Lowest common denominator

When calculating with fractions in arithmetic, a branch of mathematics, is meant by the common denominator or common denominator of several fractions is the least common multiple ( ) of the denominators of these fractions.

If fractures compared with each other or added, so they are first brought to a common denominator by extending. As a common denominator, you can always use the common denominator, this allows in many practical cases, the simplest statement.

Examples

Comparison

One way to compare two fractions that have neither numerator nor denominator common is to expand it so that they match in the numerator or denominator. Mostly it is to put it on the same denominator, conveniently the common denominator.

It is important to ensure that operations are applied, which change the numerator and denominator by the same ratio. Multiply is a lawful operation while potentiating changed the fraction equal.

Correct score with multiplication:

Incorrect result with potentiation:

Addition and subtraction

In order to add or subtract fractions with different denominators, one must be first expand all fractions to a common denominator. It is preferred, as a rule the main denominator, for example,

Is the smallest common multiple of, and thus the denominator of the three openings to be added.