of x and 4 SOLUTION 4x
Hint
“Years younger than” means less than.
d.
James is 6 years younger than Lydia, who is x years old. Write the expression that shows James’s age.
Online Connection www.SaxonMathResources.com
SOLUTION If x represents Lydia’s age, then x - 6 represents James’s age.
Lesson 17 93