Video Transcript
A factory produces 204 pieces of cloth each month. How many months does it take the factory to produce 57936 pieces of cloth?
The first piece of information that we’re told in this question is that a factory makes 204 pieces of cloth every month. And we’re asked to find the number of months that a factory will take to produce 57936 pieces of cloth. Now, if we can find out how many 204s there are in 57936. Then we can say how many months it will take to make this number of pieces of cloth. This is a division question. We need to divide 57936 by 204. And so we can find the answer using long division. Now, 204 is quite a nice number to be dividing by. It’s fairly near to 200. So we can estimate our answer each time and use this to help and give us a good idea of what the answer might be.
Now we can’t divide five by 204 or 57 by 204. So instead, we need to think about the first three digits of our number. How many 204s are there in 579? Well, as we’ve just said, we can think of 204 as about 200. So how many 200s do we think are in 579? Well, we know two lots of 200 would be 400. And three lots of 200 would be 600. This is too large. So a good estimate would be two lots of 204. Let’s find the answer to see if this fits into 579. Four multiplied by two is eight. Zero multiplied by two is zero. And two multiplied by two is four. Two lots of 204 is 408. And as we’ve said already, we can’t go higher than two lots of 204. It’d be too large. So let’s write the number two at the top. And we know there’s definitely going to be a remainder. So we’ll write the value of two lots of 204, which we said was 408. And we’ll subtract this from 579 to see what’s left. Nine take away eight is one. Seven take away zero is seven. And five take away four equals one. We have a remainder of 171.
Unfortunately again, this is too small to divide by 204. So we need to bring down a digit from our top number and include this. How many 204s are there in 1713? Once again, let’s apply our estimation skills. Let’s think about how many 200s there might be in this number. We know that, in 1000, there are five lots of 200. And we also know that three lots of 200 make 600, which is near to 700. So that’s eight lots of 200 all together. It sounds like it might be a good estimate for the number of 204s there are in 1713. Let’s multiply 204 by eight to see how close we can get. Four multiplied by eight equals 32. Zero times eight is zero. But we’ve got three that we’ve exchanged. So we can put the three in the tens column. And then two times eight is 16. Eight lots of 204 is 1632. And we know that if we added another lot of 204, the number of 100s in our number would be too great. There must be only eight lots of 204 in 1713. But there’s definitely going to be a remainder again. So we’ll write down the value of eight lots of 204, which we said was 1632. And once again, we’ll subtract to find the remainder.
Three take way two is one. We’re going to need to exchange in the tens column because we can’t take away three tens from one ten. So we’ll exchange one lot of 100. Instead of seven hundreds, we now have six hundreds. And we’ll exchange it for 10 tens. 11 tens take away three leaves us with eight tens. And if we look quickly at our other columns, they’re going to be zeros. Six hundreds take away six hundreds. And one thousand take away one thousand. So our remainder is 81. 81 is too small again to divide by 204. But we’ve got one more digit at the top that we can bring all the way down. How many 204s are there in 816?
Let’s estimate our answer again. It seems we have worked well so far. How many 200s are there in 816? Well, we know that four lots of 200 is 800. And in fact, we don’t have to work out the answer using a written method. Here, we can see that four lots of four will give us the 16 on the end. Four lots of 200 is 800. Four lots of four is 16. And so we can see that there are four lots of 204 in 816. And this time, there’s going to be no remainder. We’ve said four lots of 204 is 816. And if we take this away from 816, we’re left with zero. There’s nothing left over. So in other words, our answer is a whole number of months.
If a factory produces 204 pieces of cloth each month, then the amount of time it will take for the factory to produce 57936 pieces of cloth would be 284 months.
