Ratio, Rate, Unit Rate and the Proportion Equation

A ratio is a comparison of two numbers. This means two numbers are selected and placed together in comparison, for example, to compare 2 chairs with 3 books, write it as a ratio:

2 chairs
3 books
2 chairs:3 books
2 chairs to 3 books

Notice the three forms. The most common form is the one that looks like a fraction. Ratios look like fractions and they can be changed just like fractions.

Unlike proper fractions, ratios can be written either way - as long as you label them properly!

3 books
2 chairs
3 books:2 chairs
3 books to 2 chairs

There is a kind of ratio called a rate.

ratio
  • rate. A rate is a comparison of two measures, for example, some cars can travel 500 miles on 20 gallons of gasoline.

    500 miles
    20 gallons
    500 miles:20 gallons
    500 miles to 20 gallons

    Other examples might be 10 pounds of potatoes for $2.50 or $90.00 for 6 hours of work.
    There is a kind of rate called a unit rate.

    • unit rate. A unit rate, like a rate, is a comparison of two measures except, one of the measures is always a one, or a unit.

      To change a rate to a unit rate, divide one measure by the other, but play close attention to the labels.

      500 miles
      20 gallons
      becomes
      25 miles/1 gallon
      10 pounds of potatoes
      for $2.50
      becomes
      4 lbs/$1.00
      $90.00 for
      6 hours of work
      becomes
      $15.00/1 hour

      or

      20 gallons
      500 miles
      becomes
      0.04 miles/gallon
      $2.50 for
      10 pounds of potatoes
      becomes
      $0.25/1 lb
      6 hours of work
      for $90.00
      becomes
      0.0666 hours/$1.00

      Enter the first quantity:   Enter the second quantity:
      Divide the first quantity by the second:

        
      Pay special attention to the placement of the UNITS!