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.
