Pre Algebra Ratios and Proportions
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Ratios and Proportions

 
 Sometimes we write fractions in a different way. 
 Instead of drawing a line, we use two dots. 
 We get something like this:
 

 
 But it still means exactly the same thing:
 

 
 The difference is, 
 we usually use the line when we have one thing 
 that is chopped up into pieces. 
 Like a pizza. 
 
 We use the 2 dots (called a colon) when we are talking about 
 some of the members of a group
 or comparing two different things.
 
  The 2 dots way of writing things is sometimes called a ratio and sometimes called a proportion. But it is NEVER called a fraction.
 
 Example:
 
 Say that there are 10 people in a math class. 
 3 of them got A's on the last test. 
 So we say "3 out of 10 got A's on the test." 
 We would write this as: 

 3:10

 
 More Examples:
 

 3 out of 9 players on the team are over 6 feet tall. 

 

 3:9

 
 2 out of 3 kids in the family go to Jefferson Middle School.
 

 2:3

 
 Remember, the part on the right is the whole thing.
 We could have said that last one as:
 
 2 out kids in the family go to Jefferson Middle School.
 The other kid in the family is too young for school.
 
 It is the same problem,
 but you have to figure out how many kids are in the family.
 
 There is one way these things work just like fractions. 
 We can reduce them the same way.
 
 Example:
 
 Say we had this ...
 
 4 out of 10 people in the class are boys:
 

 4:10

 
 Can we show the same ratio with smaller numbers?
 
 Let's see ...
 
 First, find the prime factors of 4 and 10:
 

 
 So we can write our ratio like this:
 

 2 2 : 2 5

 
 If everything is multiplied together on each side (it is).
 If the same number shows up on both sides (it does).
 We can change them both to 1's just like we did with fractions.
 

 
 Try another one ...
 
 Example:
 
 Three of twelve:
 

 

   copyright 2005 Bruce Kirkpatrick

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