Variables

Variables are symbols that represent a number in algebraic equations, problems, etc. Usually, they are letters but sometimes they could also be letters of the Greek alphabet, or if you'd like, they can be drawings, if you're really that creative! As I've said, a variable can represent any number, so...


Example:

• In the algebraic expression 5 + a , a is a variable and represents any number.
• In the algebraic equation 7 (a) = 28 , a is a variable that, based on the equation, represents the number 4.
• To check if this is correct, we replace the a with 4, thus making the equation 7 · 4 = 28

Usually, we use variables for when we are talking about unknown quantities.

Example:

• I know that John is 5 years older than his sister Jane. However, I do not know how old Jane is. So, if I were told to write John's age based solely on what I know, I would have to write it as 5 + x , with x being Jane's age, which is the unknown quantity keeping me from finding out how old John is.
• If a friend tells me my book weighs 3 times more than hers, but I do not know how heavy her book actually is, then I guess I'd have to write it down as:
• x representing her book's weight
• 3x for my book's weight, which is three times heavier than hers.
• If Sam grows 5 cm more, he will finally be as tall as Pam who is 160 cm tall. This statement says that Sam's current height plus 5 cm is equal to 160 cm . Thus, we shall write
• x + 5 = 160 which represents Sam's current height
• and, upon solving the problem, we come to find out that x = 155
• Therefore, we now know that Sam is 155 cm tall.

Note:

• Remember that algebraic expressions and equations can contain more than one variable.
• Example:
• 2 × (a · b)
• This algebraic expression contains two variables: a and b