Video: Dividing Three-Digit Numbers by One-Digit Numbers Using the Partial Quotient Method

Benjamin is calculating 450 ÷ 5 using the partial quotient method. Help him to find the quotient from his calculation.


Video Transcript

Benjamin is calculating 450 divided by five using the partial quotient method. Help him to find the quotient from his calculation.

In this question, we’re told that Benjamin is trying to work out the answer to a division question. We know this because we’re given it in the first sentence. We’re told that he’s calculating 450 divided by five. But you know, we can also see the calculation written underneath here. 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. We need to find how many fives there are in 450. Now, like with any calculation, there’s more than one way Ben could find the answer. But we’re told that he’s using the partial quotient method.

Now this method is easier to understand that it looks. The word “partial” just means part of something. And a quotient is simply the answer to a division. In other words, Benjamin is finding out how many fives there are in 450 a part of the answer at a time. He’s breaking 450 into chunks. And we’re told that we need to help him find the quotient from his calculation. Now, one way to find out how many fives are in 450 would be to keep subtracting fives. 450 take away five leaves us with 445. And if we take away another lot of five, that’s 440. It’s gonna take us quite a while to get all the way down to zero, isn’t it?

So when we use the partial quotient method, we ask ourselves a question. What’s the largest multiple that I can think of that I could subtract from this number? Instead of taking away one lot of five each time, can you think of something else we could subtract? Well, we know that 10 fives are 50, so we could take away 10 lots of five at a time, take away 50s. But we could even go one better than this. What if we double the fact? If 10 fives are 50, 20 fives are worth double 50 or 100. If we take away 100, we’re going to get to the answer much quicker, aren’t we? So let’s try subtracting this partial quotient. And it might help us to consider what Ben’s thinking about at each step.

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.” And of course, 450 take away 100 leaves him with 350. Now he can look at 350 and think to himself, “Well, I can take away another lot of 25s.” 350 take away 100 is going to give him 250. And he’s still got enough to keep going. 250 take away 100 leaves him with 150. 150 take away 100 leaves him with 50. And now he can’t take away anymore chunks of 25s, can he? He’s only got 50 left. But Benjamin knows how many fives there are in 50. And if he takes away 10 lots of five, he’s going to arrive back at zero.

So by subtracting a part at a time, Benjamin split up the answer to this division calculation or the quotient into bits. He knows there are one, two, three, four lots of 25s and one lot of 10 fives. Now, how many fives is that altogether? Well, we know that four lots of 20 are worth 80. And if we add 10, we get the answer 90.

We’ve subtracted multiples of five to find the answer. This is called the partial quotient method. And we found we had to take away 90 lots of five to get back to zero. And that’s how we know 450 divided by five equals 90.

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