Maps with Fractional Distances

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  • 0:01 A Map
  • 1:11 Fractional Distances
  • 1:40 Find the Missing Distance
  • 5:50 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to solve map problems involving fractions. Learn how to use the information that is given to you to find missing distances as well as the total distance.

A Map

In this lesson, we'll talk about solving map problems where the maps show the distances in fractions. Let's see how this skill can be used in the real world.

Imagine that you are the air controller for an airport. Your job is to make sure that your pilots flying your airplanes all make it safely to your airport and to all their other destinations. You're in touch with the air controllers at the airports in the other cities. You have a map in front of you that shows you the distances to each of the airports. Your pilots and pilots from other airports will call in and ask you for various distances from one place to another.

The map that you have allows you to find that information and give them a correct answer so that they know exactly how far they need to go to reach their destinations. When you get a call, the pilot will give you the names of the cities that he needs to travel to, so when you are looking at your map, you focus your attention on just these cities and the routes between them.

Uh-oh. Here comes an incoming call. It's Pilot Bob. He is flying from Southgate to Middleton and then to Hightown. The part of the map that you are concerned with might look something like this.

maps fractions

Fractional Distances

Instead of whole numbers, though, this map uses fractions. Fractions are numbers made up of one integer divided by another integer. So, instead of seeing your distances in numbers, such as 333.33 miles or 291.67 miles, you see your distances as fractions, such as 1000/3 miles or 875/3 miles. Let's check back with Pilot Bob now and see what his question is all about.

maps fractions

Find the Missing Distance

Pilot Bob's question has to do with the distance between Middleton and Hightown. Pilot Bob knows the distance from Southgate to Middleton because he flies between these two cities all the time. But this is his first time flying from Middleton to Hightown, so he doesn't know exactly how far Hightown is from Middleton. He does know the total distance he needs to fly since that is listed on his flight chart. His question to you is how far is Hightown from Middleton if the total distance from Southgate to Hightown is 625 miles?

maps fractions

For Pilot Bob, your problem map shows the distance from Southgate to Middleton but not from Middleton to Hightown. You know the total distance from Southgate to Hightown is 625 miles. So, how do you go about solving this kind of problem?

What you need to do here is to write out your problem in math language. For this, you know that to find the total distance between two points, you need to add all the distances in between. So, you need to add the distance between Southgate and Middleton and the distance between Middleton and Hightown to get your total distance. If you use x to represent the unknown distance between Middleton and Hightown, your math problem will be 1000/3 + x = 625.

To solve this kind of problem, you see that this is an addition problem that you can solve by performing the opposite operation. You see that your variable is being added to a number, so to solve it, you subtract this number from both sides of the equation. You get 1000/3 + x - 1000/3 = 625 - 1000/3.

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