Common Denominator

A common denominator is another name for a common multiple of the denominators.

Fractions are usually expressed with a common denominator when they are compared, added or subtracted.

The common denominator that is usually preferable to use is the lowest common denominator (which is the least common multiple of the denominators).

PROBLEM

Which of the following fractions is larger?

$Example one fractions$

SOLUTION ONE (USING THE LOWEST COMMON DENOMINATOR)

Re-write the fractions wich a lowest common denominator of 60.

$Example one: fractions with the lowest common denominator$

SOLUTION TWO (USING A DIFFERENT COMMON DENOMINATOR)

Any multiple of 60 can be used as a common denominator. The product of the denominators of the fractions (15x20 = 300) can be used as 300 is a multiple of 60.

$Example one: fractions with a common denominator$

PROBLEM

What is the sum of the following?

$Example two fractions$

SOLUTION ONE (USING THE LOWEST COMMON DENOMINATOR)

Re-write the fractions wich a lowest common denominator of 36.

$Use the lowest common denominator to add the fractions$

SOLUTION TWO (USING A DIFFERENT COMMON DENOMINATOR)

Any multiple of 36 can be used as a common denominator. The product of the denominators of the fractions (12x18 = 216) can be used as 216 is a multiple of 36.

$Use a common denominator to add the fractions$

Usually fractions are displayed in reduced form, so both 30 and 216 will be divided by 6, the greatest common factor of 30 and 216.