What is 1118 divided by 43?
Although there isn’t a division symbol in this question, we can tell by the way that the calculation has been written that we’re being asked to find the number of 43s in 1118 or divide 1118 by 43. And because we’re dividing by a two-digit number, we need to use long division. So we can begin by dividing the digits from left to right.
We know that there are no 43s in one. And if we look at the first two digits, 11 is too small too. And so we need to divide the first three digits. How many 43s are in 111? We need to find the highest multiple of 43 that takes us to 111 or at least as close as we can get to 111. What about two lots of 43? Are there two 43s in 111? Well, 42 is the sort of number we can multiply by two quickly, just by doubling each of its digits. Four doubled is eight and three doubled is six. So 43 doubled is 86. So we can see that there are definitely two lots of 43 in 111.
What about three lots of 43? Rather than work out the actual answer, we can use some quick number sense to find out. We can round 43 to 40. And we know that three lots of 40 is 120 which is more than 111. If three lots of 40 is 120, then we know three lots of 43 will be more than 120. So the nearest multiple of 43 to 111 has to be 86. There are two lots of 43 in 111. So we can write the number two at the top.
But if we have to divide 111 by 43 and the nearest multiple we can make is 86, what’s the remainder? How much do we have left? We can write 86 underneath 111 and then subtract to find the answer. 111 take away 86 leaves us with 25. So now we need to divide this by 43. How many 43s are in 25? Well, again, 25 is too small. So we need to bring down the digit eight from our original number. So the question now becomes: how many 43s are in 258?
One way to find the answer might be to start with 43 times one then move on to 43 times two, times three, and so on, and keep going until we get close to or if you hit exactly 258. Or perhaps a quicker way of finding the answer is to use some of the larger facts that we do know and to jump around until we get close to 258.
To use trial and error, let’s start with a large multiplication that’s quick to do, 43 multiplied by 10. Well we know the answer is 430 which is larger than 258. But what can we use this fact to find? Half of 10 is five and so half of 430 is the same as 43 times five. What’s half of 430? Half of 400 is 200 and half of 30 is 15. So five 43s are 215. There are definitely five 43s in 258.
But are there six 43s? Let’s add another lot of 43 to see if we can get close to 258. Five ones plus three ones equals eight ones. One ten plus four tens equals five tens. And two hundreds plus zero hundreds equals two hundreds. And so we can see that there are six 43s in 258 exactly. So let’s write the digit six at the top.
Finally, just to check there’s no remainder. We need to subtract the number we made. We said that 43 multiplied by six was 258. So we need to take away this from 258. And, of course, we know the answer is going to be zero. There’s no remainder. And so by using the long division method, we can find that 1118 divided by 43 equals 26.