Section 3.1 Ratios and Rates

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Presentation transcript:

Section 3.1 Ratios and Rates

VOCABULARY Ratio: a comparison of two quantities which can be written as: a fraction - ¾, words – 3 to 4, or using a colon – 3:4. Rate: a ratio of two quantities with different unit Ex. 100 miles 2 hours Unit Rate: a rate with a denominator of 1 Ex. 55 miles 1 hour

Unit Analysis Unit Analysis is converting from one unit to another. Example 1 – John works 6 hours at a rate of $12 per 1 hour. How much money does John make working? 6 hours x $12 = $72 Notice how the hours cancel out! 1 hour Example 2 – Samantha’s car has 10 gallons of gas and gets 22 miles per 1 gallon. How many miles can Samantha drive? 10 gallons x 22 miles = 220 miles 1 gallon Notice how the gallons cancel out! Example 3 – 11560 feet is how many miles? 11560 feet x 1 mile = 11560 = 2 miles 5280 feet 5280 Notice how the feet cancel out! Example – How many seconds are in 13 minutes? 13 minutes x 60 seconds = 780 seconds 1 minute Notice how the minutes cancel out!

Notice that the order you write the ratio has to match the order in Finding Ratios, Rates, and Unit Rates Example 1 – There are 14 girls and 17 boys in the class. The ratio of girls to boys is: 14/17 or 14 to 17 or 14:17 The ratio of boys to girls is: 17/14 or 17 to 14 or 17:14 The ratio of boys to students in the class is: 17/31 or 17 to 31 or 17:31 Notice that the order you write the ratio has to match the order in which it was asked. Example 2 – John can run 400 yards in 10 seconds. John runs at a rate of: 400 yards 10 seconds The unit rate is how many yards John can run in one second. 400 yards ÷ 10 = 40 yards 10 seconds ÷ 10 1 second Example 3 – The cost of bananas is 99¢ for 3 pounds. The rate is: 99¢ 3 pounds The unit rate is how much does it cost for 1 pound. 99 ¢ ÷ 3 = 33¢ 3 pounds÷ 3 1 pound

Finding a Rate From a Table The table shows the distance the Internationals Space Station travels while Orbiting the Earth. Find the speed in miles per second. +3 +3 +3 Time (seconds) 3 6 9 12 Distance (miles) 14.4 28.8 43.2 57.6 +14.4 +14.4 +14.4 Find the change between intervals. From the graph we can see that the Space Station travels 14.4 miles per 3 seconds. Written as a rate that would be: 14.4 miles 3 seconds The unit rate (or speed in miles per 1 second) is: 14.4 miles ÷ 3 = 4.8 miles 3 seconds ÷ 3 1 second

Finding a Rate from a Line Graph Sound through Water) The graph shows the distance that sound travels through water. Find the speed in kilometers per second. Step 1 – Choose a point on the line (2,3) This point shows you that sound travels 3 kilometers in 2 seconds. Step 2 – To find the speed in kilometers per second, find the unit rate. 3 kilometers ÷ 2 = 1.5kilometers 2 seconds ÷ 2 1 second Distance (kilometers) 1 2 3 4 5 6 7 8 9 10 (2,3) 1 2 3 4 5 6 Time (seconds)