How do you add a fraction without a common denominator?

Answer 1

You have to make a common denominator between them, otherwise you can't. See if they have similar factors, or if you can't find any easily, cross-multiply and multiply the numerator and denominator of one side by the denominator of the other side and do the same thing to the other side with the denominator of the other fraction!

Answer 2

To add fractions they must have the same denominator.

If the denominators are different, you need to find a new denominator that is a common multiple of all the denominators and make all the fractions equivalent fractions with this new denominator; then you can add the fraction by adding together the numerators (and simplifying the result).

Ideally using the Lowest Common Multiple (LCM) of the denominators will keep the new numerators smaller.

If you cannot find the lowest common multiple, a simple solution is to multiply all the denominators together and use this as the new denominator.

For two fractions, using this gives a trick that always works:

The new denominator is the two denominators multiplied together.

The new numerator is the numerator of the first fraction multiplied by the

denominator of the second plus the denominator of the first multiplied by the numerator of the second:

eg 3/5 + 2/7 = (3 x 7) + (5 x 2)/(5 x 7)

= (21 + 10)/35

= 31/35

If you have more than two fractions, you can add the first two together using this trick, then add the result of this and the next fraction together, and so on until all the fractions have been added.

When doing this you can simplify as you go, keeping any improper fractions; if the final result is an improper fraction, it can be converted into a mixed number.

Look at the two (or three) common denominators,

find a number they all multiply into (e.g. something that they can all be divided by repeatedly and in the end turn into "1")

multiply everything by that number, including top halves of fractions,