1.2 Writing Algebraic
Expressions
Standard: AF 1.1
Objective: Students translate phrases
into expressions and vice versa.
Numerical Expressions
Numerical
Expression
Result
Verbal
Phrase
Add
53
sum  8
The sum of
5 and 3 is 8.
Subtract
10  7
difference  3
The difference
of 10 and 7 is 3.
Multiply
28
product  16
The product
of 2 and 8 is 16.
Divide
24  3
quotient  8
The quotient
of 24 and 3 is 8.
Operation
Backwards Words
Add 3 and 7 = 3 + 7
The sum of 3 and 7 = 3 + 7
3 increased by 7 = 3 + 7
The total of 3 and 7 = 3 + 7
3 more than 7 = 7 + 3
3 added to 7 = 7 + 3
Backwards Words
7 subtract 3 = 7 - 3
The difference of 7 and 3 = 7 - 3
7 decreased by 3 = 7 - 3
7 diminished by 3 = 7 - 3
7 less 3 = 7 - 3
7 less than 3 = 3 - 7
7 subtracted from 3 = 3 - 7
Translate the verbal phrase into a numerical
expression and evaluate.
1) The difference of 8 and 1.
8 1  7
2) The product of 12 and 6.
12  6  72
3) The sum of 5 and 9.
5  9  14
4) The quotient of 12 and 3.
12  3  4
Write a verbal phrase that represents each algebraic
expression below.
1) 10  x
The difference of 10 and x.
2) 6m
The product of 6 and m.
3) 12  y
The quotient of 12 and y.
4) k  7
The sum of k and 7.
Write a variable expression to represent the
following if x represents your age.
1) Your age 5 years ago.
x 5
2) Twice your age.
2x
3) Your age in 8 years.
x 8
Translate the following phrases.
1) Five plus x minus 3
5+x-3
2) Three times y less 4
3y  4
3) Eight multiplied by y minus 7
8y - 7
4) The product of 10 and m decreased by 7
10m - 7
5) Four more than the quotient of x and 3
x
4
x  3  4 or
3
6) Six times m plus 8
6m + 8
Define a variable to represent the unknown and
write the phrase as a variable expression.
1) 10 mph faster than the Honda
Let x = the speed of the Honda
x + 10
2) 7 inches shorter than Jill’s brother
Let b = the height of Jill’s brother
b-7
3) 5 acres larger than twice the size of my lot
Let k = the size of my lot
2k + 5
4) $7.50 times the number of people plus a
$20 group registration
Let y = the number of people
$7.5y + $20
Match each phrase with its variable expression.
d 1) Twice the sum of x and 3
a) 2x  3
e 2) Two less than the product
of 3 and x
b 3) Three times the difference
of x and 2
a 4) Twice a number x less 3
c 5) Two more than 3 times a
number x
b) 3  x  2 
c) 3x  2
d) 2  x  3
e) 3x  2