**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 |

**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=

MooMooMath provides free video lessons, tips, and resources in Pre-algebra, Algebra, Algebra 2, and Geometry along with a summary of each video lesson. Under each summary is a practice link that takes teachers, parents, and students to free, interactive websites that reinforce each concept.

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