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: equation left hand side equals right hand side 22 divided by nine division four divided by three.

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: 22 divided by nine multiplication three divided by four.

Then, we cancel and multiply out: equation sequence equals 22 super 11 divided by nine sub three multiplication three super one divided by four sub two equals 11 multiplication one divided by three multiplication two equals 11 divided by six.

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: seven.

Convert into an improper fraction: equals seven divided by four.

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 = seven divided by one, and its reciprocal is one divided by seven. Now, multiply seven divided by four by one divided by seven:

equation sequence seven divided by four division seven divided by one equals 71 divided by four multiplication one divided by seven sub one equals one divided by four

Let's make this a practical example. If you had pizzas, and wanted to share them equally among seven people, each person could eat one divided by four of a pizza. Invite your friends!

6.4.2 Dividing Fractions

6.4.4 Practice with Dividing Fractions