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Benjamin is calculating 450 divided by five using the partial quotient method.
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Help him to find the quotient from his calculation.
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In this question, we’re told that Benjamin is trying to work out the answer to a division question.
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We know this because we’re given it in the first sentence.
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We’re told that he’s calculating 450 divided by five.
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But you know, we can also see the calculation written underneath here.
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It might not have a division symbol, but wherever we see numbers written like this or sometimes like this, we know we need to divide to find the answer.
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We need to find how many fives there are in 450.
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Now, like with any calculation, there’s more than one way Ben could find the answer.
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But we’re told that he’s using the partial quotient method.
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Now this method is easier to understand that it looks.
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The word “partial” just means part of something.
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And a quotient is simply the answer to a division.
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In other words, Benjamin is finding out how many fives there are in 450 a part of the answer at a time.
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He’s breaking 450 into chunks.
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And we’re told that we need to help him find the quotient from his calculation.
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Now, one way to find out how many fives are in 450 would be to keep subtracting fives.
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450 take away five leaves us with 445.
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And if we take away another lot of five, that’s 440.
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It’s gonna take us quite a while to get all the way down to zero, isn’t it?
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So when we use the partial quotient method, we ask ourselves a question.
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What’s the largest multiple that I can think of that I could subtract from this number?
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Instead of taking away one lot of five each time, can you think of something else we could subtract?
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Well, we know that 10 fives are 50, so we could take away 10 lots of five at a time, take away 50s.
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But we could even go one better than this.
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What if we double the fact?
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If 10 fives are 50, 20 fives are worth double 50 or 100.
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If we take away 100, we’re going to get to the answer much quicker, aren’t we?
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So let’s try subtracting this partial quotient.
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And it might help us to consider what Ben’s thinking about at each step.
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So to begin with, he’s going to look at his number 450 and think to himself, “Well, I know there’s definitely 20 lots of five in 450, so I’m going to take away 20 lots of five or 100.”
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And of course, 450 take away 100 leaves him with 350.
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Now he can look at 350 and think to himself, “Well, I can take away another lot of 25s.”
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350 take away 100 is going to give him 250.
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And he’s still got enough to keep going.
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250 take away 100 leaves him with 150.
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150 take away 100 leaves him with 50.
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And now he can’t take away anymore chunks of 25s, can he?
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He’s only got 50 left.
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But Benjamin knows how many fives there are in 50.
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And if he takes away 10 lots of five, he’s going to arrive back at zero.
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So by subtracting a part at a time, Benjamin split up the answer to this division calculation or the quotient into bits.
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He knows there are one, two, three, four lots of 25s and one lot of 10 fives.
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Now, how many fives is that altogether?
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Well, we know that four lots of 20 are worth 80.
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And if we add 10, we get the answer 90.
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We’ve subtracted multiples of five to find the answer.
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This is called the partial quotient method.
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And we found we had to take away 90 lots of five to get back to zero.
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And that’s how we know 450 divided by five equals 90.