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: (3
*x*11+3*x*11+3*x*4) 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.*

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

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

*
Sun Aug 10 20:44:02 MDT 1997*

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