Averages often appear on word problems. To find the average of a collection of numbers, we add all the numbers and then divide by how many numbers there are. If someone calls you average and they haven't done all the legwork, you can disregard their judgment of you. If, however, someone can quantitatively prove that you're average, you'll need to accept it as fact.

### Sample Problem

Find the average of the five smallest positive integers.

The five smallest positive integers are 1, 2, 3, 4, and 5. Remember, integers are counting numbers, and if you're counting down to a shuttle launch, you'll rarely use the negatives. Unless there's some sort of mechanical malfunction and you're stalling for time. "Two...uh, one and a half..."

To find the average of these we add them and divide by 5, since that's how many numbers we have.

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## Averages Practice:

The average of 5 and what number is 9? | |

We can translate this question directly into symbols. Even though this one is simple enough that we can probably intuit the answer without writing it out, it is good practice for when you're faced with a problem that is more complex. It's also good practice for writing things in general. We've noticed that your handwriting has gotten a little sloppy as of late. Our unknown number is *x* and we are averaging two numbers, so $$\frac{5 + x}{2} = 9$$ Solving this equation gives us *x* = 13. | |