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Use the following part–whole model to find 84 divided by three.
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Often, we can use times tables facts we already know to help us with a division.
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But do you know a times tables fact that’s going to help you find 84 divided by three?
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It’s quite a large two-digit number we need to divide, isn’t it?
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And that’s why in this question we’re shown how to split it up into smaller parts to help us.
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The whole amount in the part–whole model that we’re given is 84; it’s the number we’re dividing.
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And we can see it’s been split into two parts, 60 and 24.
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Now, often when we break apart two-digit numbers to make them easier to work with, we split them up into their 10s and ones.
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But with this calculation, it would have meant splitting up the number into eight 10s or 80 and four ones.
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But if our part–whole model had shown 80 and four, we’d have found it really difficult to divide by three.
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Neither of these parts are multiples of three.
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And that’s why we’ve been given this particular part–whole model to help us.
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Both 60 and 24 are multiples of three.
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And they’re also multiples of three that we already know facts for.
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So we can divide each part by three to help us find the overall answer.
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First of all, how many threes are in 60?
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Well, this is still quite a large number, but we know a fact that can help us.
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We know that 10 threes are in 30.
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30 divided by three equals 10.
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And so, if we double 30 to get 60, we double the number of threes that we have.
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60 divided by three equals 20.
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Now we need to divide the second part by three.
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How many threes are there in 24?
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Three, six, nine, 12, 15, 18, 21, 24.
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There are eight threes in 24.
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We found out there are 20 threes in 60 and eight threes in 24.
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And 20 plus eight equals 28.
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We’ve used the part–whole model to find that 84 divided by three equals 28.