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## Comparing with multiplication

Current time:0:00Total duration:6:35

# Comparing with multiplication and addition: money

CCSS.Math:

## Video transcript

So we're told that Minli
has $5.00 more than James. Minli has $33.00. How much does James have? So let's use some letters to
represent the amount of money Minli has and the amount
of money James has. So let's say that m
represents the amount of money that Minli has. And j represents the
amount that James has. So we're told that Minli
has $5.00 more than James. So Minli's money, or the
amount of money Minli has, is going to be equal
to the amount of money James has plus 5. Start with the amount James has. Add 5, you have Minli's. Minli has $5.00 more than James. Now they tell us,
Minli has $33.00. So let me write this down. So we know that m is equal to--
so this the sentence right here tells us, this right here tells
us, that m is equal to $33.00. So instead of an m
here, we could say, well $33.00 is equal to the
amount of money James has plus 5. And so now we just
need to think about how much money does James have. And I encourage you
to pause the video and think about it on your own. Well, one way to visualize
this is maybe on a number line. So let me draw a number
line right over here. And let's say this is 0. This is the amount that
Minli has right up here. So Minli has $33.00. That represents that
point right over here. And j is the amount
the James has. So let's say that this
is j right over here. And we know that if we add 5
to j-- if you take j, add 5, you get to 33. Well how can I go to 33? How can I start
with m or how can I start with the amount
Minli has and then end up with the amount James has? Well, I could just go
the other way around. I could start with m,
and I could subtract 5. So we could say that 33, which
is m, the amount of money Minli has, minus 5, is
equal to the amount of money that James has. So how much money
does James have? Well, 33 minus 5
is going to be 28. So we can say that James
has, 28 is equal to j, or James has $28.00. So this right over here is 28. And you see that. 28 plus 5 is 33. 33 is 5 more than 28. So this all works out. Now let's think about
this next question. Jessica's house
is 5 times as far from school as Paulette's house. Jessica's house is
15 miles from school. How far is Paulette's
house from the school? So just like we did, let's just
look at each of these sentences and see what they're telling us. And I encourage you to
define use of letters to represent the distance
Jessica's house from school and Paulette's
house from school. And try to figure
this out on your own. Pause the video
right now, and try to figure it out on your own. So you could imagine j might
be a good letter for Jessica's, the distance from
Jessica's house to school. And let's say that p we'll
use for Paulette's house from school. So we're told that, however
far Paulette's house is from school, you
take 5 times that to see how far Jessica's
house is from school. So we could write that p, which
is how far Paulette's house is from school, times 5, is equal
to how far Jessica's house is from school. Jessica's house is 5
times as far from school as Paulette's house. p is
Paulette's house's distance from school. j is Jessica's house's
distance from school. They then tell us that Jessica's
house is 15 miles from school. So they're essentially telling
us, this sentence right over here, they're telling
us that j is equal to 15. So we can rewrite this as
the distance Paulette's house is from school times
5, which we know to be Jessica's
distance from school, or Jessica's house's
distance from school, which we now know to be 15,
is going to be equal to 15. So what would p be? Some number times 5 is
going to be equal to 15. Some number of miles times
5 is equal to 15 miles. Well, you might already
be able to think about this in your head, but
we could also visualize it. So let's draw a
number line again. And if you start
with that number, p-- so this is Paulette's
distance from school so, p-- and you multiply it by 5. So that's times 1, times 2,
times 3, times 4, times 5. So notice this is p, this
distance is p right over here, this is another p
right over here, this is another p
right over here, that's another p
right over there, and another p right over there. Or another way of
thinking about it, this whole distance
right over here is going to be p plus p plus
p plus p plus p, or p times 5. And that's equal to how
far Jessica is from school, or Jessica's house
is from school. So this right over
here is equal to 15, which is the same thing as j. So how would you figure it out? Well, if 5 times
p is equal to 15-- if I want to figure
out what p is, I could just divide 15
into 5 equal groups. So we could say that
p is equal to 15 divided into 5 equal groups. If you take 15 miles and
divide it into 5 equal groups, you're going to end up with p. So what is this? Well, we get p, 15
divided by 5 is 3. So Paulette lives 3
miles from school. And you see that. This is a 3, another 3,
another 3, plus another 3, and another 3. 3 time 5 is 15. Jessica's house, which
is 15 miles from school, is 5 times as far from
school as Paulette's house, which is 3 miles from school
so it all makes sense.