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Pre-Algebra · Quick Reference
Variables Cheat Sheet
In one line: a variable is a letter that stands in for a number we don't know yet, or a number that can change. Variables are what let math describe patterns instead of just single facts.
Key Ideas
1What is a Variable?. A symbol, usually a letter like x, y, or n, used to represent an unknown or changing quantity.
2Constants. Fixed values that don't change, like the numbers 2, 7, or -3 in an expression.
3Substituting Values. Replacing a variable with a specific number to evaluate an expression, e.g., if x=3, then x+5 becomes 3+5=8.
4Variables in Real Life. Variables model real, changing quantities: let d = distance traveled, or let p = price of an item.
5Coefficients. The number multiplied directly in front of a variable, such as the 4 in 4x.
Worked Examples
If x = 5, evaluate the expression x + 8.
13
If y = 4, evaluate 3y - 2.
10
A taxi charges a flat $3 fee plus $2 per mile (m). Write an expression for the total cost, and find the cost for a 5-mile trip.
Expression: 3 + 2m. Cost for 5 miles = $13
Practice Yourself
If x = 6, evaluate x + 10.
16
If y = 2, evaluate 5y.
10
If n = 7, evaluate n - 4.
3
What is the coefficient in the term 9x?
9