Ratios

• Expresses a part-part relationship or a part-whole relationship.
• If there are only two parts in the whole, you can derive a part-whole ratio from a part-part ratio and vice versa.
• If two quantities have a constant ratio, they are in direct proportion to each other.
• Always write units on either ratio itself or the variables you create, or both.
• Simple ratio problems:
  1) Set up a proportion
  2) Cross multiply to solve
  Note that you can cancel factors either vertically within a fraction or horizontally across an equals sign, but never diagonally across an equals sign.
• Unknown Multiplier
  M/W which is 3/4 becomes 3x/4x which cancel out
  M + W becomes 3x+4x
  Can be used once per problem, you can never have two unknown multipliers in a problem.
  Should be used when neither quantity in the ratio is already equal to a number or a variable expression.
• You can multiply each ratio to make a common term in order to combine ratios.