1. 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.

2. 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?

3. 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

4. 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

5. 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

6. 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,

7. 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,

8. 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,

9. 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,

10. 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,
So, yes. A plane can outrun a bullet.

11. 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!