Translating Words into Algebraic Expressions
Operation
Addition
Subtraction
Multiplication
Word Expression
Add, Added to, the sum of, more
than, increased by, the total of,
plus
Add x to y
y added to 7
The sum of a and b
m more than n
p increased by 10
The total of q and 10
9 plus m
Subtract, subtract from,
difference, between, less, less
than, decreased by, diminished
by, take away, reduced by,
exceeds, minus
Subtract x from y
From x, subtract y
The difference between x and 7
10 less m
10 less than m
p decreased by 11
8 diminished by w
y take away z
p reduced by 6
x exceeds y
r minus s
Multiply, times, the product of,
multiplied by, times as much, of
7 times y
The product of x and y
5 multiplied by y
one-fifth of p
Divide, divides, divided by, the
quotient of, the ratio of, equal
amounts of, per
Division
Divide x by 6
7 divides x
7 divided by x
Algebraic Expression
+
x+y
7+ y
a+b
n+m
p + 10
q + 10
9+m
y-x
x-y
x -7
10 - m
m - 10
p - 11
8-w
y-z
p-6
x-y
r-s
×
7y
xy
5y
1
p
5
÷
x
or x ÷ 6
6
x
or x ÷ 7
7
7
or 7 ÷ x
x
y
or y ÷ 5
5
u
or u ÷ v
v
u
or u ÷ 4
4
5
100
y2
k3
t4
The quotient of y and 5
The ratio of u to v
Division
u separated into 4 equal parts
(continued)
5 parts per 100 parts
Power
Equals
Multiplication by
2
Multiplication by
½
The square of y
The cube of k
t raised to the fourth power
Is equal to, the same as, is, are,
the result of, will be, are, yields
=
x is equal to y
p is the same as q
Two, two times, twice, twice as
much as, double
x=y
p=q
2
Twice z
y doubled
Half of, one-half of, half as
much as, one-half times
2z
2y
1
2
u
2
1
m
2
Half of u
one-half times m
Geometry Problems
Concept
Area of a square
Perimeter of a square
Area of a rectangle
Perimeter of a rectangle
Angles of a Triangle
Word Expression
Algebraic Expression
Side Squared
Four times the side
Length times width
Two lengths plus two widths
The sum of the angles is 180o
A = s2
P = 4s
A=LxW
P = 2L + 2W
∠A + ∠B + ∠C = 180
Word Problem Relationships
Consecutive Integer
Motion
Mixture
% Mixture
Digits
Three consecutive integers
Three consecutive odd (even)
integers
Rate times Time equals
Distance
Price times Quantity equals
Total Value
% Strength times Quantity
equals Total Amount
A two digit number
x, x + 1, x+ 2
x, x + 2, x + 4
RxT=D
PxQ=T
PxQ=T
10t + u