- Slides: 11
Ratio and Rates Coordinate Algebra
Ratio A ratio is a comparison of two numbers by division
Example of a ratio 4 9 25 to 10
Unit Rate 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). Any ratio can be converted into a unit ratio by dividing the numerator and the denominator by the denominator A = A÷B B B÷B 1
Express each ratio as a unit rate $250 for 5 concert tickets A. $ 55 per ticket C. $50 per ticket B. 250 per ticket 5 D. 2500 per ticket 50 Our Answer 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).
Now what about this…? Example On a farm, there are 6 cows for every 3 pigs. cowstotocows pigs as a unit rate? (pigs (cowsper percow) pig) What is the ratio of pigs Pigs Cows: Cows= : Pigs =36: : 63 63 == 36 ÷÷ 63==0. 5 2 36 6÷ 6 3÷ 3 11 Remember unit rate needs to have a denominator of 1
Next Example Express the ratio as a fraction in simplest form. Hint: 1 yard = 3 feet 9 yards to 48 feet 9 yards 3 feet 1 yard 27 feet 9 Now simplify!! 16 To = Fraction Line Our Answer
Dimensional Analysis Dimensional analysis is simply conversion…converting one thing to another.
Example How many seconds are in a day? Next, First, what units do weofknow? measure do we know or have in the answer? Seconds Day How many seconds are in a minute? How many minutes are in a hour? How many hours are in a day? 60 seconds 60 minutes 24 hours 1 minute 1 hour 1 day 86400 seconds 1 day
Now your turn! 35 miles / hour = ____ feet / second From the problem How many feet are in a mile How many minutes are in an hour How many seconds are in a minute 35 miles 5280 feet 1 hour 1 minute 1 hour 1 mile 60 minutes 60 seconds Round your answer to the nearest tenth 184800 feet 3600 second 51. 3 feet / second
Any Questions? ?