Which of three-fifths and two-sixths is closer in value to a half? Show all your working.
So what we’re gonna do with this question is take a look at the three fractions we have, which is three-fifths, a half, and two-sixths. And to help us look at them and compare them, what we’re gonna want to do is convert them to an equivalent fraction that has a common denominator.
So to help us do that and work out what is the lowest common multiple which is gonna be our common denominator, I’m just gonna write out a few multiples of each of the numbers that we have as the denominators. So first of all, I’ve written out the first few multiples of six. We got six, 12, 18, 24, 30, 36. And then, I’ve written out the first three multiples of five. So I got five, 10, 15, 20, 25, and 30.
And I’ve stopped at 30. And the reason I’ve stopped at 30 is because 30 is a common multiple for both six and five. And 30 is also a multiple of two because 30 divided by two gives us 15. So great, this is gonna be our common denominator. So now, what we’re gonna do is convert each of our fractions into fractions where 30 is the denominator.
So in our first fraction, to get from five as the denominator to 30 as this denominator, we have to multiply by six. Therefore, we’ll have to do the same to the numerators because whatever you do to the bottom, you must do to the top. So we’re gonna multiply three by six which is gonna give us 18. So three-fifths is equal to 18 over 30.
Then, we’ll do the same process with our second fraction. So we can see that we’d have to multiply two by 15 to get to 30. So we’re gonna do the same to the top, so the numerator. So we do one multiplied by 15 which gives us 15. So we can say that a half is equal to 15 over 30.
And then, finally, for our bottom fraction, we can say that we’d have to multiply six by five to get to 30. So therefore, again, we do the same to the top or the numerator. So we get two multiplied by five which gives us 10. So we can say that two-sixths is equal to 10 over 30.
So now, what we want to do is actually compare three-fifths and two-sixths with a half because what we want to see is which one of them is closer in value to a half. So to do that, what I’m gonna do is actually find the difference between them.
So first of all, we’re gonna find the difference between three-fifths and a half. So we’re gonna do 18 over 30 minus 15 over 30. So this is gonna give us a difference of three over 30. And then to see the difference between two-sixths and a half, I’m gonna do 15 over 30 minus 10 over 30 which is gonna give us a difference of five over 30.
Okay, so now, we need to decide which is closer in value to a half: three-fifths or two-sixths? Well, if we compare our differences, we can see that three over 30 is less than five over 30. So therefore, we can say that three-fifths is closer to a half than two-sixths. And that’s because the difference between three-fifths and a half is less than the difference between two-sixths and a half.