Factory A produces 3,000 bars of soap in seven and a half hours. Factory B produces 5,500 similar bars of soap in two and a half hours. Which factory produces more bars of soap per hour?
So what we’re gonna do in this question is first of all work out what the rate of soap production is in each of our factories. So we’re gonna start with factory A because in factory A, we’re told that it produces 3,000 bars of soap in seven and a half hours. So therefore, what we can do to work out our rate of soap production is work out how many bars of soap would be produced in one single hour.
But how are we going to do that? So if we divide seven and a half hours by seven and a half, we’re gonna get one hour. So if we do the same to the number of soap bars produced, what we’re gonna get is 400. So what we can say is that in factory A, that 400 bars are produced per hour. Well, we could’ve done that using a calculator. However, how could we work out what the bars per hour were if we were gonna use a written method?
Well, one method we could use would be to convert our mixed number into a top-heavy or improper fraction. So when we do that, we get 15 over two. And that’s because if we think about how many halves are in seven, well it’s 14, plus the half we’ve got. It’s 15. And then that gives us 15-halves or 15 over two. So this means we’d have 3,000 divided by 15 over two. Well, if we remember what we do when we’re dividing by a fraction, what we actually do is multiply by the reciprocal of that fraction. So we flip the numerator and denominator. So now, what we’ve got is 3,000 multiplied by two over 15.
Well, now what we can do is cross cancel because if we see that we’ve got 15 as the denominator and if we divide 3,000 by 15, what we’re gonna get is 200. You might think, well, how do we do that? Well, we can do that quickly mentally because 15 goes into 30 twice, and then we’ll have two more zeros. So it’s gonna be 200. So now, we’ve got 200 multiplied by two over one, which is equal to 400. So it gives us the answer we were looking for. There’d be other written methods you could use, but this is just one we could use.
Okay, so now let’s go on to our factory B. Well, factory B, what we can see is that we’ve got 5,500 bars of soap that are produced in two and a half hours. So once again, so that we can compare them, what we’re gonna do is work out how many bars are produced per hour. So this time, to work out how many bars per hour, what we’re gonna do is divide by two and a half because two and a half hours divided by two and a half is one hour. And then, if we do the same to our 5,500, we’re gonna get 2,200. So therefore, we can say that factory B produces 2,200 bars per hour.
So what we can do now is give you an alternative method. So if we had 5,500 bars made in two and a half hours and then we doubled both to get rid of the fraction, what we’d have is that it could have 11,000 bars made in five hours. So then, we could use the bus stop method for division because we could divide 11,000 by five. Five into one is zero, carry the one. Then we got five is into 11, which is two and carry the one. Then five is into 10, which is two with no remainder. Then we got five is into zero, which is zero. And finally, five is into zero again, which is zero. So it gives our 2,200.
Okay, great. So now, we’ve got the rate of production for each of our factories. So, as 2,200 is greater than 400, we can say that factory B must produce more bars of soap per hour.
Well, it’s worth noting that, okay, with this question I’ve showed you how to find out the bars per hour, and that’s helped us get to our final answer. We could’ve looked at it straightaway and said, “Well, factory B must produce more bars per hour” because we saw that factory A produced 3,000 bars in seven and a half hours. Whereas factory B produced 5,500 bars in two and a half hours. So it produced more bars in less time. So if we use logic, that would’ve also told us that factory B was, in fact, the factory which produced the more bars of soap per hour.