What is a Variable?

Algebra 1 · Axiom Academy

From an everyday question to the language of algebra — how a single letter comes to stand for a number. Imagine you're at a coffee shop where every cup costs 3. The total cost of your order depends on how many cups you buy — buy more cups, pay more dollars. The number of cups is the part that changes . Writing a separate calculation for every possible order is hopeless — there are infinitely many. Algebra's move: use a placeholder for the value that changes. We'll use the letter n for the n umber of cups. 3. The Variable: A Powerful Idea Now we have one compact rule for every order. Substitute any number of cups for n , and the expression computes the total cost — the variable acting as a placeholder for a changing value . Sometimes a variable stands for a single unknown value we need to find. Say you pay for one 3 coffee with a 10 bill and get some change back. How much change? Let x be the unknown amount: A variable does double duty. Side by side, here are the two roles you've just met. A variable is a symbol (usually a letter) that represents a quantity. Role 1 — a changing value : in Total Cost = 3n, the letter n covers every possible order at once. Role 2 — a specific unknown : in 3 + x = 10, the letter x has one hidden value to find. Variables are what let algebra state general rules instead of one calculation at a time. One rule, every case: substitute any n into 3n and the cost falls out. One hidden value to find: the equation 3 + x = 10 pins x to 7.

This is the written version of the interactive lesson above. See the full Algebra 1 course.