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How to Write Expressions in Algebra

Algebraic Expressions


Algebraic expressions are the phrases used in algebra to combine one or more variables, constants and the operational (+ - x / ) symbols. Algebraic expressions don't have an equals = sign. Letters are used to represent the variables or the constants.

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 25 + n. Let's try a few phrases and turn them in to algebraic expressions for addition:

Question: 7 plus n
Answer: 7 + n
Question: add 7 and n
Answer: 7 + n
Question: A number increased by 8
Answer: n + 8 OR 8 + n (essentially they're the same)
Question: The sum of a number and 22
Answer: n + 22 OR 22 + n (again, essentially they're the same)

Remember to think addition when you hear or read: add, plus, increase or sum. The addition sign + will be required.

Unlike addtion, when we hear words that refer to subtraction, the order cannot be changed. Remember 4+7 and 7+4 will result in the same answer. However, in subtraction, 4-7 and 7-4 do not result in the same answer and the order is important. Let's try a few phrases and turm them into algebraic expressions for subtraction:

Question: 7 less n
Answer: 7 - n
Question: 8 minus n
Answer: 8 - n
Question: A number decreased by 11
Answer: n - 11 (You can't change the order.)
Question: 2 times the difference between n and 5
Answer: 2 (n-5)
Question: 10 times a number decreased by 3
Answer: 10n - 3

Question: 12 minus n
Answer: 12 - n

Remember to think subtraction when you hear or read the following: minus, less, decrease, diminished by or difference. These words indicate subtraction. Unlike addition, subtraction is NOT commutative because 8 minus 3 is NOT the same as 3 - 8. Subtraction tends cause students greater difficulty than addition. Be sure to refer the terms of subtraction to ensure you understand.

Expressions are referred to as polynomials, an expression with one term is a monomial, an expressions with 2 terms is called a binomial and an expression with three terms is called a trinomial. All of the above examples are polynomials, however, you can see that some have one term and some have more than one term.

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