Hannah can ride her bicycle two and one-ninth miles before she starts feeling tired. Express this distance as an improper fraction.
An improper fraction has a numerator that’s greater than the denominator. The value on top of the fraction is bigger, the numerator is bigger, than the denominator. Two and one-ninth is made up of a whole number and a fraction: whole number two and a fractional piece of one-ninth. We’ll use both of these pieces together to write an improper fraction.
How do we write the whole number two as a fraction? Just imagine that these two rectangles represent our two whole pieces. We know that our fraction is one out of nine parts, so what we’ll do is we’ll divide our whole number pieces into nine parts as well like this.
Notice that we didn’t change the amount of space in the rectangles. On the left, we have nine out of nine parts — nine over nine. On the right, we also have nine out of nine parts, but how many ninths are in this two whole number? We have nine ninths for one and nine ninths for the other. Nine out of nine pieces plus nine out of nine pieces would be eighteen ninths — 18 pieces of one-ninth.
We could find this by adding up each of our one-ninth section, and that would be a total of 18. We can’t forget our fractional piece one-ninth, which would look like this as a piece out of nine. To add these together, we’ll add our numerators nine plus nine plus one. We know that nine ninths plus nine ninths equals eighteen ninths. From there, we need to add one. And our total here comes to nineteen ninths.
18 plus one is 19 and our denominator doesn’t change. If we write the mixed number two and one-ninth as an improper fraction, we turn our two whole pieces into a fraction, eighteen ninths. And then we had a remaining fraction of one-ninth. Our final answer here becoming nineteen ninths. Hannah can ride nineteen ninths miles before she starts feeling tired.