### 1.1 Order of Operations & Formulas

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• Math Help

When you work with rates, use the units given to help solve the problem. For instance, if the problem asks for an answer in miles per hour, then your solution should include a quantity in miles divided by a quantity in hours.

Similarly, if the problem asks for an answer in calories and you have a rate in calories per hour, your solution should include multiplying by hours to end up with just calories. See how this works in Example 5.

This kind of approach to problem solving is called unit analysis and is an important tool used in many mathematical applications.

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• Checkpoint Solution

The total number of calories in your lunch is

At 155 pounds, running 10 miles per hour, you burn 1126 calories. At this rate you have to run

to burn the calories you eat. This is about 70 minutes.

How Do I Write a Rate?

In the Math Help, you write the rate as

In the Checkpoint Solution, you write it as

Question:    How do I know which one to use?

Answer:    This is a good question. The answer depends on the context of the problem.

1. You know the units that are given.
2. You know the units you need for the answer.
3. Use unit analysis. That is, use the version of the rate that will convert the given units into the desired units.

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|_|\/|_||  \____//   `__ `     /_____// |______//
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