# Tag Archives: unit rates

## Partitive fraction division

As promised, more notebook pages on fraction division. This is based on the work I did a while back on trying to write authentic partitive division problems with fractional divisors. (As I wrote that last sentence, I reminded myself what a bizarre niche market I am trying to occupy on this here blog.)

I settled on situations involving fractional values of unit rates, such as the following.

If $\frac{2}{3}$ of a lawn takes $\frac{3}{4}$ of an hour, how much can I mow in one hour?

Before we begin, remember that if the problem were about 2 lawns in 3 hours, we would easily and naturally divide by 3. Only the numbers have changed, so the mathematical structure remains the same and we need to find $\frac{2}{3} \div \frac{3}{4}$.

Click each image to see it full size. If you’re into this sort of thing.

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I was feeling guilty the other day about spending $7.00 on a gallon of cider. We are at the end of cider season here in Minnesota. It’s a seasonal treat that doesn’t come cheaply. But we are on a budget (community college salaries only go so far!) and I was feeling bad about the expense-guilty for giving in to the sweet, sweet temptation of delicious fresh cider. And then my daughter asked for a juice box. There they were, side by side…a$7.00 gallon of cider and a \$2.39 pack of eight 4.23 boxes.