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our product expresses one hundred times as many 2
as pur multiplicand, though of no greater value;
because cenis express only the hundredths of a 100
do-lar. But from our rules given in multiplicaAns. 200 cts. tion, this work may be abridged; for to multiply
by 100 we have only to annex two ciphers at the
right of our multiplicand, and we have the product of our multiplicand, multiplied by one hundred; and to reduce 3 dollars to cents, we have only to annex at the right hand of the 2, two ciphers; for $2, by annexing two ciphers, stand thus, 200 cts.=2 dollars.--Now it must appear plain to the student, that as 1 dollar is 100 cts., and two dollars, 200 cts. ; $3 must be 300 cts., and 4 dollars, 400 ets., and so on. 2. Reduce 2 dollars to mills.
Ans. 2000. $2
DEM.-It has already been proved that 100
multiplying by 100, reduces dollars to cents.
And it is also evident that by multiplying 200
cents by ten, our product is mills; because we 10
want ten times the number of mills, that we
have of cents, to equal our cents in value; Ans. 2000 mills.
for one mill is only the tenth of a cent. But
we may abridge our work by annexing three eiphers to the dollars; our product will then express mills, because a mill is the thousandth of a dollar, and annexing three ciphers to dollars, is multiplying the dollars by one thousand; thus, $2, by annexing three ciphers, becomes 2000 mills. 3. In $3 and 96 cents; how many cents ? Ans. 396 cts. $ cts.
This may be shortened by annexing 3,96
the cents to the dollars; it will then 100
stand reduced to cents; thus, #3,96 cts.
becomes by taking away the separatrix, 3 00
396 cents, because, joining the cents is Add the 96
multiplying the dollars by one hundred,
and the cents have their proper places, Ans. 396 cts. counting the same that they do standing
alone; thus, $4,56 cents, by taking away the separatrix, expresses 456 cents; the reason of this is plain, bé cause by annexing the cents the dollars have the place of hundreds. 4. In $4,91 cts. 3 mills; how many
mills? Ans. 4913 mills. Note.- This is reduced to mills by taking away the separatrix and joining all the figures together, because dollars take the place of thousands, their proper local value when expressed in mills, and so on, of the rest. And to prove your work, you have only to place your sepatrix; thus, 4913 mills, proved $4,91 cts. 3 mills. 5. Reduce 36 dollars 95 cents and 4 mills, to mills.
Ans. 36954 mills. 6. In $45,95 cents; how many
cents ? Ans. 4595 cts,
7. In $45; how many mills ?
Ans. 45000 m. 8. In $36 and 1 cent; how many cts. ? Ans. 3601 cts. .9. In $400 and 1 mill; how many mills ? Ans. 400001. 10. In 1 dollar and 1 dime; how many dimes ?
Ans. 11 dimes. 11. In 1 dollar and 5 dimes; how many cents ?
Ans. 150 cts. 12. In one dollar, one dime, one cent and one mill; how many mills ?
Ans. 1111 mills. 13. In 15 dimes; how many cents ? Ans. 150 cts. 14. In 9 dimes; how many mills ? Ans. 900 mills.
£. A Groat is four
pence. Note.-Farthings are often written thus, 1 farthing. I of a penny, 2 farthings, of a penny, and 3 farthings, of a penny.
* This is the money of account now in England. And it was the only mode of reckoning in the United States till after an act of Congress in 1792, establishing a mint and regulating the standard of our coins; but since, it has gradually grown out of use.
EXAMPLES 1. In 4 pounds; how many shillings?
Ans. 80s. e
Dem.-It is plain, since it takes 20 4
shillings to make obe pound, that we 20
must have twenty times as many shil
lings as pounds, to equal our pounds in Proof 210)810 s. Ans. value; and multiply £4, our multi
plicand, by 20, our product expresses 4 £
twenty times as many as our multipli
cand; and it should express 20 times as many, to equal the pounds in value; because a shilling is the twentieth of a pound. 2. Reduce £5 and 2s., to shillings.
Ans. 102s. £ s.
Here, according to our rule, we 5 2
multiply our highest denomination,
and add to the product the 2 shil20
lings, the next inferioar denominaProof 2]0) 1028. Ans.
tion, and our product then expresses
the number of shillings contained in £5 2s.
5 pounds and 2 shillings, because 20 times 5 are 100, and 2 make 102
Ans. 46923 Farthings in £48
3. Reduce £48 17s.6d. and 3 farthings to farthings.
Ans. 46923 qrs. £
DEM.-We first multiply 48. 17 63
our pounds by 20, because it
takes 20s. to make a pound; 20
and add the shillings, be977 S Shillings in cause our product expresses 12 ) £48 178.
shillings. We then multi
ply our shillings by 12, be11730
Pence in £48 cause a unit in shillings is 17s. 6d.
equal to 12 pence; and we add the pence in the given
sum to the product, because 175. 6d. 3qrs.
our product is pence; we
then multiply the pence by 4, because a unit in pence is equal to four times as many farthings; and we add the farthings in our given sum to the product, because our product expresses farthings.
4) 4 6 9 2 3 qrs.
210) 9 717-6 d.
Proof. £4 8 17s. 6d. 3 qrs. 4. In £6; how many shillings?
Ans. 120s. 5. In £1; how many shillings and pence?
Ans. 20s. 240d. Ô. In £2; how many pence?
Ans. 480. 9. In £3; how many farthings ?
Ans. 2880qrs. B. In £16 14s. 6d. ; how many pence? Ans. 4014d. 9. In £34; how many shillings, pence, and farthings?
Ans. 680s., 8160d., 32640qrs. 10. In £96; how
Ans. 46080. 11. In £46 12s. and 6d.; how many farthings ?
Ans. 44760qrs. 12. In £86 14s. 6d. 2qrs; how many farthings?
Ans. 83258grs. 13. In £39; how many shillings, pence, and farthings?
Ans. 1780s., 9360d., 37440qrs. 14. In 48 Guineas at 28 shillings each; how many shil. ings and pence?
Ans. 1344s., 16128d. 15. In 24 Moidores at 36 shillings each ; how many shiliings?
Ans. 864s. 16. In 320 Pistoles at 22 shillings each; how many shillings and pence?
Ans. 7040s., 84480d.
17. In 4 dollars at 8 shillings each; how many shillings, and pence?
Ans. 325., 384d. 18. In 32 dollars at 8 shillings each; how many pence, and half pence?
Ans. 3072d., 6144 half pence. REDUCTION ASCENDING. RULE.—Divide the given sum by that number which it requires of the given denomination, to make a unit in the next higher denomination; and so proceed, dividing in each operation the last quotient by the number which it requires to make a unit in the next higher, till you have reduced the given sum to the denomination required; the last quotient, with the several remainders, if any, will be the true answer.
EXAMPLES 1. In 16qrs.; how many pence?
Ans. 4d. 4 ) 16qrs.
DEM.—The reason of our divi4d. Ans.
ding by 4 is plain; because it takes
four farthings to make a penny, Proof. 4
and one fourth the given number 1 6qrs.
in pence must: equal the farthings
in value; for every penny is equal to four farthings; and when we divide by 4; our quotient expresses one fourth part of our dividend, though the same in value; because a number in pence is equal to four times the same number in farthings. 2. In 145 farthings how many shillings?
Ans. 35. Od. lqr. qrs.
Note.-The remainder is of the same 4 ) 145
name of the dividend that produced it.
DEM.-When we divide by 4, our quo12 ) 36d. 1qr.
tient is one fourth part of the dividend in Ans. 3s. Od. 1qr:
number, but the same in value; because
any number of pence is equal to four times the same number in farthings; and when we divide the pence by twelve our quotient is one twelfth of our dividend in number, but the same in value; for any number of shillings is equal to twelve times the same number in pence. 3. In 35339 farthings; how many pounds ?
Ans. £36 16s. 3qrs. qrs.
DEM-Here, we first 4 ) 35339
divide by 4, because four 12 ) 8834-3 qrs.
farthings make a penny,
then by 12, because 12 20 ) 7316-22.
pence make a shilling, Ans. £36–16s. 2d. 3qrs. and lastly, by 20, be
Ans. £36 16s. 2d. 3qrs. .Brought over. 20
cause 20 shillings make Proof. 736s.=£36 16s.
35339qrs.=£36 16s. 2d. 3qrs. 4. In 46382 farthings; how many pence?
Ans: 11595d. 2grs. 5. In 16486 pence; how many shillings?
Ans. 1373s. 10d. 6. In 85 shillings; how many pounds? Ans. £4 5s. 7. In 2880 farthings; how many pounds? Ans. £3. 8. In 46080 half pence; how many pounds ? Ans. £96. 9. In 1344 shillings; how many guineas ? Ans. 48g 10. In 864 shillings; how many moidores? Ans 24m. 11. In 660 shillings; how many pistoles ? Ans. 30. 12. In 3468 farthings; how many guineas?
Ans. 2guin. 16s. 3d. 13. In 36463 pence; how many pounds ?
Ans. £151 18s. 78 14. In 74981 half-pence; how many pounds?
Ans. £156 4s. 23d. 15. In 3452 sixpences; how many pounds ?
Ans. £86 6s. Od.
REDUCTION ASCENDING AND DESCENDING 1. In 476 pounds; how many guineas ? Ans. 340guin. €
DEMONSTRATION.-It is 476
plain, that we reduce pounds
to shillings by multiplying by 28 ) 9520 ( 340 Ans. 20; then our product, which 84
is shillings, must give guineas
when divided by 28, because 112
28 shillings make a guinea. 112
0 2. In 30 guineas; how many pounds?