Algebra is a language that uses letters, symbols, and numbers to express relationships. In order to write algebraic expressions it helps to know the key words and their algebraic definition. Learning these key terms helps one to write and read an algebraic expression that includes a variable. Remember a variable is simply a letter that takes the place of a number. Here is a list of many of the common key words used in Algebra.

Math OperationKey words

increased by, more than, combined, together, total of, sum, added to


decreased by, minus, less, difference between, less than, fewer than


times, multiplied by, product of , increased/ decreased by a factor of (this type can involve both addition or subtraction and multiplication​!)


per, a, out of, ration of, quotient of, percent (divide by 100)


is, are, was, were, will be, gives, yields, sold for

Written ExpressionAlgebraic Expressions
Six less than twice the value2x-6
12 fewer than a valuex-12
5 less than a numberx-5
Half a number1/2x
24 per 3 acres24÷3
The quotient 2 and x2/x
Five more than four times a number4x + 5

Examples of Writing Algebraic Expressions

Example Problem 1 Examples of Algebraic Expressions,
Rewrite the ratio of x and 4 into an algebraic expression.
Ratio means division so …. it becomes x÷4 or x⁄4

Example Problem 2 Writing Algebraic Expressions,
How would you rewrite 5 less than a number in an algebraic expression?
The less than equals subtraction so it becomes ……… x-5

Example Problem 3 Algebraic Expressions Examples.
Rewrite 24 per 3 acres into an algebraic expression.
per equals division so it becomes…. 24 ÷3=