Multiplying and Dividing Fractions

This article covers hot to multiply and divide fractions.

You probably already know all about fractions and can easily answer the question below:

What is the fraction of colour blue in the figure below?

Yes, that’s right, it is ! The whole figure is divided into four parts and one part of the whole can be written as fraction . Now what if you are asked that what is of ? In other words, if th part is divided into further four parts what will be the fraction of one sub-part of that division with repect to the whole figure? Lets divide the blue portion and see what happens.

Notice that dividing the blue portion further into parts, has resulted into unequal partition of the figure and we cannot write the shaded blue part as fraction unless the whole of the figure is divided into equal parts. In order to achieve equal portion size, all the cloured boxes must be divided into four.

Now, there are 16 equal parts of the figure and the fraction of shaded blue part is . This means that of is equal to ! Mathematically translating this statement, ‘of’ means multiplication.

This teaches us the important concept of fraction multiplication! When we have no figures available, and just plain old fractions, what do we do then? How to multiply? Its very easy! Just follow one simple step:

Multiply the numerator by numerator and multiply the denominator by denominator!

See! How easy it is! Here are some other examples:

If your final answer needs further simplification, you can simply the fractions. See our article on ‘simplifying fractions’ to learn how to do that!

Multiplying Fractions and Integers

Multiplying fractions and integers is very simple and you follow the same procedure as above. The important thing to remember is that integers are also fractions with denominator equal to 1!

This is illustrated by some examples:

Multiplying Mixed Numbers

Mixed numbers consist of whole numbers and fractions like: , 5, In order to multiply mixed numbers, you first need to convert mixed numbers into fractions. The steps to do that are explained below:

Convert to fraction:

Step 1: Multiply the whole number and the denominator of the fraction.

Step 2: Add numerator to the answer of step 1.

Step 3: The final answer obtained in the step two is the numerator of the fraction and the denominator remains the same as in the original mixed number. So, the final answer is:


Remember: Converting mixed number into a fraction always results in an improper fraction.

Once the mixed number is converted to fraction, follow the same procedure as outlined above to multiply them.


Firstly, convert both mixed numbers into improper fractions.

Now multiply:

The final answer in the form of improper fraction is ! If you want to convert the final answer to mixed number form, see our article on simplifying fractions. We have covered this conversion in that article.

Dividing Fractions

Multiplications sounds easy enough, but how to divide two fractions? Before we do that, lets learn about reciprocals. What is reciprocal of a fraction?

When we replace numerator by denominator and denominator by numerator, we get the reciprocal of a fraction.

If the statement sounds confusing, see the example given below and re-read the statement.

When we divide one fraction by another, first fraction is the dividend and the second is the divisor. In case of the example below, is the dividend and is the divisor.

How to solve this? Follow this simple procedure:

Take reciprocal of the divisor and multiply it by the dividend!

The same goes for dividing fractions and integers. See the examples below for understanding:

For dividing mixed numbers, convert them to improper fraction first and the take reciprocal of the divisor and multiply it by dividend.

Final Thoughts!

So, this was all about multiplying and dividing fractions. The main concept to learn and remember here is how to multiply fractions. As you have seen, division of fractions also involves multiplication step, so if you know multiplication, you are all set to learn little tricks to tackle division and complications involving integers and mixed numbers. In this article, conversion of mixed numbers into fractions was also shown, but if you want to learn how to convert improper fraction to a mixed number, see our article on Simplifying Fractions. Explore our resources further, to enhance your mathematical learning in an easy and fun way!


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