Multiplying fractions is a challenge with a standard calculator unless you can easily convert the fractions to decimal values. Often that’s not the case. You can always use a fraction calculator online, but learning how to multiply mixed fractions by hand is a skill every student (and adult!) should be able to do easily with a little help.
What are Mixed Fractions?
A simple fraction is an amount less than a whole, for example, one-third of a pizza. In this example, we imagine a pizza is cut into three slices and that number becomes the value on the bottom of the fraction (the denominator). The single slice is how many of those parts the fraction is describing, in this case, the one on the top of the fraction (the numerator).
A mixed fraction includes some number of wholes as well as a partial amount, for example, four and a half pizzas.
Steps to Multiply Mixed Fractions
Multiplying two simple fractions is straightforward. You just multiply the two problem numerators to get the numerator in the answer, and then multiply the two problem denominators to get the denominator in the answer, then reduce the fraction. To multiply mixed fractions, we need to follow a few extra steps. For our example in this post, we’ll multiply the fraction 4 1/2 times 1/3.
This would be similar to a word problem where we asked, “If a group of three friends shared four and a half pizzas, how much pizza would each friend get?”
First, Convert to Improper Fractions
In the case of mixed fractions, the work is slightly more complicated because of the wholes. You need to turn any mixed fractions into improper fractions so you can perform the multiplication step with just numerators and denominators. For our problem, only one of the multiplicands is a mixed fraction, so we only need to convert the value 4 1/2 to an improper fraction.
To do this, we multiply the whole number part of the mixed fraction by the denominator in the fraction part of the mixed number, then add it to the numerator to get a total number of fractional parts. That process looks like this…
This is still the same amount even though the numbers look slightly different… If you put together nine half pizzas, you would still have a total of four whole pizzas plus a half pizza, so this is just a representation of the same quantity.
Second, Multiply the Improper Fractions
Now we can multiply the two simple (but improper fractions) the same way we would multiply a less complicated pair of fractions. Multiply the two numerators to get the answer’s numerator and multiply the two denominators to get the answer’s denominator.
That gives us an answer, but it’s not yet in simplest form so there’s still some work left to do.
Third, If the Product is Improper, Convert it to a Mixed Fraction
For this problem our answer from the multiplication step is an improper fraction, so we should convert it back to a mixed number.
Fourth, Reduce the Answer to Simplest Form
Finally, if the fractional part of the answer can be reduced by finding a common denominator that divides both the top and bottom of the fraction evenly, then the answer should be reduced to its simplest form. For our problem, for the fraction 3/6, the numerator 3 and the denominator 6 can both be divided by 3, so we can reduce the fraction to get the final answer…
By following all of these steps, our original mixed fraction multiplication problem and final answer look like this…
…which is another way of saying, if a group of three friends share four and a half pizzas, each friend will get to eat one and one-half pizzas apiece.
More Resources for Learning Fractions
Fraction arithmetic is a topic that has many other challenges and learning how to find common denominators or reduce fractions or convert between improper and mixed numbers can take practice. A good strategy is to focus on specific problems and gradually build the skills needed to approach higher-level fraction problems that combine all the steps learned along the way. A great way to do this is to work through a set of fractions worksheets that gradually introduces these concepts and provides detailed steps in their answer keys.
I hope this example of multiplying mixed fractions helped on your math journey and made some of the more complex parts of fraction arithmetic easier to understand. Keep practicing!