What is a variable?
A variable is a letter such as x, y or n that stands for a number we do not yet know, or a number that can change. A fixed number like 5 or −3 is called a constant. When we combine variables and numbers using +, −, × or ÷, we get an algebraic expression, for example 3x + 5.
Writing 3x means 3 × x. We usually leave out the multiplication sign, so 3x, xy and 5ab are all products. We also write x × x as x2.
Terms and coefficients
A term is a single part of an expression separated by + or −. In 4x − 7y + 2, the terms are 4x, −7y and 2. In the term 4x, the number 4 is the coefficient and x is the variable. A term made of only a number, like 2, is a constant term.
Key idea / Key idea
In a term such as −7y: coefficient = −7, variable = y. Include the sign in front with the coefficient.
Writing and evaluating expressions
We turn word phrases into expressions. "5 more than a number n" becomes n + 5. "Twice a number, then subtract 3" becomes 2m − 3. To evaluate an expression, replace the variable with a value.
Worked example / Worked example
Find the value of 3x + 4 when x = 2.
3x + 4 = 3 × 2 + 4 = 6 + 4 = 10.
Now find 2a − b when a = 5 and b = 3:
2a − b = 2 × 5 − 3 = 10 − 3 = 7.
Remember / Remember
- 3x means 3 × x; the sign belongs to the coefficient.
- Terms are separated by + or −.
- Substitute carefully, then work out the value.