Multiplying Mixed Fractions

After all multiplying mixed fractions is not much different from any other fraction multiplication.

Hey there! Hope you got a good feeling of dealing with fractions by now. In this lesson you will learn about finding the product of two mixed fractions. There is a lot of similarity between multiplication of mixed fractions and that of proper fractions.

When starting with mixed fractions you must dress it up such that it’s ready for multiplication. Let’s have a look at how that works.

To illustrate the process we will work out one example by multiplying mixed fractions.

Let’s multiply 2 1/3 with 3 2/5

Now you cannot just go about multiplying the numerator and the denominator as you do in case of proper fractions. That’s because there is no properly defined numerator and denominator for mixed fractions. However we know from the earlier lessons on mixed fractions that they can be converted to improper fractions that possess well defined numerator and denominator.

So the first step to multiplying mixed fractions is to convert the mixed numbers into improper fractions.

Let’s do that

First we take 2 1/3 and convert it to its equivalent improper form. To do that, first multiply the denominator of the fraction part with the whole number. That means we multiply 3 with 2. The resultant obtained is 6. Now add the numerator of the fraction part that is 1 to the result we just obtained by multiplying the denominator with the whole part that is 6. This gives us 7. Now 7 becomes the numerator of the equivalent improper fraction. The denominator on the other hand will be same as that of the fractional part that is 3.

Thus the improper fraction equivalent of 2 1/3 is 7/3

Similarly the equivalent fraction of 3 2/5 is 17/2.

Now multiplying the two equivalent fractions is same as multiplying mixed fractions we were given in the question.

If you observe carefully the improper fractions created can be multiplied by using the multiplication techniques we have discussed in the relevant section on this website.

First we take the numerators of the two fractions and multiply them. The numerator of the first term 17 when multiplied by the numerator of the second fraction 7 gives 119.

Let’s head on to find the denominator of the product of the two fractions. The two denominators are 3 and 2. When multiplied they yield 6.

Thus the product of the fraction becomes 119/6.

There are two more steps to follow.

You must simplify the resulting fraction. However we see that the fraction is already in the simplest form here.

Next step is to convert the improper fraction to its mixed equivalent. Thus when we convert 119/6 to its mixed equivalent factor we get 19 5/6.


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