Are you working on multiplying mixed fractions and have no idea where to start? I know that looking at these mixed numbers and trying to figure out the first step can be very confusing.
If you can multiply fractions, then you can multiply mixed numbers. There's only one more step that you must complete at the beginning of the problem in order to multiply mixed fractions.
Let's first take a look at the steps.
Steps for Multiplying Mixed Numbers
- Rewrite the mixed numbers as improper fractions.
- Simplify within the problem if necessary.
- Multiply the numerators.
- Multiply the denominators.
- Rewrite the answer as a mixed number if needed. Always check to make sure that your fractions are in simplest form.
So, as you can see from the list of steps above, the only "new" step is to first change the mixed numbers to improper fractions.
You may want to review the lesson on rewriting improper fractions as mixed numbers.
OK... let's see it in action!
Example 1 - Multiplying Mixed Fractions
That was pretty easy, right? Nothing to it, once you rewrite mixed numbers as improper fractions.
Let's take a look at one more example, and for this example we will simplify within the problem so that we don't have to simplify at the end of the problem.
Example 2
I know these types of problems can be confusing, especially if you are not proficient with rewriting mixed fractions and improper fractions.
If you want to hear this problem explained, watch the video below.
I hope these examples and videos have helped you to understand how to multiply mixed fractions.
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- Multiplying Mixed Numbers
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Knowing how to multiply fractions will help when it comes to multiplying two mixed numbers. This is because when multiplying mixed numbers, you first have to change them to improper fractions. You then multiply the numerators and denominators, and reduce the results, if possible. Then, at the end, you can change the
fraction back to a mixed number. Example:Sadie worked 10 2/3 hours at time-and-a-half. How many hours will she get paid for? Change all the mixed numbers to improper fractions. In Sadie’s case, you have two mixed numbers, 10 2/3 and 1 1/2, that need to become improper fractions. Follow this formula to convert each mixed number into an improper fraction:
In a fraction, the Numerator is always North of (above) the fraction line. The Denominator is always Down below the fraction line.
You convert the mixed numbers to improper fractions as follows:
Reduce the fractions.
To do this, break down both the numerator and denominator of each fraction into their prime factors (shown below in parentheses):
Cross out any common factors.
In this example, you cross out 2 and 3 because they’re common factors — that is, they appear in both the numerator and denominator:
Multiply the numerators together and the denominators together.
Reduce the answer.
If the result is an improper fraction, change it to a mixed number.
So, Sadie worked 10 2/3 hours at time-and-a-half and gets paid for 16 hours — what a payday!
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