Circle the fraction that is less than two-fifths: one-half, forty-one one hundredths, seven fifteenths, or two-sevenths.
So we want to know which of these fractions is less than two-fifths. Well, there’s two routes that we could take. We could either make each of these fractions have the exact same denominator and then compare or convert each of these fractions to decimals. Our denominators are five, two, 100, 15, and seven. So we will have to find a number that all of these numbers go into evenly. That might take a while.
So instead, let’s convert each of these fractions to decimals using our calculator. First, to convert two-fifths to be a decimal, in our calculator, we take two divided by five, which is 0.4. So now let’s do the same for the rest of the fractions. One divided by two gives us 0.5. 41 divided by 100 is 0.41. Seven divided by 15 is approximately 0.466. And two divided by seven is approximately 0.285. So which of these decimals is less than 0.4?
Well, for our first fraction, one-half, 0.5 is actually greater than 0.4. So one-half is not our answer. 0.41 is also greater than 0.4. So it’s not our answer either. 0.466 is greater than 0.4. So seven fifteenths is not less than our two-fifths. But finally, two-sevenths, which is approximately 0.285, is indeed less than 0.4. Therefore, two-sevenths is the fraction that is less than two-fifths.
And this answer might actually be a bit intuitive because notice the numerators are the same. We have two-sevenths and we have two-fifths. Well, sevenths are smaller than fifths. So if we have two-sevenths and two-fifths, the two-sevenths will be smaller than the two-fifths. So once again, the fraction that’s less than two-fifths would be two-sevenths.