scale drawings and models: if 5 cm = 2 km, find km for 10 cm

[krgarrett]

I am working on Scale Drawings and Models I do not understand it. The problem is 5 centimeters = 2 kilometers. Find the missing distances. If the map distance is 10cm how do I find the actual distance? How do I set the problem up?

 

[fasteddie65]

Re: Pre-Algebra

"5 centimeters = 2 kilometers. Find the missing distances. If the map distance is 10cm how do I find the actual distance? How do I set the problem up?"

Use a proportion: 5 cm: 2 km = 10 cm: x km

2 • 10 = 5 • x
20 = 5x
4 = x

The actual distance is 4 km.

Think about this: If the map distance is doubled (5 cm to 10 cm), wouldn't the actual distance also be doubled? 2 km to ?

 

[chivox]

Re: Pre-Algebra

Although there are many times when students think cross-multiplying is the way to solve anything, this is one time when it is actually the right thing to do. Any time with a map legend, krgarrett, set up the proportion like this:

5 cm is to 2 km (from the legend), written 5/2

as 10 cm is to ? km (from your measurement), which is unknown (to you, anyway) written 10/?.

Make sure you put cm on the top both times, set those two fractions equal to each other, and cross-multiply to figure out the unknown distance:

\(\displaystyle \frac{5}{2} = \frac{10}{?}\)

Cross-multiply:

(5) (?) = 20

Now, what number times 5 gives you 20? Does this remind you of writing equivalent fractions from your younger days?

? = 4

With legends on maps, this actually works, as long as you think of it correctly. Just remember cm over kilometers in the legend, cm over kilometers in the measurement. Don't get sloppy.