Find all the fractions between one and two whose denominators are six.
We’re moving from one to two, but we want to work with fractions whose denominator is six. The first thing we want to do is to write the number one and the number two as a fraction with the denominator of six. To write the whole number one as a fraction with the denominator of six, we write six over six. The whole number one is equal to a fraction of six over six.
We know that two is equal to one plus one. We could write two as a fraction with the denominator of six by adding six over six plus six over six. When we do that, we add the numerators together. Six plus six equals 12. And the denominator doesn’t change.
Now we need to make all the fractions we can between six over six and 12 over six. The first thing that comes between six-sixths and 12 sixths is seven-sixths. After that, we have eight-sixths, nine-sixths, 10 sixths, and 11 sixths. There are five fractions with a denominator of six that fall between one and two.