Dividing mixed fractions forces you to take into account all that you’ve learned so far about fractions. At this point, you should know how to convert a mixed fraction into an improper fraction and back again, multiply fractions, divide fractions, and reduce fractions. These simple steps should help you combine these concepts in order to divide mixed fractions effectively.
Step 1 - Convert
First, you’ll need to convert the mixed fractions into improper fractions. To do this conversion on a mixed fraction, simply multiply the denominator by the whole number, and then add the numerator. The result is the numerator of the improper fraction. The denominator stays the same. For example, if you are given the problem “3 1/2 / 1 3/4,” you would first convert the two mixed fractions:
For 3 1/2, the numerator would be (2X3) +1, or 7. The denominator would remain 2, leaving us with 7/2.
For 1 3/4, the numerator would be (4X1) +3, or 7. The denominator would remain 4, leaving us with 7/4.
Step 2 - Flip
The second step is easy. Just like in any other division problem, you would flip - or take the reciprocal of - the second fraction, and change the division sign to a multiplication sign. In our example, therefore, the problem would now read “7/2 X 4/7.”
Step 3 - Multiply
Next, just multiply across the top and the bottom, as if you were multiplying any two fractions together. In our example, multiplying across the top would give you 7X4 = 28, and 2X7 = 14. The resulting fraction would be 28/14.
Step 4 - Reduce
The last step is to reduce the fraction in your answer. In our example, you would reduce 28/14 by dividing the numerator and denominator by 14, leaving you with 2/1, or just 2.
Note that you could change this sequence around by simplifying before you multiply. To do this, you would see the 7 in the numerator of one fraction and the 7 in the denominator of the other fraction, divide both by 7 and replace them with 1’s. You would then see the 2 in the denominator of the first fraction and the 4 in the numerator of the second fraction, and divide both by 2. This would leave you with 1/1 X 2/1, or 1X2, which also equals 2. This may be too complex if you are still getting used to multiplying fractions, but as you get more comfortable with the concept, it will make the problems easier and faster to solve.
An Alternative Method
An alternative method for dividing mixed fractions is to convert both fractions to decimals and then divide them using long division. This is often a complicated process, which is why the other method is preferred. Here’s an example of how it would work:
Problem: 3 1/2 / 1 3/4
Solution: 3.5 / 1.75 = 350/175 = 2
Try these problems for additional practice:
- 1 3/4 / 1 1/2
- 2 3/5 / 1 1/5
- 1 2/3 / 2 5/6
- 4 1/2 / 1 1/8
References and Additional Resources
Math.com. “Dividing Mixed Numbers.” https://www.math.com/school/subject1/lessons/S1U4L8GL.html
This post is part of the series: Math Study Guides
Confused in math class? These math study guides span various topics, from square roots to improper fractions.