In this lesson, 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
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 
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 
Phrase 
Expression 
4 times some number 
4x 
twice a number 
2y 
onethird of some number 

the product of a number and 12 
12w 
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 
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) 
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 
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) 
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