Math 6A( Periods 1 & 2)

Rates 5-3

A RATE is a ratio of two quantities using different units!  

A UNIT RATE compares a quantity to one unit of another quantity

For example, you pay $27 for 3 pizzas.  The UNIT RATE is $ 9 : 1 pizza

Notice there are LABELS!  LABELS are essential when describing all rates!

Some well know unit rates: Miles Per Hour (MPH, Miles Per Gallon ( MPG), Revolutions Per Minute (RPM) or Revolutions Per Second ( RPS) and  Heartbeats per minute. Do you know any?

 Equivalent rates have the same  UNIT RATE

Rate  a units: b units     Unit Rate: a units : 1 unit
                                    b

A double number line can show the rate at which you earn points for hitting notes in a music video game.  Write a rate that represents this situation.

Rate: 600 points for 4 notes or 300 points for 2 notes or 450 points for 3 notes or 750 points for 5 notes.

150 points for every note would be the unit rate!

Finding UNIT RATE

A piece of space junk travels 5 miles in 8 seconds. How far does it travel per second?

You can set up a Ratio table to see

Distance ( mi)	5	5/8
Time ( seconds)	8	1

          

It travels 5/8 mile PER second

Notice the TIME must be 1 second!

Japanese Bullet Train traveled 558 miles in 3 hours. How far did it travel every hour?

Again, you can set up the RATIO Table

Distance ( miles)	558	558/3
Time ( Hours)	3	1

 Really do the division, carefully!                                                                             

Did you check to see if it was divisible by 3—BEFORE you began?

Chef has 6 pounds of salmon fillet for $51.00. How much will the chef pay for 9 MORE pounds of salmon?

Think: Will UNIT RATE help me find the solutions?

Cost $	51	8.50	76.50
Salmon ( lb)	6	1	9

 $76.50 for 9 more pounds of salmon
Show your division     What is the next step here:   

Could you have done it a different way?  Hmmm… 51 and 6 are both divisible by 3. Would that help?

Cost $	51	25.50	76.50
Salmon ( lb)	6	3	9

   SAME Result:  $76.50 for 9 more pounds of salmon     

Two pounds of Ahi for $ 16.00 What is the cost for 7 lbs of Ahi?

Because 16 is easily divided into pieces, you might want to use a double number line

                        

Several ways to think about this problem! Unit rate is just one of them!

7 is halfway between 6 and 8 (You can visualize that with the number line) … so What value is halfway between 48 and 64?      

The cost is $56.00 for 7 pounds of Ahi.