Matthew is six and nine twentieths feet tall. Express his height as an improper fraction.
First, we need to remember what an improper fraction is. In a fraction, we know that the numerator is the number on top and the denominator is a number on the bottom. In an improper fraction, there is a larger numerator than the denominator.
Matthew’s height is given to us with a whole number and a fraction. In the fractional piece, nine, the numerator, is smaller than 20, which is the denominator. Nine over 20 is not an improper fraction. In order to make an improper fraction, we’ll need to turn this whole number six into a fraction and add that value to the nine twentieths. So how do we do that?
We want to turn the whole number six into a fraction and then add that to nine twentieths. That means that the fraction that we turn six into must have a denominator of 20. We must have something that’s equal to six with a denominator of 20. To do that, imagine that the whole number six has a denominator of one, and we multiply one times 20 to get a denominator of 20.
If we multiply something on the bottom of a fraction, we need to multiply something on the top of our fraction. So we multiply our numerator six by 20. Six times 20 equals 120. To write the whole number six as a fraction out of 20, you write 120 over 20. And that is equal to six.
Our next step is to add this value to the nine twentieths we already had. 120 over 20 plus nine over 20 equals 129 over 20. Six and nine twentieths represented as an improper fraction looks like this: 129 over 20. Matthew is one hundred and twenty-nine twentieths feet tall.