Common Denominator

A common denominator is a denominator that is shared between two or more fractions. Consider a few examples.

Fractions can always be rewritten to all have a common denominator. This process requires writing equivalent fractions by expanding or simplifying the fractions. As an example, take a look at a pair of fractions with different denominators. 1/3 and 1/2 These fractions are in their simplest form, which means that they can only be expanded. Write the multiples of their denominators, 3 and 2, to find the factor of expansion. Multiples of3:& 3, 6, 9, 12, 15, 18, ... Multiples of2:& 2, 4, 6, 8, 10, 12, 14, ... There are two potential common denominators in these lists. Expand the first fraction by 123= 4 and the second fraction by 122= 6 to make them have a common denominator of 12. 1 * 4/3 * 4&=4/12 [0.3cm] 1 * 6/2 * 6&=6/12 Now the fractions share a common denominator. 4/12 and 6/12