Pre Algebra Unit Conversion
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It's Time For a Change
Unit Conversion

 
 If you wanted to find out how many feet were in two yards you might say
 "Well let's see, there's 3 feet in one yard so there must be 6 feet in 2 yards." 
 That works just fine.
 
 But what if you wanted to find out how many inches there are in 2,500 miles. 
 Or find out how many feet per second there are in 55 miles per hour. 
 Then we need a better plan.
 
 Good news! We have one. 
 Here it is:
 
 Take another look at that 
 "How many feet are in 2 yards?" problem.
 
 We have 2 yards, and we want to have our answer in feet. 
 To get there, we need to do something very, very tricky.
 We need to multiply ...
 
 by 1.
 
 OK, OK, there really IS a trick. 
 The trick is the way we write the number 1 that we use to multiply.
 Any time we have a fraction 
 with the same amount on the top and the bottom 
 we have a fraction equal to 1 (except when that amount is zero). 
 
 Anyway, 
 if we have a fraction with 1 yard on the top and 1 yard on the bottom, 
 we have a fraction equal to 1:
 

 

 We also know that 1 yard is equal to 3 feet. 
 
 So instead of 1 yard, 
 we can write 3 feet for either the top part
 or the bottom part of our fraction 
 and we haven't changed anything. 
 
 Like this:
 

 

 THIS IS OUR BIG NEW TRICK ON THIS PAGE!

 
 The trick is the way we write the fraction that is equal to 1. 
 We write it with things that LOOK different on the top and the bottom, 
 but are actually worth the same amount.
 
 Now we have our new special name for 1. 
 We are ready to multiply the 2 yards:
 

 
 To make things even out, we can put a denominator of 1 under the 2 Yards.
 

 
 
 OK, We did it, but look! 
 What kind of a thing is "6 Yards x Feet" ???
 
 Who Knows! 
 
 And if we had to leave it looking like that 
 we wouldn't have anything too great. 
 
 But look! We have the word yards in the top 
 and the word yard (close enough) in the bottom part. 
 
 We can cancel them out.
 
 You're kidding!
 
 Nope! Works every time. 
 The only thing is that everything on top and everything on the bottom 
 must be multiplied. No addition or subtraction.
 
 So ...
 

 
 That means:
 

 2 Yards = 6 Feet

 
 Hey, we KNEW that 6 Feet was the answer all along. 
 So this is no shock.
 
 But let's go over exactly how we come up with the funny name for 1.
 
 The fraction gets units that are what we have to begin with 
 and what we want to end up with. 
 
 We had yards and wanted to get to feet. 
 We know we want feet for 1 number and yards for the other. 
 
 Which gets which?
 
 Do we want:
 

 
 Here's the deal. 
 Put the units you want on top and the units you have on the bottom.
 
 The units you have go on the bottom so you can cancel them!
 
 We had yards to begin with, so the one we want is:
 

 
 Try another one ...
 
 Example:
 
 Suppose we're really bored and want to find out 
 how many feet there are in 2500 miles. 
 You look up (or maybe you know) that there are 5,280 feet in a mile. 
 
 That is:
 

 5,280 Feet = 1 Mile

 
 Since these 2 things are worth the same amount, 
 we can use them in a fraction as our names for 1.
 We have miles and want feet, 
 so miles goes on the bottom and feet goes on the top:
 

 
 Now we multiply 2500 miles by this fraction that's equal to 1. 
 So everybody has a denominator, we put a 1 under the 2500 miles 
 (a calculator really helps here):
 

 
 Since we have miles on the top  and mile on the bottom, 
 and everything is multiplied, 
 we can get rid of them.
 

 
 Hey that's a lot of feet!
 
 OK, One more and we're done.
 
 Example:
 
 Tennessee Ernie Ford asks you to change 16 tons to ounces.
 
 If you look in a reference book, you will find that:
 

 1 ton = 2000 pounds

 
 You will also find that
 

 1 pound = 16 ounces

 
 But you probably won't find how many ounces are in a ton.
 
 So here's the plan. 
 First we change 16 tons to some number of pounds.
 Then we change that number of pounds to ounces.
 
 Ready? 
 OK, we have 16 tons and want pounds.
 That means pounds goes on the top and ounces goes on the bottom.
 2,000 Pounds = 1 Ton.
 

 
 We have Tons on the top and Ton on the bottom. 
 Everything is multiplied. 
 So we can cancel tons of stuff. (he he he ... OK, it wasn't funny)
 

 
 One part down and one to go. 
 Now we have pounds and want ounces.
 So 16 Ounces goes on top and 1 Pound goes on the bottom.
 1 Pound = 16 Ounces. 
 

 
 We have Pounds on the top and Pounds on the bottom. 
 Everything is multiplied. 
 We can cancel the Pounds.
 

 

   copyright 2005 Bruce Kirkpatrick

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