Unit Analysis Reference: Charles, R., Kennedy, D., & Hall, B. (2017). Pearson Integrated High School Mathematics - Mathematics II Common Core. Pearson Education, Inc. Reference: Hall, Basia, et al (2014). Pearson Integrated High School Mathematics - Mathematics III Common Core, Pearson Education, Inc. Reference: Sullivan, M., & Sullivan III, M. (2012). Precalculus Enhanced with Graphing Utilities, 6/e. Pearson Education, Inc. Reference: Sullivan, M., & Sullivan III, M. (2012). Precalculus Enhanced with Graphing Utilities, 6/e. Pearson Education, Inc. Reference: Hall, Basia, et al (2014). Pearson Integrated High School Mathematics - Mathematics III Common Core, Pearson Education, Inc.

Why use it? Often the measurements we get are not in the units we need. For example, Can a plane outrun a bullet? Plane speeds are usually in mph. Bullet speeds are in ft/s. Which is faster?

Common Equalities 12 inches = 1 foot 3 feet = 1 yard 5280 feet = 1 mile 60 seconds = 1 minute 60 minutes = 1 hour 3600 seconds = 1 hour

Converting Units Since each statement we just saw is an equality, dividing one side by the other is 1. For example: So, we can multiply these ratios by any measurement, without actually changing the value

Back to the Plane A typical speed for a warplane is 1500 mph. Many guns shoot under 1500 ft/s. Which is faster? We need the same units, ft/s. Remember 1500 mph is 1500 1 mile = 5280 ft gives us a ratio of We put the ft on top, because that is what we want in the final answer

The Plane (Continued) With time, we want seconds on the bottom. Remember the gun was in ft/s 1 hour = 3600 s gives us So, 1500 . .

The Plane (Continued) With time, we want seconds on the bottom. Remember the gun was in ft/s 1 hour = 3600 s gives us So, 1500 . .

The Plane (Continued) With time, we want seconds on the bottom. Remember the gun was in ft/s 1 hour = 3600 s gives us So, 1500 . .

The Plane (Continued) With time, we want seconds on the bottom. Remember the gun was in ft/s 1 hour = 3600 s gives us So, 1500 . .

The Plane (Continued) With time, we want seconds on the bottom. Remember the gun was in ft/s 1 hour = 3600 s gives us So, 1500 . . So, yes. A plane can outrun a bullet.

Summary Reviewed some common unit equalities Used these equalities to find a unit ratio Used these ratios to change measurements from one units to another Thank you!