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Studying for a test? Prepare with these 6 lessons on Module 1: Properties of multiplication and division and solving problems with units of 2–5 and 10.

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# 2-step estimation problem: marbles

Video transcript

Bill has 198 marbles
in this collection. He then buys another 44. A year later, he decides he
has had enough of marbles and decides to split them
as evenly as possible between the other 31
students in his math class. Roughly how many marbles will
each of his classmates get? And the fact that we
have the word "roughly" here means we don't need
to get the exact answer. If it said roughly
or estimate how many marbles each of his classmates
will get, that says, hey, maybe we can round these
numbers a little bit to make our calculations
a little bit easier. So let's give a go at that. So we start with 198 marbles. Well, let's round everything
to the nearest ten, and maybe that'll
simplify things. So 198, if we were to round
it to the nearest ten, well, we'd want to
look at the ones place. The ones place we have an 8. If you have a ones place
that's 5 or greater, then you're going to
round up, if you're going to round to
the nearest ten. So the nearest ten, if you round
up from 198 is actually 200. We'll just go up to 200. That's also the nearest hundred. So this is approximately
equal to 200. And this little
squiggly equal sign, that means roughly equal to
or approximately equal to. And so this is what
he starts off with. Then he buys another 44. 44 is approximately equal to--
if we round to the nearest ten, we look at our ones place. It's less than 5, so we're going
to round to the ten below 44. The ten below 44 is 40. If we go to the nearest
ten going down, we get 240. So how many total
marbles did he have before he distributes them? Well, if we take our two rough
estimates and if we add them, 200 plus 40-- he has roughly
240 marbles before he distributes them. Now, how many
students is he going to distribute them between? Well, there's a
total of 31 students. There's 31 students, but
once again, let's round this. If we round this
to the nearest ten we're going to round down,
because our ones place has a 1 in it. It's less than 5. So we're going to round
to the ten below 31. So that is going to be 30. So if you have
roughly 240 marbles and you're going to distribute
them amongst roughly 30 folks, then how many are each
of them going to get? Well, each of them are going
to get 240 divided by 30. Once again this is just a rough
estimate-- roughly 240 marbles divided by 30 folks. Well, what's 240 divided by 30? Well, if we say that this
is equal to the marbles per student, so let's say
that this is M-- M for marbles per student-- this is another
way of saying that M times 30 is equal to 240, or that
240 is equal to M times 30. Let me write it that way. So that's the same
thing as saying that 240 is equal
to M times 30, where M is what we're
trying to figure out-- the rough number of
marbles per student. So let's think about what M is. And there's a bunch of
ways we could do it. We could just look at our
multiples of 30, so 30, 60, 90. Notice, this is very similar
taking to multiples of 3, but we just have a 0 now. The multiples of 3 are
now in the tens place, and now we have a 0
in the ones place. 90, 120, which is just a 12
with a 0, 150, 180, 210, 240, so what is this? This is 30 times one, two,
three, four, five, six, seven, eight. So we know that 240 is
equal to 30 times 8. So we could write 240 is
equal to-- and 30 times 8 is the same thing as 8 times
30, is equal to 8 times 30. Or another way we could say
it is the number of marbles each of his friends is
going to get is roughly 8. So this is going to be 8. So each of his classmates is
going to get roughly 8 marbles. Once again, this is an estimate. It's not an exact answer. Now, you might have tried to get
a slightly more precise answer. If you didn't want
to round 198 and 44, you could have
just added the two. 8 plus 4 is 12, and then
1 plus 9 plus 4 is 14. 1 plus 1 is 2. So the exact number
of marbles he had was 242, which is
pretty close to 240. So 240 was a good approximation. And then when you divide
that by-- dividing it by 31 is a bit of a pain, and
luckily we can just estimate. So we divided by
30, and we got 8. And just as another kind
of aside here, notice, 24 divided by 3 is equal to 8. And if you divide 240 divided
by 30, this is also equal to 8. So if you divide something
10 times as large by something 10 times
as large, you're still going to get
the same value. But either way, each
of his classmates are going to get
roughly 8 marbles.