A shipment of 9504 kilograms of sugar is divided into 528 packages. What is the weight of sugar in each package?
The first piece of information that we’re given in this problem is the weight of a shipment of sugar. This’s 9504 kilograms. The next piece of information that we’re told is what happens to it. It’s divided. What’s it divided into? 528 packages. And we’re then asked what the weight of sugar is in each package. So to find the answer, we need to divide 9504 by 528. And to do this, we’re going to need to use long division.
How many lots of 528 are there in 9504. There are no lots of 528 in nine or even in 95. So we need to look at the first three digits of our number to begin with. How many lots of 528 are there in 950? Rather than try out every multiple of 528, we can use estimation here to help us. We can think of 528 as being approximately equal to 500. So how many lots of 500 would we expect to be in 950? Well, two lots of 500 are 1000. So we know that only be one lot of 500 in 950. And as 528 is greater than 500, we know that there’s only going to be one lot of 528 in this number too. So we can write a one at the top.
One lot of 528 is 528. And if we subtract this from 950, we can find out what we’ve got as a remainder. We can’t subtract eight ones from zero ones. So we’re going to need to exchange. We’ll take one ten. So the five tens, we now have four tens and we’ll exchange it for 10 ones. Now, we can subtract our eight ones. 10 ones take away eight ones leaves us with two ones. In the tens column, four tens subtract two tens leaves us with two tens. And in the hundreds column, 900 take away 500 leaves us with 400. Now, we can continue dividing.
How many lots of 528 are there in 422? 422 is too small. We’re going to have to include another digit. And the place we’re going to get our digit from is the top number. So we’re going to bring down the next digit along, so actually the final digit in our number. It’s a four. And it’s going to turn our number 422 into 4224. How many lots of 528 are there in this number? What we’re going to do, start with one lot of 528 and carry on counting? No, let’s use our estimation skills again.
4224 is approximately equal to 4000. And as we’ve said already, 528 is approximately the same as 500. We know there are two lots of 500 in 1000. And so, there must be eight lots of 500 in 4000. So let’s estimate that there’s going to be around about eight lots of 528 in this number. There’s only one way to find out. Let’s multiply 528 by eight. Eight ones multiplied by eight equals 64. So we’ll write a four in the ones place and exchange 60 ones for six tens. Two tens multiplied by eight equals 16 tens. We’ve already got six tens that we’ve exchanged. So that takes us to 22 tens. So we’ll write a two in the tens place and exchange 20 of our tens for two hundreds.
Finally, five hundreds multiplied by eight equals 40 hundreds. It’s the same as 4000. But we’ve also got two hundreds underneath. If we add this to our 40 hundreds, we have 42 hundreds or 4200. And this number is exactly the number we’re looking for. We used estimation to find which number to try and it worked. There are eight lots of 528 in 4224. And because we know that eight lots of this number fit exactly, we know that if we subtract eight lots of 528 from 4224, we’re going to be left with zero. There is no remainder. And we can see the answer to our problem at the top of the calculation. We use long division to divide this four-digit number by a three-digit number.
If a shipment of 9504 kilograms of sugar is divided into 528 packages, the weight of sugar in each package will be 18 kilograms.