*Check to see if the number is reasonable (for example, your average automobile can't be expected to go 1,000,000 miles per hour! Before we look at a few example problems, we need to first consider the use of units and unit analysis.*

As a subject, it generally denotes the study of calculations on some set.

In high school, this can the study of examining, manipulating, and solving equations, inequalities, and other mathematical expressions.

Let's look at a couple quick examples (note that although these examples use plural and singular units for ease of reading, whether a unit is written in its plural or singular form has no bearing on the meaning or the math): This second example is actually a case of identity, because 12 inches = 1 foot. We can thus see how the presence of units has an effect on the math, but the same general principles that we have studied still hold. Let's multiply by factors with corresponding units that convert from years to seconds as follows.

(Again, note that we are actually multiplying in each case by 1 because of the relationship of the units.) Thus, 1 year = 525,600 minutes, or (alternatively) there are 525,600 minutes in a year.

If the boiling point of water is and the melting point of water is , find the linear functions that convert from one scale to the other.

This problem asks us to find a conversion function that takes a Fahrenheit temperature reading and turns it into a Celsius temperature reading.

You've been using algebra since your early schooling, when you learned formulas like the area of a rectangle, with width We used letters to stand for numbers.

Once we knew the width and height, we could substitute them into the formula and find our area.

This problem illustrates the process of unit conversion; a year is the same as 525,600 minutes even though 1 ≠ 525,600.

Bill takes a trip in which he drives a third of the time at 30 miles per hour, a third of the time at 50 miles per hour, and a third of the time at 70 miles per hour.

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