In these lessons, we will learn how to write algebraic expressions for word problems. We will start with some common phrases found in word problems.
Related Topics:
More Algebra Word Problems
More Algebra Topics
To write an expression, we often have to interpret a written phrase.
For example, the phrase “ 6 added to some number” can be written as the expression x + 6, where the variable x represents the unknown number.
Some examples of common phrases and corresponding expressions that involve addition are:
Phrase 
Expression 
4 more than some number 
x + 4 
a number increased by 10 
y + 10 
8 plus some number 
t + 8 
the sum of a number and 12 
w + 12 
Some examples of common phrases and corresponding expressions that involve subtraction are:
Phrase 
Expression 
4 less than some number 
x – 4 
a number decreased by 10 
y – 10 
8 minus some number 
8 – t 
the difference between a number and 12 
w – 12 
Some examples of common phrases and corresponding expressions that involve multiplication are:
Phrase 
Expression 
4 times some number 
4x 
twice a number 
2y 
onethird of some number 

the product of a number and 12 
12w 
Some examples of common phrases and corresponding expressions that involve division are:
Phrase 
Expression 
the quotient of 4 and some number 

a number divided by 2 

the ratio of 8 and some number 

the quotient of a number and 12 
Some examples of common phrases and corresponding expressions that involve two operations are:
Phrase 
Expression 
6 more than 5 times a number 
5x + 6 
4 times the sum of a number and 7 
4(y + 7) 
5 less than the product of 3 and a number 
3w – 5 
twice the difference between a number and 9 
2(z – 9) 