Arrange six-sevenths, one twelfth, and five elevenths in ascending order.
Immediately, I recognize that each of these fractions have a different denominator. This means we’ll have to think carefully about how we order them. We have a few options. One option that comes to mind is to convert each of these fractions to a decimal. Another option would be find a common denominator for all three of these fractions. A third option would be to compare each of these fractions to one-half.
I’m gonna start here and see if by comparing each of these fractions to one-half, we can arrange them in ascending order. Starting with six-sevenths, how does six-sevenths compare to one-half? Six-sevenths is greater than one-half. In fact, six-sevenths is almost one whole. I’m gonna take that information and use it to try and graph six-sevenths, where I think it would go, on a number line. We think six-sevenths is almost one whole.
Next step, one twelfth. How does one twelfth compare to one-half? One-half is much bigger than one twelfth. In fact, one twelfth is closer to zero than it is one-half. So I’ll mark one twelfth closer to zero on our number line.
Last, we need to compare five elevenths to one-half. Five elevenths is almost one-half. I know this because 11 divided by two equals five and a half. So half of 11 is five and a half. One-half equals five and a half over 11. But we only have five. Which means that one-half is still a little bit larger than five elevenths. And that means that on our number line, five elevenths is just below the one-half mark. It would go there.
We now have enough information to arrange these fractions in ascending order. That means, start on the left and move to the right, from the smallest to the largest. In ascending order, one twelfth, five elevenths and six-sevenths.