I’m in between sections in our Prealgebra book with my younger son, so we took a break today to look at some AMC 8 problems. A problem about dividing fractions tripped him up a little, and that led to a short review of fraction division.

First up: basically the only thing that anyone remembers – flip the denominator:

Next: Let’s try thinking through the same problem using geometry and slicing up circles pizzas:

Next: Much of the difficulty comes from having a fraction in the denominator of our fraction, so what can we do to deal with that difficulty?

Finally, off to the kitchen to look at dividing fractions using snap cubes. We find a collection of snap cubes that we can divide by 2 and by 5, and use that collection to get a better understanding of what (1/2) / (1/5) looks like:

So, a fun little review exercise. I’m sure there are other nice ways of reviewing fraction division, but this short review hopefully provide a nice starting point for understanding beyond just the “flip the denominator” trick.

If you see a division as a ratio then multiplying top and bottom by the same number is clearly(!) not going to alter the ratio.
If you see a/b as having some value or other then give it a name.
a/b = result, so multiply by b and get a = b x result
If a and b are fractions the rest is obvious(!)

another comment from MTBoS recently is to include a number line representation along any pie presentation of fractions. Dividing pies seems to be an action while the number line shows the fraction as an object. This facilitates the thought process howardat58 talks about above.

## Comments

If you see a division as a ratio then multiplying top and bottom by the same number is clearly(!) not going to alter the ratio.

If you see a/b as having some value or other then give it a name.

a/b = result, so multiply by b and get a = b x result

If a and b are fractions the rest is obvious(!)

another comment from MTBoS recently is to include a number line representation along any pie presentation of fractions. Dividing pies seems to be an action while the number line shows the fraction as an object. This facilitates the thought process howardat58 talks about above.