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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 Operation Key words Addition increased by, more than, combined, together, total of, sum, added to Subtraction decreased by, minus, less, difference between, less than, fewer than Multiplication times, multiplied by, product of , increased/ decreased by a factor of (this type can involve both addition or subtraction and multiplication​!) Division per, a, out of, ration of, quotient of, percent (divide by 100) Equals is, are, was, were, will be, gives, yields, sold for
 Written Expression Algebraic Expressions Six less than twice the value 2x-6 12 fewer than a value x-12 5 less than a number x-5 Half a number 1/2x 24 per 3 acres 24÷3 The quotient 2 and x 2/x Five more than four times a number 4x + 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=