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Fraction Multiplication and Division

We will consider only the multiplication and division of two fractions here, see the help on Complex calculations after reading this section for details on the multiplication and division of more than two fractions.

If mixed fractions are involved then they have to be converted to improper fractions, multiplication and division is not easily performed on mixed fractions. The Fraction calculator automatically converts mixed fractions to improper fractions for multiplication and division and converts resulting improper fractions back to mixed fractions at the end.

There is a special rule for division, when dividing by a proper or improper fraction simply reverse the numerator (top) and denominator (bottom) and multiply. In very simple words turn the fraction upside down and multiply. When dividing by a whole number alone then remember that a whole number can be written as an improper fraction (the whole number is the top and the number 1 the bottom), do this and then turn it upside down and multiply.

Some examples:

So we now only need to consider how to perform multiplication on fractions.

The simple way to do multiplication is to multiply the two numerators (tops) together and the two denominators (bottoms) together. The results being the numerator (top) and denominator bottom of the resulting fraction which then needs to be simplified.

The problem with multiplication is the numbers can get quite big quite quickly, which means it is easy to make mistakes in the multiplication and hard to simplify the resulting fraction. To prevent this we do not multiply out the numerators (tops) and denominators (bottoms) immediately. First of all we break all the numbers involved down in to there factors and then look for common factors between the numerators (tops) and denominators (bottoms), any that are found are cancelled out. Repeating the above example:

Now we can see there is one 5 in a numerator (top) and two 5's in a denominator (bottom), so one 5 can be cancelled out from top and bottom (remove one 5 from top and bottom). Also there is one 7 in both a numerator (top) and denominator (bottom) so this can also be removed from both.

There are clearly no more common factors and the multiplication is now very simply and comes to the same as above. Also there is no need to attempt to simplify as the process of cancellation we perform means the result is in its lowest form.

Complex Calculations with Fractions

Fraction Calculator and Cheat Homepage

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