Units of Conversion: Square (Area) Measure

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

Example 1: Convert 180 square inches to square feet.

Solution:

• 180 square inches can be written as 180 x 1 square inch.

• Since 1 square inch can be written as 1 inch x 1 inch,

• 180 square inches can be written 180 x 1 inch x 1 inch.

• Note that 1 inch can be written as 1 inch x 1 and the 1 can be written as a fraction where the numerator and the denominator are equivalent.

• Write 1 inch x 1 as 1 inch x

• This can be further simplified to read

• 180 square inches = 180 x 1 inch x 1 inch = 180 x 1 inch x 1 x 1 inch x 1

  =

• Multiply the fractions.

• Rearrange the numerator and rearrange the denominator.

  

• Rewrite as five fractions where as many fractions as possible have an equivalent value of 1.

  1.25 x 1 x 1 x 1 foot x 1 foot

• Note: 1 foot x 1 foot is the same as one foot squared is the same as one square foot.

• The answer is 1.25 square feet.

• Since 1 square foot is equivalent to 144 square inches, the fraction is equivalent to 1.

  Therefore, another way to work the problem is as follows:

  

  = 1.25 x 1 x 1 square foot = 1.25 square feet

If you would like to review another example, click on Example.

If you would like to work some problems, click on Problems.

If you would like to go back to the table of contents, click on Table of Contents.

[Units of Conversion]

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