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REDUCTION OF FEDERAL MONEY. Federal money is decimally divided.
The learner having acquired a competent knowledge of decimals will readily see the propriety of the following rules, for reducing Federal Money.
CASE I. To reduce dollars to cents.
RULE. Annex two ciphers to 'the dollars, and the whole will be cents.
EXAMPLES. Reduce $ 956 to cents.
Answer 95600 cents. In $ 4736, how many cents ?
47 3600 In $ 9735, how many cents ?
CASE II. To reduce dollars to mills. Rule. Annex three ciphers to the dollars, the whole will be mills.
Note. This and case IX. prove each other.
EXAMPLES. In $596, how many mills? Answer 596000 mills. In $ 7369, how many mills ?
7369000 In $ 4362, how many mills ?
RULE. Take away the separating point from between the dollars and cents, and the whole will be cents.
Note. This and Case VIII. prove each other.
EXAMPLES In $ 4,36, 75, how many cents ? Answer 43675 cents. In $ 964, 31, how inany cents ?
96431 In $ 493, 50, how many cents ?
RULE. Take away the separating point, and annex 2 cipher.
EXAMPLES. In $ 495, 20, how many mills ? Answer 495200 mills, In $ 576, 37, how many mills ?
576370 In $ 231, 49, how
many mills ?
EXAMPLES. In $ 4739, 16, 4, how many mills ? Ans.4739164 mills. In $ 537, 11, 2, how many mills ? 537112 In $ 9364, 74, 3, how many mills ? 4364743 Nore. This and Case IX. prove each other.
EXAMPLES. In cents 36, 5, how many mills ?
Ans. 365 mills.
EXAMPLES In 51 cents, how many mills ? Ans. 510 mills. 47
990 Case VIII. To reduce cents to dollars.
Rule. Point off the two right hand figures for cents, the others will be dollars.
EXAMPLES In 43675 cents, how many dollars ? Ans. $ 436, 75 In 96431 cents, how many dollars ?
964, 31 In 49350 cents, how many dollars?
4.93, 50 Nore. This Case, and Case III. prove each other.
CASE IX. To reduce mills to dollars.
Rule, Point off the right hand figure for mills, the next two for cents ; the others will be dollars.
EXAMPLES. In 4739164 mills, how many dols. ? Ans. $ 4739,16,4 537112
4364,74,3 Note, This and Case V.
REDUCTION OF CURRENCIES, which are not decimally divided, as pounds, shillings, pence, &c. or of weights, measures, &c; as, tons, hundreds, quarters, &c; pounds, ounces, penny-weights, and grains, &c. Observe this one general rule.
1. If high denominations are to be reduced to lower, multiply the highest denomination given, by as many of the next lower, as make one of this highest.
2. If any figures stand in the place of the next lower denomination, they must be taken in, or added to the product, as in proving Division.
3. If it be required to reduce it still lower, multiply it by as many of the next lower denomination, as are equal to one of this last ; and if any figures stand in the next lower to this, they must be taken in, or added to this product, as above, &c.
4. If low denominations, are to be reduced to high, divide the lowest given, by as many of that denomination, as are equal to one of the next higher.
5. If still higher be required, divide this quotient by as many of its denomination, as are equal to one of the next higher, &c.
6. If any figures remain in any of these divisions, they are so many of the same denomination, you was then dividing, which must be put each in its proper place, after the highest denomination required is obtained, and you will have the highest, and all its lower denominations in their due order.
EXAMPLES. 1. In £ 75, how many far. 2. In £ 36, 12, 6f how mathings?
ny farthings? 75
36,12,61 20 shillings in a pound. 20 shillings in a pound.
12 pence in a shilling.
12 pence in a shilling.
4 farthings in a penny.
4 farthings in a penny.
72000 farthings, Ans. 35162 farthings, Ans.
farthings in a penny 4)72000
Note. This proves the first example.
farthings in a penny 4)35162
Answer, £ 36 12 61 Note. This proves the second example. 5. Reduce 937246 farthings, to pounds.
Answer £ 97 1273 6. Reduce 73528 pence, to pounds.
Ans. £ 306 7 4. 7. In 936 shillings, how many farthings?
Ans. 44928. 8. In £ 964, how many six-pences ? Ans. 38560.
Note. According to the preceding Rule, this last exampie is to be multiplied by 20, to bring it into shillings ; and then (as there are 2 81x-penccs in one shilling, these shillings are to be multiplied by 2. But as there are 40. six-pences in a pound, it may be more speedily performed, by multiplying the pounds by 40.
9. In £ 86 16, how many six-pences, three-pences, pence, and farthings ?
6944 three-pences. Ans.
83328 farthings. 10. In £ 53 4 5, how many eight-pences, four-pences, pence, and farthings ; and the number of each equal ?
Answer, 964 of each. NOTE. To answer this question, reduce the given sum to farthings, and divide those farthings by as many as there are farthings, in one of each of the required denominations, when added together.
11. Reduce £ 57 11 74 to six-pences, three-pences, pence and farthings, and let the number of pence be double the number of farthings ; the three-pences, double the number of pence ; and the six-pences double the number of three-pençes.
Ans. 222 farthings, 444 pence, 888 three-pences, and 1776 six-pences. 12. In £ 120 12 3, how many three-pences ?
Ans. 9649. In £ 17 6 8, how many eight-pences ? Ans. 520. 13. In £ 97 12 74, how many farthings?
Ans. 937246. 14. In £ 306 7 4, how many pence? Ans. 73528. 15. In 44928 farthings, how many shillings?
Ans. 936. 16. In 38560 six-pences, how many pounds?
Ans. £ 964 17. How many pounds are there in 3472 six-pences; in 6944 three-pences ; in 20832 pence : Or, in-83328 farthings?
Answer: In either of these sums, 'there are k 86 16.