We need to order one-twelfth, one-tenth, one-third, and one-twentieth in order from least to greatest.
I immediately noticed that each of these fractions has the same numerator. The numerator for all four of our fractions is one. That’s going to be an important key in helping us order these fractions. Let’s start off by imagining that we have four equally sized circles. Each one of these circles is going to represent one of our fractions. Now, we’re going to sketch each one of these fractions in our circles.
First step, one-third: this circle is divided into three parts. And our fraction is talking about one of the three parts. Next step, one-tenth: this circle is divided into 10 parts. And we’re talking about one of those 10 parts. Here’s our example of one-twelfth. We divided our circle into 12 pieces and shaded one of them. And finally, here’s our sketch for one-twentieth. We’ve divided our circle into 20 pieces and shaded one of them.
What I hope you’re starting to see is that when the numerator is equal, in our case all of our numerators are one, then you look at the denominator. And the smaller the denominator, the larger the value. Because this circle is only divided into three parts, one-third is a significant portion of the circle. And this circle is divided into 20 pieces. And you only get one of those pieces. One-twentieth is the least of these four fractions and then it’s followed by one-twelfth then one-tenth with the largest being one-third. So we’ve ordered them from the least to the greatest.