Video Transcript
A map of Egypt was drawn at a scale
of one to 340,000. A second map was drawn at a scale
of one to 160,000. The distance between two cities on
the first map is 16 centimeters. What is the distance between the
same two cities on the second map?
But what we know is our first map
has a scale of one to 340,000. And we know that the distance on
the first map is 16 centimeters between the two cities. What we can see is that if we
multiply one by 16, that gives us our 16. And that’s because our scale means
that one centimeter on the map is worth 340,000 centimeters in real life. And we could use a calculator to
work this out. So we get 340,000 multiplied by 16,
which would give us 5,440,000, and that’s centimeters.
We could’ve also worked it out with
a written method. That’s by multiplying 16 and 34,
which would’ve given us 544. Then we’d see that we’d have one,
two, three, four zeros out on the end, which would give us our 5,440,000
centimeters. Okay, so what would we do now? Well, in usual questions like this,
what we would do is convert this into something that makes more sense, like
kilometers. However, as we’re gonna transfer
onto the second map, I’m gonna keep things in centimeters. We won’t change here what the units
are in.
Well, with the second map, we know
the scale is one to 160,000. So we know one centimeter on the
map is worth 160,000 centimeters in real life. Well, we know the distance between
the two cities in real life is 5,440,000 centimeters. So we’ve got to see how would we
get there from 160,000. Well, in fact, we’d multiply by
34. If we take a look at the first map,
we can see that because we’ve actually got numbers 34, 16, and 544 all involved with
the calculations over there.
However, if we couldn’t work that
out from the first map, what we could’ve done is use the bus stop method for short
division. And we can see that 16 goes into
544 34 times. So therefore, 160,000 goes into
5,440,000 34 times. So therefore, if we do this for the
first part of our scale multiplied by 34, we’re gonna get 34 centimeters. So therefore, we can say that the
distance between two cities on the second map is 34 centimeters.
