Introduction to Ratios

We've got some apples here, and we've got some oranges, and what I want to think about is what is the ratio? What is the ratio of apples to oranges?

To clarify what we're even talking about, a ratio is giving us the relationship between quantities of two different things. So there's a couple of ways that we can specify this. We can literally count the number of apples: one, two, three, four, five, six. So we have six apples, and we could say the ratio is going to be six to six.

Then how many oranges do we have? One, two, three, four, five, six, seven, eight, nine. It is a six to nine ratio of apples to oranges. You could use different notation. You could also write it this way: 6 to 9. You would still read it as the ratio being 6 to 9.

But we don't have to just satisfy ourselves with this because one way to think about ratios, especially if we're thinking about apples to oranges, is how many apples we have for a certain number of oranges. When you think about it that way, both six and nine are divisible by three.

So, if you divide six and nine both by three, six divided by three is two. Nine divided by three is three. So we could also say that the ratio of apples to oranges is two to three, or if we want to use this notation, 2 to 3.

Now, does that make sense? Well, look, we divided each of these groups into three. So one way to think about it is, if you divide this whole total into three equal groups, we see that in each of those groups, for every two apples, we have three oranges.

For two apples, we have three oranges. So once again, the ratio of apples to oranges is, for every two apples, we have three oranges.

But we could think about things the other way around as well. We could also think about what is the ratio of oranges to apples? Oranges to apples. And here, we would essentially switch the numbers.

The ratio of oranges to apples. Notice up here we said apples to oranges, which is six to nine or two to three, which is an equivalent ratio. Here, we're going to say the ratio of oranges to apples, so we've swapped these two.

We have nine oranges for every six apples, so we could say the ratio is going to be 9 to 6. The ratio is 9 to 6. Or, an equivalent ratio, for every three oranges, we are going to have two apples.

So notice this is just exactly what we had up here. When we had apples to oranges, it was six to nine—six apples for every nine oranges. Now, in its oranges to apples, we say it's nine to six—nine oranges for every six apples—or we could say for every three oranges, we have exactly two apples.