6.4.3 Dividing Mixed Numbers and Fractions
The same principles apply to dividing mixed numbers as dividing proper fractions.
Let's try to calculate .
First, we know to rewrite the mixed numbers as improper fractions: .
Then, we find the reciprocal of the fraction after the ÷ sign, and change the division symbol to the multiplication symbol, so our new calculation is: .
Then, we cancel and multiply out: .
Because our original numbers were mixed numbers, it may be appropriate to rewrite our answer as a mixed number as well. In this case, our answer is equivalent to .
Do you see what happened there? We used an approach we already knew from before on a new type of problem, and arrived at the correct answer!
Here’s another example: .
Convert into an improper fraction: .
What is the reciprocal of 7? Remember, any whole number can be expressed as an improper fraction by using 1 as the denominator, thus 7 = , and its reciprocal is . Now, multiply by :
Let's make this a practical example. If you had pizzas, and wanted to share them equally among seven people, each person could eat of a pizza. Invite your friends!