Which fraction is shown here with the pink spot? Hint: count the parts between each endpoint to find the denominator.
Here we can see the pink spot is in between one and two. So our fraction should be more than one but less than two. So it’s safe to say our fraction should be one plus this fraction portion. But what is that fraction portion?
Well, between one and two, how many markings are there? One, two, three. So that means we’ve taken one whole number and split it equally into three parts. So these would have to represent one thirds, so it was one plus one-third plus one-third.
In order to add fractions, we have to have a common denominator. So we have three as two of the denominators, but one we need to change. And we can change one to be three over three. So we add the numerators, the numbers on top, so three plus one plus one, which is five. And we keep our common denominator of three. So our fraction would be five-thirds.
Another way we could have done this is, if we had known, which we did — we found out — that each marking represents a third, we could’ve started at zero and said one-third plus one-third plus one-third plus one-third plus one-third will get us to the pink spot. So as we said before, we add the numerators, which is five, and we keep our common denominator of three. So once again, we would get the fraction of five-thirds, and five-thirds is greater than one but less than two.