Ratio, Proportion and Variation

Ratio, Proportion and Variation

1. Ratio

   • Is a quotient of two quotients
   • Example
     • The ration 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
   • Unit Pricing
     • Application
       • Ratios can be applied in Unit pricing, to see which size of the of an item offered in different sizes produces the best prize per unit
     • To do this...
       • Set up the radio of the price of the item, to the number of units on the label. Then divide to obtain the price per unit

2. Proportion

   • Is a statement that says that two ratios are equal
   • Example
     • a/b = c/d ( b,d =/= 0)
       • 3/4 = 15/20
         • a, b, c and d are the terms of the proportion
       • a, b, c and d are the terms of the proportion
         • a and d are called extremers b and c are called means
         • We read the proportion a/b = c/d as a is to b and c is to d, Multiplying each side of this proportion by the common denominator, bs gives
           • Example
             • bd . a/b = a/b . bd
         • We can also find the products ad and bc, by multiplying diagonally. This is called cross products
           • Cross Products
             • If a/b = c/d, the the cross product ad and bc are equal

3. Variation

   • Direct Variation
     • y varies directly to x, or y directly proportional to x, if there exist a non-zero constant k such that
       • y = kx, or equivalently y/x = k
       • The constant k is a numerical value call, the constant of variation
     • Direction Variation as a Power
       • In some cases, one quantity will vary directly as a power of another
         • y varies directly as the nth power directly of x, if there exists a nonzero real number k such that
           • y = kx (n)
   • Indirect Variation
     • y varies inversly as x, if there exists a non-zero real number k such that
       • y= k/x or equivalently xy= k
     • Also y varies inversly as the nth power of x, if there exists a nonzero real number k such that
       • y= k/x(n)