On a map, one centimeter represents 500 meters. What is the distance represented by 10 centimeters?
This statement, one centimeter represents 500 meters, gives us the map scale. The scale of the map is the ratio of a distance on the map corresponding to the distance on the ground. The ratio of map to ground, one centimeter on our map equals 500 meters on the ground, 500 meters in real life. If our map shows a distance of 10 centimeters, how far is that in real life?
I know that each dash represents one centimeter. And that would be 500 meters. Every time we go one centimeter on our map, we would add 500 more meters. And we would need to do that 10 times. But there’s actually a better way. We want to set up a proportion.
For every one centimeter, it’s 500 meters. And that would be equal to 10 centimeters over how much? How would we go from one centimeter to 10 centimeters? We would multiply by 10. One times 10 equals 10.
If we want to keep our ratios the same, if we want equivalent fractions, that means, if we multiply by 10 in the numerator, we need to multiply by 10 in the denominator. We need to multiply 500 meters times 10. 500 meters times 10 equals 5000 meters. And that means, 10 centimeters on our map equals 5000 meters on the ground.