Fraction division in context

We're told that a group of three friends is practicing for the track meet. The group is going to run one half of a mile total. If they each run the same distance, how far will each person run? Which expression could represent the situation?

So pause this video and try to figure this out on your own.

All right, the way I think about it is there's some distance that they're going to try to travel. So, in this case, it's half of a mile, and they're going to divide that distance amongst the three friends.

The distance that each of them is going to run is the total distance divided by the number of folks that are running. So, an expression that represents this is one half, the total distance they are running, divided by the number of people who are going to split that distance divided by three.

And so, that is choice C right over here. Now, it might have confused you a little because you're not used to dividing a smaller number, especially a fraction, by a larger number. But that's exactly what's going on over here. You're taking the total distance, and it's being split amongst three friends. So, the total distance divided by three friends will tell you how far each of them has to run.

Let's do another example.

So here we are actually, they're telling us that there's some problem that can be solved with one half divided by seven. They say, which problem can we solve with one half divided by seven? Then they give us three different scenarios that we could try to solve.

So pause this video and think of which of these three scenarios can be solved with this expression.

All right, let's go through each of the choices.

Cara ordered seven pizzas for her birthday party. Her parents ate one half of a pizza before the party. How much pizza is left for the party?

All right, so what's going on here? She started with seven pizzas. She starts with seven. Her parents ate one half of a pizza, so one half of a pizza is taken away. That would tell you how much is left, so this is definitely the expression you would solve to figure out. Not this expression up here, so I would rule this out.

Walt has seven hamsters. Each hamster weighs one half of a kilogram. What is the total weight of the hamsters?

Well, to figure out the total weight, you would start with the number of hamsters and you would multiply that by the weight of each hamster. So that would be seven times one half, so we could rule that one out.

So it's likely going to be C, but let's figure this, let’s make sure it makes sense.

Janae has one half kilogram of trail mix. She splits her trail mix evenly between seven friends. How much trail mix will each friend get?

All right, she has a total amount, one half of a kilogram, and she's going to divide that total amount. She splits her trail mix evenly amongst seven friends to get a certain amount per friend.

How much trail mix will each friend get? And that's exactly what that expression up there is. So, I am liking this choice.