# Units of Conversion: Square (Area) Measure - Problem 3

Basic to the understanding of unit conversion is the understanding of equivalence, the understanding of the multiplicative identity of 1, and how the two are related. For a review of these concepts, click on Review.

If you have forgotten how to manipulate fractions, visit Fractions for Adults on SOSMath for an in-depth review.

Review the following table (Webster's New World Dictionary, Second Edition, Simon and Schuster, 1982) of Standard Units of Conversion to see if you can create fractions that have a value of 1. You can click to examples following each table.

Square Measure

Problem 3: Convert 8 square yards to square centimeters

Solution: Look for a series of links from square yards to square centimeters.

• From the table you can see that there are links from square yards to square feet to square centimeters.

• According to the table, 1 square yard is equivalent to 9 square feet.

Therefore, the fraction is equivalent to 1.

• According to the table, 1 square foot is equivalent to 929.03 square centimeters.

Therefore, the fraction is equivalent to 1.

• Rewrite 8 square yards as a fraction and multiply the fraction by 1 two times.

• Convert the above 1's to equivalent fractions.

• Multiply the numerators and multiply the denominators:

• Rewrite the fraction so that the units stand alone:

• Rearrange the numerator and the denominator:

• Rewrite as several fractions where most fractions have an equivalent value of 1:

• Simplify: 66,890.16 1 1 1 square centimeter = 66,890.16 square centimeters

As you work more and more of this conversion problems, you can leave out a lot of steps and simply "cross out" similar units. In the original set-up

, you would simply cross out common units and go straight to the expression

= 66,890.16 square centimeters.

Just be sure that you remember why you are allowed to do the cancelling.

If you would like to go to problems click on Problems.

[Units of Conversion]