Conversions


 * TASK: Define "convert" (look at your flashcards if you need a hint)**


 * What do we do if we need to solve a word problem using a proportion, but they don't give us the same units in each situation?**

This happens a lot of on the Regents. Most of the time they give us a measurement in one unit in the problem and then ask for the answer in a different unit (for example, the problem might tell us a person drove 6 miles in 90 minutes and want us to find out how far they could drive in 5 hours). In these situations, we need to change (or convert) one unit into the other unit. We know that in order to write a proportion we need to have the same units in the numerator and denominator of each ratio. Therefore, we will need to take what they give us in the problem at **convert** (or change) it to another unit.


 * How do we convert between units?**

We convert between units **by using proportions that compare the original unit and the unit that we're changing it int**o. For example, in the problem given above (a person drove 6 miles in 90 //minutes// and we want to find out how far they could drive in 5 //hours//) we need to either convert the minutes into hours OR the hours into minutes. You can convert the units either way, but it makes more sense to convert the minutes into hours because hours is the units we need in the answer.


 * An important note:** When we talked about proportions in the previous few lessons, we said that we are writing the two ratios comparing two situations that are given in the problem. When we're talking about conversions, one of the situations in the proportion will be a standard conversion that you either have to remember or will be given (for example, 60 minutes = 1 hour, 3 feet = 1 yard, 12 inches = 1 foot, etc) and the other situation will be given to you in the problem.

In order to do convert the units in the previous example, we need to set up a proportion that compares minutes and hours. We know that 60 minutes is 1 hour. We want to know how many hours there are in 90 minutes. Using that information, we can set up a proportion to convert between minutes and hours:

The proportion will be set up with the following units:

When we substitute in the information from the problem we get: To solve the proportion, we cross multiply:

And divide by 60 on both sides to get "x" by itself:

Then we simplify to get:



Therefore, 90 minutes is 1.5 hours.

Now that we have the minutes in hours, we can solve the problem.


 * Here's another example of a problem where we have to convert units:**

Looking at this problem, we know that we have to convert the units because the information given in the problem is in minutes and the answer is in hours. Therefore, we need to convert the minutes (given) into hours (what's needed for our answer). Again, we will set up a proportion comparing the original units and the units we want.



We know that 1 hour is 60 minutes and we are given 1.5 minutes. So we can set up our proportion using those two situations:

And we solve the proportion:







Therefore, 1.5 minutes = 0.025 hours. Then we can solve the problem using what we already know about rate or by setting up another proportion:











Therefore, he runs 6,000 meters per hour (in one hour).

**TASK: How do you know when you need to convert units in a given problem?**

**TASK: How do you set up the proportion needed to convert units?**

Sometimes we have to do more than one conversion in order to solve a particular problem. **Here's one last example:**



In this problem, we are given Andy's height in feet and a conversion rate in inches and centimeters. We also know that 1 foot = 12 inches. Before, we can convert Andy's height in feet into centimeters, we first need to convert it into inches.







Now we know that 6 feet = 72 inches. Then, we can convert the 72 inches into centimeters.







Rounded to the nearest centimeter (like the problem asked for), we can say that Andy's height is 183 cm.

There is one **EXCEPTION** to all of this conversion stuff. If the problem GIVES YOU THE RATE and it asks for the RATE IN DIFFERENT UNITS, can just multiply (or divide) by the conversion rate. For example:



This problem GIVES YOU THE RATE (344 meters per second) and wants THE RATE in DIFFERENT UNITS. So, all you have to do it multiply the rate given by the different conversions. If you multiply 344 meters per second by 60 seconds, you get the rate in meters per minute.

344 x 60 = 20,640 meters per minute

Then, if you multiply 20,640 meters per minutes by 60 minutes, you get the rate in meters per hour:

20,640 x 60 = 1,238,400 meters per hour.

TASK: For each problem below, a) state if the problem follows the general rule or is an exception b) solve each problem using the appropriate method (proportion if it follows the rule and multiply or divide by the rate if it's an exception).

1. 2. 3.

4.