MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Ratios can be used to understand scaled maps. Set up a ratio using the given scale. Use this given ratio to find the actual or scale distance on a map.
One of the most common places you see ratios in real life is on scaled maps. Anyone whose read a map has seen the little scale on the corner where they do like a little line like this and they break it up and say how much is one mile or how much is 10 miles or whatever. That's what this problem's about. On a scaled map, 2 inches represent 1000 miles. If you measure that the distance on the map from San Francisco to New York is 5 ½ inches, how many miles apart are the two cities?
One thing to keep in mind is that any time you use a scaled map you're probably going to be doing an approximation so whatever answer I get for this problem is probably not going to be exact, but you can still use these kinds of techniques to get a good approximation. I'm going to write a ratio like this; 1000 miles to 2 inches. You could also write it as a fraction, or using the word to. If you want to you could reduce this fraction. I personally like to use reduced fractions whenever possible. It's the same thing as 500 over 1 or like with this ratio I could write 500:1 or 500 to 1. What that means is that 1 inch represents 500 miles. And that makes sense. I've kind of cut both of these in half. If 2 inches is 1000 miles, then 1 inch would be 500 miles.
Okay once I have a ratio that makes sense in my brain I can answer this question. If I measure the distance is 5½ inches how many miles apart are the two cities? So what I'm going to want to do is do 5½ times 500, because 500 represents how many miles there are in my inches number. It used to be 1 but now it's 5½ . I'm like multiplying by 5½. So 500 times 5½, you can do it on your calculator or if you want to do it out by hand either way should be fine. You get the answer 2750 miles.
Whenever you're doing math word problems, be sure to pause and make sure your answer makes sense, like think about what you know in the real world. I personally live in San Francisco and I know it's about 400 miles, 300 miles to LA so if I want to think about that in relation to the whole continent all the way across to New York City, that answer makes sense based on what I know about the real world. That's always a good strategy when you have word problems. You want to come to your final answer and just make sure that the answer actually makes sense in the real world.
