Algebraic Translations of English Phrases
Front Range Community College
Alan Dinwiddie – Mathematics Dept.
The following is to help you get the correct operation in application problems.
Warning: some of the words or phrases can have different meanings.
Example: 5 greater than a number (expression)
x+5
5 is greater than x (inequality)
5>x
Variable x is used in the examples, but any letter could be used.
Words or phrases that suggest:
Addition
7 added to a number
a number added to 6
the sum of a number and 9
the sum of 12 and a number
a number increased by 5
15 increased by a number
increasing a number by 12
16 more than a number
a number plus 3
7 plus a number
5 greater than a number
x+7
6+x
x+9
12 + x
x+5
15 + x
x + 12
x + 16
x+3
7+x
x+5
(x + 6 is also correct)
(x + 12 is also correct)
(x + 15 is also correct)
(x + 7 is also correct)
Subtraction
a number minus 15
6 minus a number
7 subtracted from a number
a number subtracted from 8
-4 subtracted from a number
the difference between a number and 7
the difference between 12 and a number
5 less than a number
-3 less than a number
a number decreased by 8
-6 decreased by a number
11 fewer than a number
x – 15
6–x
(not x – 6 )
x–7
8–x
(not x – 8 )
x – (-4)
x-7
12 – x (not x – 12 )
x–5
x – (-3)
x–8
-6 – x
x - 11
Multiplication
A number multiplied by 7
6 times a number
a number times 12
the product of 8 and a number
the product of a number and –4
eight percent of a number
7x
6x
12x
8x
-4x
3
x
4
0.08x
twice a number
2x
three-fourths of a number
(12  x also correct)
(when taking a fractional part)
(percent of – write as decimal or
fraction.)
Division
the quotient of a number and 6
the quotient of –3 and a number
a number divided by 7
the ratio of a number and 5
the reciprocal of a number
x
 x 6  x/6
6
3
 3  x  3 / x
x
x
7
x
5
1
x