We saw yesterday that a quantity is made up of a number and a unit of measure, e.g., 5 fingers, 3 pens, two meters, 8 kilograms. A rate relates one quantity with another quantity. For example, 2 pounds of potatoes costs 99 cents, a gorilla can eat 500 pounds of grass in one day, $1.69 will get you one Big Mac. Rates can be expressed by dividing one quantity by the other the other quantity.
- 12 pencils/ box
- 2 pounds/99 cents
- 50 miles/ 2 hours
- 3 dollars/ 6 Snickers
A unitary rate is a rate where the denominator is one. If a unit does not have a number before it, it is understood that the number is one. "Per" is a word that means the same thing as the "division sign."
- 25 miles/hour
- 50 cents/1 Snicker
- 48.5 cents/pound
- 2 cents per gallon
If you know the rate that can tell you how much per one of any quantity, then you can calculate how much per any multiple of that one quantity.
- List every rate in the following problem, but do not solve the problem: Mike has read in a book on health that he should drink eight glasses of water a day, this equals 1/2 gallon. He has decided that he will try it. The water in his neighborhood is taken from a source that Mike's mother, who is 43 years old, is polluted so she buy water. How many gallons of water each week will she be sure to buy just for Mike alone?
- Write down three ways of saying "25 cents for one apple."
- Express the following as unitary rates: 48 players/6 teams, 75 pills/5 bottles, 3 T-shirts/$8, 1 pack/30 matches.
- How much for a dozen soccer balls if they are sold at $19 per ball?
- What is the number of woofs if you have seven glops and there are six woofs per glop?
- How many miles does Jim travel if he averages 60 miles a day for 5 days?
- Break up into groups of four and determine the thickness of a page of one of your books using your knowledge of rates. Use a ruler to measure the thickness of 30, 55, and 70 pages. Reduce each of these rates to the equivalent unitary rate. Average all three of the rates to obtain the answer.