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3. Reduce $4229.20 to Canada currency, &c.
21146+20=41057 68. Anse
The present currency of England reduced to the present
currency of the United States.
When the sum is pounds only.* RULE.-Multiply the pounds by 4.44 and point off 2 figures from the right, for cents, the rest are dollars.
16X4.44 $71•04 cts. Ans. 2. Reduce 223 pounds, sterling to dols. &c.
If the sum consists of pounds and shillings. RULE.-To the pounds annex half the number of shillings, in the place of tenths ; multiply the whole by 4.44, and point off three figures from the right, for cents and inills, the rest are dollars : If the shillings are odd; annex the greatest even half, and for the odd shilling annex 5 in the place of hundredths, multiply by 4.44, and point off 4 figures for cents, &c. the rest are dollars.
19.95 X4-44 $88-5780 Ans. 2. Reduce £127 16s. to dollars, &c.
* In England accounts are kept in pounds, shillings, pence and farthings, sterling: 4 farthings make 1 penny ; 12 pence 1 shilling; 20 shillings 1 pound, sterling.
DEFINITION-Duodecimals is a rule used much in the mensuration of superficies and solids; and teaches to multiply feet and inches, by feet and inches without reducing. Inches are called primes and are marked thus ('); inches are divided into twelfths, or seconds, and marked thus ("); thirds, or the twelfth part of a second is marked thus (""); thus all denominations less than a foot decrease in a twelve fold proportion and are designated by these characters, inches ), seconds ("), thirds (""), fourths (""' ), fifths ("), &c.
RULE. —Write down the number to be multiplied, in feet and primes, or inches, &c. and under it write down the number to multiply by ; observing to write every denomination under that of the same name; multiply the highest denomination of the multiplier into all the denominations of the multiplicand, obserying to set down all over twelve, and carry the twelves to the next higher denomination; continue to multiply by every denomination of the multiplier, observing to remove the products as many places to the right, as the number you are multiplying by stands to the right of the highest; add up the products in the same order in which they stand, carry one for every twelve, the sum is the answer or product required,
Examples 1. It is required to multiply 12ft. 9in. by 6ft. 4in.
Nore. In this example the highest denomination of the multiplier, vis. 6 feet, was multiplied into the lowest denomination of the multiplicand, vix. 9 inches ; and the product was 54', in which was 4 of the next denomination, vis: 4 tweltes, and 6 left which was set down, and the 4 was carried to the next denominations I then multiplied the 6 feet into the 12 feet, and added the 4 to the product, and set the whole down: I then multiplied the 4 inches into the 9 ibches, (removing the product one place to the right) and fonnd the product to be 36; three twelves, none over. ;:1 then multiplied the 4 in. into the 12 ft. and added in the 3 I carried which made 51, which was 4. twelves and 3 over ; I then added the products together, the sum is the product required..
2. It is required to multiply 3ft. 2' 3" by 3ft. 2' 3".
Ans, 10ft. 1' 11" ong!'".
RULE:~Multiply the highest denomination in the multiplier into all the denominations of the multiplicand, and set down the whole products, &c. then multiply the next highest denomination in the multiplier into all the denominations of the multiplicand, and remove the products one place to the right, and set them all down; proceed thus through all the denominations, observing to set down the whole products each time of multiplying ; then add up the several products in the order in which they stand, and carry the same as in Compound Addition, the sum will be the product required.
pro. 80 9
O Ans. 2. What is the product of 3 ft. 2' 3" multiplied by 3. ft. 23"?
pro. 10 1 11 0 9 Ans.. 3. What is the product of 12 ft. 11 in. 11 sec. multiplied by 12 ft. 11 in. 11 sec.
Ans. 168 ft. 9' 101 Oir Note. This method need not be confined to 12, as some imagine, but may be extended to any denomination, as rods, yards, feet, and inches, &c.
Eramples. 1. Required to multiply 22 yds. 2 ft. 11 in. by 7 yds. 2 ft. 2 in.
yds. ft. in.
154 14 77 44 4
3 10 Ans.
2. It is required to multiply 10 rods, 20 links, by 12 rods and 20 links, allowing 25 links to a rd. ?
Ans. 138 rods, 6 links. Note.--In the last example 1 multiplied 12 rds. by 20 links and set down the product, viz. 240 ; I then multiplied the 12 rds, by the 10 rds. and set down the product, viz. 120 ; I then multiplied the 20 lin, by the 20 lin. and removed the product one place to the right and set it down, viz, 400 ; I then multiplied 20 lin. by 10 rds. and set down the product, viz. 200; 1 then added the products together and carried by 25.
3. It is required to multiply 7 fto. 3 in. by 3 ft. 3 in.
Ans. 23 ft. 6' 9'237 ft. Note.-The 6 inches are = and the 9" of a foot, and that is as expressed above; any question that is solved by duodecimals may be solved by vulgar, or decimal fractions.
4. It is required to multiply 8 ft. 3 in. by 4 ft. 3 in.
Ans. 35 ft. Of 9'=3516 ft. The same question by vulgar fractions. 8 ft. 3 in.=8and 84 is equal to 3.4 ft. 3 in., and 41 to 5, and x4=2354 ft. Ans.
The same question by decimal fractions. 8 ft. 3 in.=8.25 ft. and 4 ft. 3 in.=4.25 ft. and 8.25 X4.25=35.0625 ft., or 351 ft. Ans.
5. It is required to multiply 3 ft. 9 in. by 6 ft. 9 in.
Ans. 25 ft. 3' 9" or 25 The same question solved by vulgar fractions. 3, j = 1 and 6.1=fixi=** =2511. ft. Ans.
SUPERFICIAL MEASURE. DEFINITION.- Superficial measure is that which respects length and breadth, without regard to thickness; the dimensions are various according to the nature of