1. Ratio and Rates Coordinate Algebra

2. Ratio A ratio is a comparison of two numbers by division

3. Example of a ratio 4949 25 to 10

4. Unit Rate Any ratio can be converted into a unit ratio by dividing the numerator and the denominator by the denominator A unit rate is a ratio that has a denominator of 1. A unit rate is also called a unit ratio (they mean the same thing). A = A÷B = A÷B B B÷B 1

5. Express each ratio as a unit rate $250 for 5 concert tickets A.$ 55 per ticketC. $50 per ticket B.250 per ticket D. 2500 per ticket 5 50 What do you think is the answer?? Option B is how we calculate the answer but it’s not expressed as a unit rate (remember unit rate is a ratio that has a denominator of 1). Our Answer

6. Example On a farm, there are 6 cows for every 3 pigs. What is the ratio of cows to pigs as a unit rate? (cows per pig) Cows : Pigs = 6 : 3 6 = 6 ÷ 3 = 2 3 3÷3 1 Remember unit rate needs to have a denominator of 1 Now what about this…? What is the ratio of pigs to cows as a unit rate? (pigs per cow) Pigs : Cows= 3 : 6 3 = 3 ÷ 6 = 0.5 6 6÷6 1

7. Next Example Express the ratio as a fraction in simplest form. Hint: 1 yard = 3 feet 9 yards to 48 feet 9 yards 1 yard 3 feet 27 feet To = Fraction Line 48 feet Now simplify!! 9 16 Our Answer

8. Dimensional Analysis Dimensional analysis is simply conversion…converting one thing to another.

9. Example How many seconds are in a day? First, what units of measure do we know or have in the answer? Seconds Day Next, what do we know? 60 seconds60 minutes 1 hour1 minute 24 hours 1 day 86400 seconds 1 day How many seconds are in a minute? How many minutes are in a hour? How many hours are in a day?

10. Now your turn! 35 miles / hour = ____ feet / second 35 miles 1 mile 5280 feet 1 hour 60 minutes 1 minute 60 seconds From the problem How many feet are in a mile How many minutes are in an hour How many seconds are in a minute 184800 feet 3600 second Round your answer to the nearest tenth51.3 feet / second

11. Any Questions??