2 100 Ans. 200 cts. our product expresses one hundred times as many as our multiplicand, though of no greater value; because cents express only the hundredths of a do lar. But from our rules given in multiplication, 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 ? 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. $2 10 Ans. 2000. DEM.-It has already been proved that multiplying by 100, reduces dollars to cents. And it is also evident that by multiplying cents by ten, our product is mills; because we want ten times the number of mills, that we I have of cents, to equal our cents in value; 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. Ans. 2000 mills. 3. In $3 and 96 cents; how many cents? Ans. 396 cts. $cts. 3,96 100 3 00 Add the 96 This may be shortened by annexing the cents to the dollars; it will then stand reduced to cents; thus, $3,96 cts. becomes by taking away the separatrix, 396 cents, because, joining the cents is multiplying the dollars by one hundred, and the cents have their proper places, 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, because by annexing the cents the dollars have the place of hundreds. Ans. 396 cts. 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 sepa trix; 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? 8. In $36 and 1 cent; how many cts.? Ans. 45000 m. Ans. 3601 cts. Ans. 400001. 9. In $400 and 1 mill; how many mills? 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? 13. In 15 dimes; how many cents? 14. In 9 dimes; how many mills? ENGLISH MONEY.* Ans. 1111 mills. Ans. 150 cts. Ans. 900 mills. 4 Farthing (qrs.) make 1 Penny, marked d. 12 Pence 20 Shillings 1 Shilling 1 Pound 66 £. A Groat is four pence. NOTE.-Farthings are often written thus, 1 farthing, 1 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. 3. Reduce £48 17s. 6d. and 3 farthings to farthings. Ans. 46923 qrs. DEM.-We first multiply our pounds by 20, because it takes 20s. to make a pound; and add the shillings, because our product expresses shillings. We then multiply our shillings by 12, because a unit in shillings is equal to 12 pence; and we add the pence in the given sum to the product, because 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. 12) 1 1 7 3 0-3 qrs. Proof. £48 17s. 6d. 3 qrs. 4. In £6; how many shillings? 5. In £1; how many shillings and pence? 5. In £2; how many pence ? 7. In £3; how many farthings? B. In £16 14s. 6d. ; how many pence ? Ans. 120s. Ans. 20s. 240d. Ans. 480. Ans. 2880qrs. 9. In £34; how many shillings, pence, and farthings? 10. In £96; how many half pence? Ans. 46080. Ans. 44760qrs. 12. In £86 14s. 6d. 2qrs; how many farthings? Ans. 83258qrs. 13. In £39; how many shillings, pence, and farthings? Ans. 780s., 9360d., 37440qrs. 14. In 48 Guineas at 28 shillings each; how many shilAns. 13449., 16128d. ings and pence? 15. In 24 Moidores at 36 shillings each; how many shil iings? 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, Ans. 32s., 384d. and pence? 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 cach 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? 4) 16qrs. 4$ 4d. Ans. Proof. 1 6qrs. Ans. 4d. DEM.-The reason of our dividing by 4 is plain; because it takes four farthings to make a penny, and one fourth the given number 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? qrs. 4) 145 12) 36d. 1qr. Ans. 3s. Od. 1qr. NOTE.-The remainder is of the same name of the dividend that produced it. DEM.-When we divide by 4, our quotient is one fourth part of the dividend in 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. Ans. 3s. Od. 1qr. 3. In 35339 farthings; how many pounds? Ans. £36 16s. 3qrs. DEM-Here, we first divide by 4, because four farthings make a penny, then by 12, because 12 pence make a shilling, and lastly, by 20, be 35339qrs.=£36 16s. 2d. 3qrs. 4. In 46382 farthings; how many pence? Ans. 11595d. 2qrs. 5. In 16486 pence; how many shillings? Ans. 1373s. 10d. 6. In 85 shillings; how many pounds? Ans. 2guin. 16s. 3d. 13. In 36463 pence; how many pounds? Ans. £151 18s. 7d 14. In 74981 half-pence; how many pounds? Ans. £156 4s. 2 d. |