11. Reduce of 3 of 2 to a decimal fraction. To reduce Integers of different denominations to a Decimal Fraction of a higher denomination, and the reverse. 1. Reduce 4 pence 2 far- 2. Reduce,375 of a shilthings to the decimal of alling to integers of lower deshilling. nominations. Operation. 4/20 As this question is the re2 farthings is verse of the former, and as of a penny; the decimal,375, was obtainthen, by the ed by dividing the integers, it rule for reduc-is plain, that the integers may ing vulgar fractions to deci-be obtained by multiplying mal, we have =,5 or 5% of the decimal by the same numa penny. This, placed at bers. 1,375 the right of 4 pence, 4,5, and divided by 12, the number of pence in a shilling, or because 4 pence is of a shilling, gives ,375 of a shilling. Hence the RULE. Operation. ,375 12 4,500 4 2,000 Place the numbers one above another, the highest denomination at the bottom. Hence the RULE-MultiDivide the lowest denomina-ply the given decimal by as tion by as many of that as it many of the next lower detakes to make 1 of the next nomination as it takes to higher denomination, writing make one of that in which the quotient at the right of the decimal is given; observthe next higher denomination, ing to point off as many pla QUESTIONS. 1. What is the rule for reducing integers of different denominations to a decimal fraction of a higher denomination? 2. What is the rule for the reverse? 3. Pointing off the product is the same as what? and so proceed until the ces in the product for deciwhole shall be reduced to mals as there are figures in the required decimal. the given decimal; and so NOTE. Integers of different proceed through all the dedenominations may be reduced to nominations-and the several a decimal of a higher, by reduc ing the given numbers to the low-numbers at the left of the est denomination mentioned for a decimal points will be the annumerator, and the integer, to swer required. which the given numbers are to NOTE. Pointing off the probe reduced, reduced to the same duct is the same as dividing by denomination for a denominator, the denominator of the decimal. and dividing the numerator by the 4. Reduce ,41875 to inte denominator. 3. Reduce 8s. 4d. 2qrs. togers of lower denominations. the decimal of a pound. Operation. Operation. 4/20 124,500 s. 8,37500 208,37500 12 sec. to the decimal of a day.,845 of a day? 15. Reduce 24s. 6d. to the decimal of a guinea. 17. Reduce 8 rds. to the decimal of an acre. 16. What is the value of ,875 of a guinea? 18. What is the value of 1,05 of an acre? To reduce shillings, pence and farthings to the decimal of a pound, by Inspection. 1. Reduce 7s. 8d. 2qrs. to the decimal of a pound. One shilling is of a pound: therefore, 2 shillings is or. Having therefore, any number of shillings giv QUESTIONS. 1. Rule for reducing shillings, pence and farthings to the decimal of a pound, by Inspection? 2. Rule for the reverse? en, if we take one half the even number, they will be reduced at once, to the decimal of a pound. If there is an odd shilling, it is the same as T of a pound: =,05. Every farthing is of a pound, which, reduced to a decimal, is a little more than Too, but, if we add 1 to the number when they exceed 12 and do not exceed 36, and 2 when they exceed 36, the farthings in the given pence and farthings will be so many 1000ths of a pound. Thus-7s. 8d. is reduced to the decimal of a pound. Operation. ,3 half of the even shillings ,05 for the odd shilling ,001 for excess of 12. ,385 Answer. 2. Find by inspection the decimal expression of 18s. 31 pence, and 17s. 81d. Answer, £,914 and £,885. 3. Reduce to a decimal by inspection the following sums and add them together, viz:-15s. 3d.; 8s. 111⁄2d.; 10s. 61d.; 1s. 8d.; 23d. Answer, 1,832. Decimals may be reduced back to shillings, pence and farthings by reversing the above process. Double the left hand figure, or tenths, for the shillings; if the second figure be 5, or greater than 5, deduct 5 from it, and add 1 to the shillings. Then consider the second and third figures so many farthings: if they exceed 12 deduct 1; if they exceed 36, deduct 2. 4. Find by inspection the value of £,385. 5. Find by inspection the value of £,927. Answer, 18s. 6d. 2qrs. 6. Find by inspection the value of £,491, and £,984. Answer, 9s. 9d. 3qrs.-19s. 8d. 1qr. SUPPLEMENT TO FRACTIONS. EXAMPLES. 1. What is the sum of and }? Ans., 13-1§. 2. If a man receive of a dollar for 1 day's work, for another, and for another, how much does he receive for the three days' work? 3. If I receive of a cord of bark from another, what part of a cord both? Answer, $24. from one man, and do I receive from Answer, 1 7. Bought a piece of land 4914 acres, sold 21 acres, how many were there left ? Answer, 28. 8. From of a day, take of a minute. 9. From of of 4 take Answer, 5 h. 59 m. 2. of 2 of 4. Ans., . 10. A man had three bags of money, containing in all 450 pounds; in the first bag he had 23047 lbs., in the second 1001, how many were there in the third? 11. From of a pound take of 3 shillings. 12. If a bushel of corn cost of a Answer, 119. of 4 of 3 of 8 of 7 Answer, £21. dollar, what will Answer, f. of a bushel cost? 13. If of a bushel of corn cost much must be paid for 1 bushel ? of a dollar, how Answer, 14. If of a hogshead cost £3, what will be the cost of of a hhd.? 15. Multiply 30 by 4 of of product by of 8 of 3 of 24. 16. Divide of by 3 of 3. Answer, £17. of, and divide the Answer, 69. Answer, . 17. Reduce of a pound, Avoirdupois, to the fraction of a cwt. Answer, 126 18. Multiply of a day by of a minute. Answer, 315 m. 19. Reduce 3s. 6d. to the fraction of a pound. Answer, 20. Reduce 26 cwt. to the fraction of a pound, Avoir dupois. 21. What is the value of 1% of a dollar? Answer, & Answer, 5s. 7d. 22. What is the value of 12 of a Julian year? Answer, 257 d. 19 h. 45 m. 5219 sec. 23. What is the value of of a guinea? Answer, 18s. Answer, 24. Reduce 4 cwt. 2 qrs. 12 lbs. 14 oz. 12 drs. to the fraction of a ton. 25. Reduce 16h. 36 m. 55, s. to the fraction of a day? Answer, 3. 26. Reduce 2 qrs, 9 lbs. 10 oz. 73 drs. to the fraction of a cwt. Answer, 27. If 100 oranges cost 10s., how many hundred be bought for 1051s.? 28. How much will cwt. cost at 152s. per cwt? may Ans., 101. Answer, 3s. 11td. 29. If of a yard cost 18d., what will 1 yard cost? Answer, 2s. of of 1% of is the value of Answer, $45,000. 30. If of of of a ship be worth the cargo, valued at 36,000 dollars, what the ship? SIMPLE PROPORTION: OR, RULE OF THREE. "The ratio, or relation of two numbers, is the quotient arising from dividing one by the other. We introduce some examples to illustrate the theory of ratios and proportions. 1. If 13 yards of cloth cost 130 dollars, what will be the price of 18 yards of the same cloth? If we know the price of one yard of the cloth, it is plain that we can repeat this price 18 times and thus obtain the price of 18 yards. And since 13 yards cost 130 dollars, one yard must have cost the 13th part of 130 dollars; or, performing the division, we find the result 10 dollars, which multiplied by 18, gives 180 dollars as the price of 18 yards. 2. A courier, who travels always at the same rate, having gone 5 leagues in 3 hours, how many will he go in 11 hours? He goes in 1 hour of 5 leagues, or of one league, and of course in 11 hours he will go 11 times as far, i. e. of a league multiplied by 11=55, that is, 18 leagues and one mile. 3. In how many hours will the courier of the preceding question go 22 leagues? If we know the time he would occupy in going 1 league we should have only to repeat this number 22 times, and the result would be the number of hours required. And since it requires 3 hours to go 5 leagues, it will require QUESTIONS. 1. What is ratio? |