Which is greater, nine elevenths or twenty-four thirds?
In this problem, we need to decide which is the larger of two fractions. Nine elevenths or twenty-four thirds? What are we going to look at to help us to tell which is the largest fraction? Should we look at the numerator? Is the fraction with the largest numerator the largest fraction? Or perhaps we should look at the denominator. The first fraction has 11 as a denominator compared with only three in the second fraction. Denominators in the fractions are different. To be able to compare them directly, we’d have to convert both denominators so they were the same. But there is actually a much much quicker way to find the answer than this.
All we need to do is look at these fraction and think about what they mean. What does nine elevenths mean? It means that the whole amount has been split into 11 equal parts. And we’ve selected nine of them, nine out of 11 equal parts, nine elevenths. This is less than one. And we notice because the numerator, the top number, is smaller than the denominator, the bottom number. This isn’t the same with our second fraction. The numerator is larger than the denominator, twenty-four thirds. Three-thirds make one whole. So twenty-four thirds must be more than one whole. So we don’t even need to draw the whole diagram to be able to say that twenty-four thirds is going to be the larger fraction.
But let’s just complete the diagram to prove it, three-thirds, six-thirds. So far we’ve made three wholes. And we’ve only used up nine of our twenty-four thirds. In fact twenty-four thirds looks like this. It is the same as eight wholes. Although the diagram was helpful in proving our answer, we didn’t need to use it. We just needed to look carefully at each fraction. We knew that nine elevenths was a proper fraction which means the numerator was smaller than the denominator. And it was less than one. But twenty-four thirds was an improper fraction. The numerator was a lot larger than the denominator. So we knew this was going to be greater than one. So the greater fraction is twenty-four thirds.