# How to Write Expressions in Algebra Algebraic expressions are the phrases used in algebra to combine one or more variables (represented by letters), constants, and the operational (+ - x / ) symbols. Algebraic expressions, however, don't have an equals (=) sign.

When working in algebra, you will need to change words and phrases into some form of mathematical language. For instance, think about the word sum. What comes to your mind? Usually, when we hear the word sum, we think of addition or the total of adding numbers.

When you have gone grocery shopping, you get a receipt with the sum of your grocery bill. The prices have been added together to give you the sum. In algebra, when you hear "the sum of 35 and n" we know it refers to addition and we think 35 + n. Let's try a few phrases and turn them into algebraic expressions for addition.

### Testing Knowledge of Mathematical Phrasing for Addition

• Question: Write seven plus n as an Algebraic expression.
• Question: What Algebraic expression is used to mean "add seven and n."
• Question: What expression is used to mean "a number increased by eight."
• Answer: n + 8 or 8 + n
• Question: Write an expression for "the sum of a number and 22."
• Answer: n + 22 or 22 + n

As you can tell, all of the questions above deal with Algebraic expressions that deal with the addition of numbers - remember to think "addition" when you hear or read the words add, plus, increase or sum, as the resulting Algebraic expression will require the addition sign (+).

### Understanding Algebraic Expressions with Subtraction

Unlike with addition expressions, when we hear words that refer to subtraction, the order of numbers cannot be changed. Remember 4+7 and 7+4 will result in the same answer but 4-7 and 7-4 in subtraction do not have the same results. Let's try a few phrases and turn them into algebraic expressions for subtraction:

• Question: Write seven less n as an Algebraic expression.
• Question: What expression can be used to represent "eight minus n?"
• Question: Write "a number decreased by 11" as an Algebraic expression.
• Answer: n - 11 (You can't change the order.)
• Question: How can you express the expression "two times the difference between n and five?"