What is 8827 divided by 97?
In other words, how many 97s go into 8827? And the way we can find this is by using long division, which means looking at each of the digits from left to right and seeing how many lots of 97 go into them. Eight is too small. There are no 97s in eight. So we need to look at the first two digits.
How many 97s are in 88? 88 is too small too. So we need to look at the first three digits. How many 97s are in 882? I’m guessing we don’t know our 97 times table. So we need to use facts that we do know to help. We’re looking for the greatest multiple of 97 that’s equal to 882 or less than 882. Which multiples of 97 do we know?
Well, when we’re looking for a large multiple, multiplying by 10 is always a good one to start with. 97 multiplied by 10 equals 970. So although we know 970 is too large and we can’t fit 10 97s in 882, perhaps we could fit nine 97s. Nine 97s is one less 97 than 10 97s. So if we subtract 97 from 970, we can find the answer.
97 is only three away from 100. What if we subtracted 100 and then added three to the answer? This is a sort of thing we could do in our heads. But we can show a number line just so that we can see what we’re doing mentally.
Start with 970. Subtract 100 cause it’s quick to do and it’s close to 97. 970 take away 100 equals 870. And then remember that we’ve taken away three too many. So we need to adjust our answer by adding three. 870 plus three equals 873. So now we know what nine lots of 97 are, 873. And we can see that this does fit within 882. We know there are nine 97s in 882. So we can write the number nine at the top.
Remember, nine 97s were 873, which was less than 882. So we can write 873 underneath 882 and then subtract to find the remainder. Rather than taking away 873 from 882, it’s quicker just to count up from the smaller number. 882 take away 873 equals nine. There are no 97s in nine cause it’s too small. But we’ve got one more digit we can look at.
So we can bring down the seven ones from 8827 and include these two. How many 97s are in 97? Well, this one’s an easy one. The answer is one.
Just to check there’s nothing left over, we can subtract 97 from 97 and see that the answer is zero. There’s nothing more to divide. To find the answer, we used long division. First, we looked at the number of 97s that were in 882. This was quite a large multiple of 97. So we used a known fact to help us and then worked backwards.
We knew 10 97s was 970, but that was too large. So we subtracted one lot of 97 to find out what nine 97s were. And we could fit this into 882. It fitted nine times. We subtracted to find a remainder of nine. But we knew this was too small. So we brought down the seven digit from the first number to make 97. And of course, there’s only one lot of 97 in 97. Finally, we did a quick subtraction to check that there was no remainder. 8827 divided by 97 equals 91.