### Video Transcript

We want to divide 6025 by 241 using
the standard division algorithm. This question has six parts. And weβll take each part in turn,
beginning with βwhat result do you expect?β a) Around two, b) around three, c)
around 30, d) around 200, or e) around 3000.

Our first step requires us to do
some estimating. We can round 6025 down to 6000 and
we can round 241 down to 200. We do this because weβre rounding
to the hundreds place. To the right of the hundreds place,
the tens place, thereβs a four. This is less than five, which means
we would round this number down. When we were dealing with 6025, we
rounded to the nearest 1000. And we looked to the right of the
thousands place to the hundreds, where there was a zero, indicating that we should
round down.

And now, we need to consider
dividing 6000 by 200. We know that 200 is 100 times
two. We could divide 6000 by 100 which
is 60. We then take that 60 and divide it
by two, which gives us 30. And that tells us we can expect a
result for 6025 divided by 241 of around 30. Now that we have a good estimate,
we can move on to the second part.

The diagram below shows the first
stage of the division algorithm. The digit π, between one and nine,
represents how many 241s there are in 602 tens. What is the place value of π in
the quotient?

First, letβs think about the place
value. Underneath the division bar, we
have 6025. The digit six is in the thousands
place. There are zero hundreds, two tens,
and five ones. And our divisor 241 has a two in
the hundreds place, a four in the tens place, and a one in the ones place. Now, when we use the standard
algorithm, we line up the quotient with its place value thatβs underneath it. In our problem, the dividend 6025
has an π above the tens place. Since our question asked what is
the place value of π in the quotient, we can say that π is in the tens place.

The next part of our question wants
to know what is the value of π.

Weβve already said that π is in
the tens place. This π is answering the question,
how many times does 241 go in to 602 tens? It can be helpful to remember that
this means weβre looking for a value of π that multiplies by 241 and gets us as
close to 602 as possible without going over that amount. We could try three because 200
times three equals 600 and that seems pretty close. But remember, we also have four
tens and 40 times three is 120. And, of course, one times three is
three.

When we add up these three values,
we get 723. It also means that 241 times three
is greater than 602. And therefore, π cannot be
three. And so, we need to try again with
the smaller π value. We can try two. 200 times two equals 400. 40 times two equals 80 and one
times two equals two. When we add those together, we get
482. And we can say that 241 times two
is a less than 602. Since there are no whole numbers
between two and three, the value of π must be two.

Since we found that there are two
241s in 602, π equals two, or 241 times two tens in 602 tens. The number π is two times 241
tens. Which of the following is true? a)
π equals two times 241, b) π equals two times 241 plus 10, c) π equals two times
241 minus 10, d) π equals two times 241 times 10, or e) π equals two times 241
times 100.

Letβs go back to the beginning when
we were thinking about place value underneath this division bar. We have thousands, hundreds, tens,
ones. And we said that the π value, the
value above the tens place, was tens. After which, we found out that π
equals two. In the same way that order matters
above the division bar, it also matters underneath. The value π is in the tens
place. We find π by multiplying two times
241. We did that on the previous slide,
and we got 482. But we know that this is 482
tens. 482 tens equals 482 times 10. And we know that we could find 482
by multiplying two times 241. And so, we can say that π equals
two times 241 times 10, which is option d in the answer choices.

The number π is the remainder of
the previous division. Which of the following is true? a)
6025 equals two times 241 plus π, b) 6025 equals two times 241 minus π, c) 6025
equals 20 times 241 plus π, d) 6025 equals 20 times 241 minus π, or e) 6025 equals
200 times 241 plus π.

We know that π is the remainder
from the previous division. So letβs focus on whatβs happening
here. 6025 minus 4820 equals π. If we take away 4820 from 6025, we
get π. And that also means that if we add
4820 and π together, we would get 6025. And all five of our answer choices
are in the form 6025 is equal to something. In our previous stage, we wrote
4820 as 482 tens. And we said that 482 tens was equal
to two times 241 times 10. And that means we can say 6025 is
equal to two times 241 times 10 plus π. That looks in some way similar to
answer choice a, but itβs missing the times 10. So thatβs not an option.

Answer choice b and d are
subtracting π. Those arenβt options. What we need to do is try to
regroup this two times 10. We know that two times 10 equals
20. And so, 20 times 241 plus π should
be equal to 6025. And we can say that 6025 equals 20
times 241 plus π.

The diagram below shows the second
stage of the division algorithm. The number π is between one and
nine and represents the number of 241s in 1205. What are the values of π, π, and
π?

To find π, we want to know how
many times does 241 go into 1205. As we did in stage one, weβre
trying to figure out what multiplied by 241 will be as close to 1205 as possible
without going over. I know that 200 times five is 1000
and 40 times five equals 200. One times five equals five, which
tells me that 241 times five is exactly 1205, which means π must be equal to
five.

If we plug five in for π, we then
need to multiply five times 241, which weβve already done over here. That value is substituted in for
π. Five times 241 is 1205, which means
π equals 1205. And π is what we get when we
subtract 1205 from 1205. The remainder is zero. π is equal to zero. We found that 6025 divided by 241
equals 25.

Our final question was asking the
values of π, π, and π, which we found π equals five, π equals 1205, and π
equals zero.