Divide fractions: sharing divisions and fitting the divisor (We can use mental math!)

These two videos show two special cases of fraction division problems where we can use mental math and visual models. The first one has to do with equal sharing (sharing divisions), and the second with thinking of how many times the divisor fits into the dividend.

Sharing divisions

In this video, the problems are such that the divisor is a whole number. We can solve these by thinking of equal sharing. For example, 6/8 divided by 3 can be framed as: "There is 6/8 of a pizza left, and three people share it evenly. How much does each one get?"

Now, 6/8 means six slices. So, each person gets two slices. Those slices are eighths, which means each person gets 2/8 (of the entire pizza).

After looking at those, we then divide unit fractions by a whole number. For example, we look visually at (1/2) ÷ 4. Half of a pie is divided into four further pieces. Each of these pieces is an eighth, so 1/2 divided by 4 is 1/8.

Fitting the divisor

In the second part, we solve divisions such as 2 divided by 1/4 by thinking how many times the divisor fits into the dividend. In this case, how many times does 1/4 fit into 2? Or, how many fourths are in 2 whole pies? The answer is eight.

We look at a variety of such questions, relying on visual models. Solving these types of division problems also leads us to notice that division problems seem to be related to MULTIPLICATION. And that is indeed the case: the shortcut for fraction division (not taught here) has to do with changing a division problem into a multiplication.

This video addresses the standard 5.NF.B.7: divide whole numbers by unit fractions.

See also

Fractions are divisions

Reciprocal numbers and the shortcut for fraction division

Math Mammoth Grade 5 curriculum

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