When you take a real-world situation and translate it into math, you are actually 'expressing' it; hence the mathematical term 'expression'. Everything that is left of the equal sign is considered to be something you are expressing. Everything to the right of the equal sign (or inequality) is yet another expression. Simply stated, an expression is a combination of numbers, variables (letters) and operations. Expressions have a numerical value. Equations are sometimes confused with expressions. To keep these two terms separate, simply ask yourself if you can answer with a true/false. If so, you have an equation, not an expression that would have a numerical value. When simplifying equations, one often drops expressions such as 7-7 that equal 0.
A few samples:
Word Expression | Algebraic Expression |
x plus 5
10 times x y - 12 |
x 5
5 x y - 12 |
Getting Started
Word problems consist of sentences. You will need to read the problem through carefully to ensure you have some understanding of what you are being asked to solve. Pay close attention to the problem to determine the key clues. Focus on the final question of the word problem. Read the problem again to make sure you understand what you're being asked for. Then, jot down the expression.
Let's get started:
1. On my last birthday, I weighed 125 pounds. One year later I have put on x pounds. Which expression gives my weight one year later?
a) x 125 b) 125 - x c) x 125 d) 125x
2. If you multiply the square of a number n by 6 and then added 3 to the product, the sum is equal to 57. One of the expressions equals 57, which one is it?
a) (6n)^{2} 3 b) (n 3)^{2} c) 6(n^{2} 3)d) 6n^{2} 3
Answer for 1 is a) x 125
Answer for 2 is d) 6n^{2} 3
Word Problems to Try
Sample 1
The price of a new radio is p dollars. The radio is on sale for 30% off. What expression will you write that will tell the savings that are being offered on the radio?
Answer: 0.p3
Sample 2
Your friend Doug has given you the following algebraic expression: "Subtract 15 times a number n from twice the square of the number. What is the expression that your friend is saying?
Answer: 2b2-15b
Sample 3
Jane and her three college friends are going to be sharing the cost of a 3 bedroom apartment. The cost of rent is n dollars. What expression can you write that will tell you what Jane's share is?
Answer: n/5
Ultimately, becoming quite familiar with the use of algebraic expressions is an important skill for learning and conquering algebra.