Reduction Ascending
Rules: 1. Divide the given denomination by the number which will reduce it to the next higher denomination. Divide the quotient in the same manner, and continue the operation until the entire quantity is reduced.
2. To the last quotient annex the several remainders in their proper order. The result will be the answer.
Example: Reduce 201458 inches to higher denominations.
| Work: | Solution: | |||
|---|---|---|---|---|
| 12 | 201458 inches | 201458 inches = 16788 feet 2 inches. | ||
| 3 | 16788 feet 2 inches | 16788 feet 2 inches = 5596 yards 2 inches. | ||
| 5 | 1⁄2 | 5596 yards | 5596 yards 2 inches = 1017 rods 2 yards 1 foot 8 inches. | |
| 2 | 2 | |||
| 11 | 11192 half yards | |||
| 320 | 1017 rods | 5 half yards | 1017 rods 2 yards 1 foot 8 inches = 3 miles 57 rods 2 yards 1 foot 8 inches. | |
 | ||||
| 3 miles 57 rods | | | |||
 | ||||
| 2 yds. 1 ft. 6 in. | ||||
201458 inches = 3 miles 57 rods 2 yards 1 foot 8 inches.
Reduction Descending
Rules: 1. Write the given quantity in the order of its denominations, beginning with the highest, and supply vacant denominations with ciphers.
2. Multiply the highest denomination by the number which will reduce it to the next lower denomination, and add to the product the units of the lower denomination, if there be any.
3. Proceed in the same manner until the entire quantity is reduced to the required denomination.