Find the quotient of 531 divided by six and the remainder if it exists.
Now we know that the quotient is what we get when we divide one number by another. So if we divide 531 by six, the answer is the quotient. The question also tells us to find the remainder if it exists. Sometimes the division will have a remainder; sometimes it won’t. Look at the two numbers in our division. Can we predict whether the calculation is gonna have a remainder or not? Well, yes, we can predict the answer to that question. Every multiple of six is an even number, and 531 is not even. So we know it’s definitely not going to be a perfect multiple of six. There is going to be a remainder. It’s an odd number that we’re dividing by six. So we must make sure that we get the remainder at the end.
So we need to divide 531 by six. Let’s use long division to find the answer. There are no sixes in five. So we need to look at the first two digits. 53, how many sixes are there in 53? Let’s use our knowledge of the six times table to help. What facts do we remember? Firstly, we know that 10 sixes are 60. This is greater than 53. But if we take away one lot of six from 60 we’ll get the answer to nine lots of six. 60 take away six equals 54. This is still too large, but at least we can see that the answer is going to be that there are eight sixes in 53. Let’s subtract six from 54 to find out what eight times six is worth.
54 take away six equals 48. And this is as near to 53 we can go without going above 53. So we know there are eight sixes in 53. But, of course, we know there is a remainder. So we need to subtract the value of eight sixes, which we said was worth 48, from 53 to see what’s left. We can’t take away eight ones from three ones, so we’re going to need to exchange. Instead of five 10s, we’ve now got four 10s. Exchange them for 10 ones. 13 ones take away eight ones equals five, and four take away four equals zero. The remainder is five. Now, there are no sixes in five because it’s too small. So we can bring down another digit to make our number a two-digit number. The last digit is one, so our number becomes 51.
How many sixes are there in 51? Well, we can use the number facts we’ve already discussed to help us. Nine sixes, which equals 54, is too large. So we know that there are eight sixes in 51 because eight sixes are 48. So that’s right, eight at the top. So we’ve started by calculating the quotient of 531 divided by six. And the quotient is equal to 88. But as we predicted, there is going to be a remainder. Let’s calculate what that remainder is. We said the value of eight times six is 48, and the number we wanted to divide by six was 51. So what’s the difference between 51 and 48?
Instead of using column subtraction this time, we could use a method that perhaps we should have used the first time around. We can count up from 48 to 51 and find the difference between these two numbers. They’re so close together. 48, 49, 50, 51. The difference is three. And so, we can say that the remainder is three as well. We found the quotient and the remainder of 531 divided by six. We divided 531 by six to find both the quotient and the remainder. The quotient is 88 and the remainder is three.