# Letters, Variables and Algebraic Expressions

Letters and symbols represent numbers and objects in mathematics. However, many of us are probably not aware that we use them in different ways. Below are the different uses of letters and symbols in algebra.

1.) **Generalized Arithmetic** – symbols/letters stand as “pattern generalizers”

Example 1 : 3 + 5 = 5 + 3 is generalized as *a *+ *b* = *b* + *a*

Example 2 : – 2 · 3 = -6, – 1 · 5 = – 5 is generalized as – *x* · *y* = -6

Example 3: *y* = *m*x + *b*

2.) **Unknowns **– symbols/letters are used as place holders of a specific value

Example 1 : 2*x* + 3 = 15* *

Example 2 : 3x = 4

3.) **Variables** – symbols/letters represent a varying quantity

Example 1 : y = 5*x* + 3

Example 2 : *y = 2 ^{x} *

4.) **Constants** – symbols/letters with a constant value

Example 1 : ≈ 3.1416

Example 2 : *e* ≈ 2.71828

* *