A farm is 200 acres. How many square miles is the farm if one square mile is equal to 640 acres?

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In order to convert between different units of measurement, we use what is called a conversion factor. A conversion factor is a ratio (written as a fraction) where one of the units is the numerator and one is the denominator. In order to convert one type of unit to another, you will cross-multiply the starting value by the conversion factor. *We decide which unit goes on the top based on what we are trying to convert. Basically, the units have to match - the units of one numerator should be the same as the numerator of the second fraction. In this case, we know the conversion factor to be the number of acres in one square mile. This can be written as either of the following: ^{640 acres}/_{1 mile²} OR ^{1 mile2} / _{640 acres} These can both be used as conversion factors because the ratio of acres to a square mile is the SAME in both. In order to decide which version to use, we come to our problem. We are told that the farm is 200 acres, and we're trying to convert the acres to square miles. Since the number of square miles (the size of the farm, in square miles) is unknown, we're going to represent It as x. In order to solve using ratios, we need to write the first ratio as a fraction. We know that the size in acres is 200 acres, so that will be the numerator in our fraction (ratio) to start. We have decided to use x to represent the unknown number of square miles, so our fraction (ratio) will look like this: ^{200 acres}/ _x Now, we know which version of the conversion factor to use. Acres is the unit used in the numerator, so we will use the conversion factor that also has acres in the numerator: ^{640 acres}/_{1 mile²} Now we can set the ratios equal to one another in preparation to solve. ^{200 acres}/_x= ^{640 acres}/_{1 mile²} You will notice there is a squared unit here, but it's a bit different from other examples. We are converting from acres to square miles, not from one squared unit to another. For example, if we are trying to convert squared inches to squared centimeters, the starting conversion factor includes no squared values. In this case, the conversion factor itself contains a squared unit, so we just use it as it is. You can also think about it this way: If we were to square the entire conversion factor, the acres would become acres²and we would not be able to compute the rest of the problem because those units aren't the same. Now, we can move forward and solve. ^{200 acres}/_x= ^{640 acres}/_{1 mile²} Cross multiply across the equal sign to eliminate the ratios. This means you multiply the first numerator by the second denominator, and the first denominator by the second numerator. 200 acres • 1 mi² = x • 640 acres 200 acres • mi² = x • 640 acres Now, we can see that we have the 640 multiplying the x, so we have to divide both sides by 640. Note that when you divide, you also divide by the units. This cancels out the acres on the left hand side as well. 200 acres • mi² ÷ 640 acres = x • 640 acres ÷ 640 acres 0.3125 mi²= x

A Farm Is 200 Acres