Lesson 4.2 — Writing & Evaluating Expressions

Welcome back! Today we're going to let letters into our math. Sounds strange, but it's really powerful.

Here's the core idea. A variable is just a letter that stands for a number we don't know yet, or a number that can change. Letters like x, n, or t. When we combine numbers, variables, and operations, we get an expression, like three x plus five.

Let's name the parts. The terms are the pieces separated by plus or minus signs, so in three x plus five, the terms are three x and five. The number attached to the variable is the coefficient, that's the three in three x. And a number sitting on its own, like the five, is a constant. Quick note: three x means three times x. When a number sits right next to a letter, the multiplication sign is just hidden.

Expressions show up everywhere. Tickets at eight dollars each? That's eight t. Five years older than Sam? That's s plus five. The perimeter of a square with side s is four s.

Now, here's a key word: evaluate. To evaluate an expression, you substitute a value for the variable and then compute. Notice an expression has no equals sign, so you don't solve it, you evaluate it.

Let's try it. Evaluate three x plus five when x equals four. First, substitute. I like to use parentheses: three times four, plus five. Then follow PEMDAS, so multiply first: three times four is twelve. Twelve plus five is seventeen. Done!

One thing to watch out for with words. "Five less than n" is n minus five, not five minus n. The order flips, so read carefully.

So, recap. A variable stands for a number, an expression mixes numbers and variables and operations, and you evaluate by substituting and using PEMDAS. See you next time!