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In this section we'll help you understand how to deal with ratios.
A fraction is also known as a ratio.  For example, 3/4 is also the ratio of 3 to 4.  Any statement (or equation) that says two ratios are equal is called a proportion.  An important thing to remember when dealing with equal ratios is illustrated below.

3   15                   4 * 15
- = --  Cross multiply.  
4   20                   3 * 20


4 * 15 = 3 * 20
    60 = 60

You can solve for unknowns in proportions by using that process.

             4   21
1.   Solve:  - = --
             m   5
         
  Solution: Set the cross products equal.


            4 * 5 = 21m


            Finish the problem by dividing both sides
            by 21.

 
            20
            -- = m
            21

 

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Many times, you use ratios to make solving word problems easier.  Many times, you are expected to gather information from the problem that is not directly stated in words.  Gathering this information is called inferring.  This section will help you better understand how to infer information from a word problem and solve using ratios.

If you are told there is a ratio of red marbles to blue marbles that equals 5:7 you are also told about two other ratios!  You know there are 12 total marbles (5 + 7 = 12), so you know the ratio of red marbles to total marbles must be 5:12 and the ratio of blue marbles to total marbles must be 7:12.  Also, it is usually helpful to write all these statements and then reread the problem to find any more information and to better understand the problem.

1. Problem:   The ratio of red marbles to blue marbles is 5 to 7.
              If there are 156 marbles total, how many red marbles
              are there?
      

  Solution:   Write down the information given and inferred.


              R = 5
              B = 7
              T = 12


              With this information, there are three different
              proportions you can write.


              R   5    R   5     B   7
              - = -    - = --    - = --
              B   7    T   12    T   12


              The problem asks about red marbles and total marbles,
              so we will use the second proportion and replace the
              variable T with 156.


                R    5
               --- = -- -> 12 * R = 5 * 156 -> R = 65
               156   12