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