Pre-algebra
Skill-Builder # T – 6
Translating English to Algebra: Two Operations Combined
English phrases can also translate into algebraic expressions involving more than one operation. Here
we will focus on two operations.
In the following we will use x to denote a number. If there are two or three, we will use y and z.
Examples Translate the given English phrase to an algebraic expression.
1) The sum of the square of a number and 9
Translation:
Translation:
The sum
square of a number and 9
of the
+
2) 10 added to the difference of a number and 6
x2
Thus the phrase translates to
10 added
to the difference
ofa
number and
6
Thus the phrase translates to
10 + ( x − 6 ) or
x2 + 9 .
3) Twice the quantity 3 more than a number
Translation:
x −6
+
( x − 6 ) + 10 .
4) The quotient of a number and the difference of
the number and 1
Translation:
Twice
more than
a number
the quantity 3
2⋅
x +3
The quotient of a
number
difference of
the number and
and the
1
x −1
x
Thus the phrase translates to
2( x + 3) .
Thus the phrase translates to
x
.
x −1
Pre-algebra
Skill-Builder # T – 6
Translating English to Algebra: Two Operations Combined
Translate the given English phrase to an algebraic expression.
1) 4 added to the square of a number
2) The difference of 1 and the cube of a number
3) The sum of two numbers decreased by 10
4) 12 less than the difference of two numbers
5) The square of the sum of a number and 3
6) The cube of the difference of a number and 2
7) The quotient of a number and the quantity 5
less the number
8) The ratio of a number and the quantity 1 more
than the number
9) The square of the quotient of a number and 6
10) The quotient of the square of a number and 6
Pre-algebra
Skill-Builder # T – 6
Translating English to Algebra: Two Operations Combined
Answer Key:
1) x 2 + 4
2) 1 − x 3
3) x + y − 10
4) x − y − 12
5)
( x + 3 )2
6)
( x − 2 )3
7)
x
5−x
8)
x
x +1
10)
x2
6
x
9)  
6
2
Prepared by: Dr. Teresa V. Sutcliffe
Summer 2010