There are 80 counters in a bag. 16 of the counters are purple. What fraction of the counters are purple? Circle your answer.
So from reading the question, we can see that 16 out of the 80 counters are purple. And the other way of writing 16 out of 80 is to write it as a fraction, so 16 over 80. So we can say that 16 over 80 of our counters are purple. So we’ve got it as a fraction. But if we look at the fraction options that we’ve got, we’ve got a quarter, a third, two-fifths, and a fifth. So this doesn’t match any of these. So what do we need to do? Well, what we’re gonna do is simplify our fraction. So to do this, we need to find a common factor that goes into both 16 and 80.
Well, in fact, there’s a number of common factors of 16 and 80. But the most obvious one would be eight because we can see that eight goes into 16 twice. And eight goes into 80 10 times. So therefore, we’re gonna divide the numerator and denominator by eight. So when we do this, we’re gonna get two over 10. Now, can this be simplified any further? Are there any common factors of two and 10? Well, yes, we can see that two goes into both two and 10. So again, we divide the numerator and denominator, this time, by two. So when we do that, we get one over five or one-fifth.
Now, if you’re really hot with your factors, you could’ve noticed that you could’ve just divided the numerator and denominator by 16. And you would’ve arrived at the same answer. So that would’ve given us one over five because 16 divided by 16 is one. And 80 divided by 16 is five. And that’s because five multiplied by 16 — you got five tens is 50. Five sixes is 30, added together gives us our 80. So therefore, we can say that a fifth of the counters are purple.
It is worth saying however that if you’re struggling to find factors of a number, then a good way to go about a question like this is to look at them both. And if they’re both even numbers, just divide by two. So if we did that, we go from 16 over 80 to eight over 40. And again, if you still can’t see any, you can divide by two again. And that’ll give you four over 20. And then, you could divide by four or just go by two again. You would’ve got two over 10 and then one over five. So eventually, you would’ve got to the correct answer. So if you do struggle to find the factors, this is a way that you could use to make sure that you get to the right answer anyway.