ratio, proportion, and variation

ratio, proportion, and variation

1. ratio

   • is a quotient of two quantities.
     • the ratio of the number a to the number b is written:
       • a to b, a/b or a:b
       • when ratios are used in comparing units of measure the units should be the same

2. proportion

   • is a statement that says that two ratios are equal
     • for example:
       • 3/4 = 15/20
     • cross products
       • if a/b = c/d then the cross product ad and bc are equal

3. variation

   • direct variation
     • y varies directly as x, or is directly prportional to x
       • direct variation as a power
         • y varies directly as the nth power of x
           • if there exists a nonzero real number k such that y= kxn
   • inverse variation
     • y varies inversely as x if there exists a nonzero real number such that
       • y= k/x or xy=k
   • to solve a variation problem
     • 1 write the variation equations
       • 2 substitude the initial values and solve for k
         • 3 rewrite the variation equation with the value of k from step two
           • 4 substitude the remaining values, solve the unknown, and find the requiered answer