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