Notes for Lesson 1-1: Variables and Expressions
1. Translating between Algebra and words.
Vocabulary:
Quantity – Anything that can be measured or counted
Variable - A letter or symbol used to represent a value that can change
Constant - A value that does not change
Numerical Expression - An expression that may contain only constants and operations
Algebraic Expression - An expression that contains variables, constants and operations
***You will need to be able to translate between Algebraic expressions and words. To do this you need to
recognize what words mean what operations.
Addition
plus
sum
increased by
Subtraction
minus
quotient
less than
Multiplication
times
product
equal groups of
Division
divided by
quotient
goes into
Examples: Give two ways to write each algebraic expression in words
A. x  3
sum of x and 3
x increased by 3
B. m  7
difference of m and 7
7 less than m
C. 2  y
product of 2 and y
2 times y
D. k  5
quotient of k and 5
k divided by 5
Examples: Translating for words to algebra
A. Eve reads 25 pages per hour. Write an expression for the number of pages she reads in h hours.
25h
B. Sam is 2 years younger than Sue, who is y years old. Write an expression for Sam's age.
y2
C. Williams runs a mile in 12 minutes. Write an expression for the number of miles that William can run in m
minutes.
m 12
We can use two operations at once such as:
D. Nine less than the quotient of 6 and a number x
E. The product of 4 and the sum of a number and 4
F. The quotient of 5 and the sum of 12 and a number x
6
𝑥
−9
4(x+4)
5
12+𝑥