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Feb 022014

Do you understand the difference between a formula, expression, identity and equation?

A formula is a rule written using symbols that describe a relationship between different quantities. Typical maths formulae include

A = πr² (area of a circle)

C=πd (circumference of a circle)

An expression is a group of mathematical symbols representing a number or quantity. Expressions never have equality or inequality signs like =, >, <, ≠ ,≥ ,≤. Some examples


3xy + 4x

t² + t³

An identity is an equation that is always true, no matter what values are chosen.


3a + 2a =  5a

x²+x² = 2x²

5 x 10 = 10 x 5

An equation is a mathematical statement that shows that two expressions are equal. It always includes an equals sign.


x² =100

3x(x+5)= 42


Use this exercise to make sure you understand the difference.

  2 Responses to “Formula, expression, identity, equation?”

  1. Hi,
    Please can you give an example of a formula that isn’t an equation and visa versa? The way I read your post they are the same thing.

    • An equation can be solved- so for example in the equation 2x=8, x=4. There is usually just one solution, but sometimes there is more than one solutuion.
      A formula is a method of working something out that will work for all the possible values. So for the area of a rectangle the formula is area =length x width. This always works no matter how big or small the length and width are.
      Hope this makes sense!

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