Video: KS2-M17 • Paper 1 • Question 36

2242 divided by 59 equals what?


Video Transcript

2242 divided by 59 equals what?

We can tell by the way that this calculation has been written out that we’re expected to use long division to find the answer. We’re being asked to divide 2242 by 59 or, if we look at it in another way, to find how many 59s fit in to 2242. Normally, we’d look at the digits one by one. But of course, there are no 59s in two. And if we look at the first two digits, there are no 59s in 22 either.

So we need to extend our first division to include a third digit, 224. How many 59s are in 224? We could sit and try to think about multiples of 59 and see how close to 224 we could get. But there is an easier way. 59 is very close to 60. What if we used this fact to help us?

Multiples of 60 are just multiples of six multiplied by 10. So here are some multiples of six. And if we multiply them by 10, here are some multiples of 60. Which multiple of 60 takes us closest to 224? Well, four times 60 and five times 60 are two large. The nearest multiple of 60 less than 224 is 180, which is the same as three times 60.

Now we know that three lots of 60 equals 180, we can use this to find what three lots of 59 are. We know that 59 is one less than 60. And so if we’re multiplying 59 by three, the answer will be three less than 180 which is 177. There are three lots of 59 that fit in to 224. So let’s write the number three at the top.

But there’s a reminder that we need to think about. Let’s subtract three lots of 59 from 224 to see what’s left. So we need to calculate 224 take away 177. These two numbers are fairly close to each other. So we could use counting on to find the answer. Start with 177 and let’s write 224 as our target number. What’s the difference between them?

First, we can add three to take us to the nearest multiple of 10. 177 plus three equals 180. Then, we can add several multiples of 10 until we get as close to 224 as we can. We know that 18 plus four equals 22. So 180 plus 40 equals 220. And then, finally, we can add four to take us to 224.

There are lots of different methods that we could have used to count on. But in this one, we’ve managed to do it in three jumps: three, 40, and four. 40 plus three plus four equals 47. So we know the difference is 47. We have 47 left over as a remainder.

How many 59s are in 47? Well, 47 is too small. We’ve got one more digit at the top that we can include. We can bring down the two to make 472. How many 59s are in 472? Again, instead of thinking about multiples of 59, let’s use multiples of 60 to help. How close can we get to 472 by thinking about multiples of 60?

We know that six-eights are 48. And so, 60 times eight equals 10 times this amount, 480. Now, 480 is larger than 472. But remember we’re looking to divide 472 by 59, not by 60. So what are eight 59s? As we said already, 59 is one less than 60. So if we have eight numbers that are one less than 60, we need to take away eight to find the answer.

Eight lots of 59 is the same as 480 take away eight, 472. There are eight 59s in 472. So let’s write the digit eight at the top. We seem to have found our answer. We can finish the calculation just by checking there’s no remainder. We’re going to take away eight lots of 59 or 472 from the number that we had which was 472. And of course, the answer is zero. There’s no remainder.

We found the answer using long division. In particular, we saw that 59 was only one away from 60. And so, we tried to find multiples of 60 that could help us. And once we found the multiple of 60 that was about right, we could then adjust it to find the multiple of 59.

And so, 2242 divided by 59 equals 38.

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