# Units of Conversion: Square (Area) Measure - Example 2

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 2: You have decided to carpet a 21-foot by 33-foot room in your house, and you have decided on a carpet that costs \$22.00 per yard. The carpet comes from the mill in rolls that are 9 feet wide. Decide how to cut the carpet so that your cost is minimized. How much will it cost you to carpet the room?

Solution:

• 21 feet translates to 7 yards and 33 feet translates to 11 yards. This means that we need at least 7 yards x 11 yards of carpet.

• Note: 7 yards x 11 yards can be written as 7 x 1 yard x 11 x 1 yard which in turn can be written as 7 x 11 x 1 yard x 1 yard = 77 x or 77 square yards.

• The roll of carpet is 9 feet wide which translates to3 yards wide. How do we cut the roll to minimize the amount of left-over carpet? You have to pay for the left-over carpet.

• Let's let the first and second cuts both be 3 yards wide by 11 yards deep. This will cover 6 yards by 11 yards of the room leaving 1 yard by 11 yards to cover. Now let's cut 3 yards wide by 4 yards deep. Now cut this last section into three, 1-yard-wide pieces. They will cover the remaining 1 yard by 11 yards of the room with 1 square yard left over.

• The costs: (3x11+3x11+3x4) yards @ \$22.00 per yard = \$1,716 to carpet the room.

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

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

[Units of Conversion]