XXIII. If a horse will eat of a bushel of outs in a day, how long will 12 bushels last him? In this question it is required to find how many times of a bushel is contained in 12 bushels. In 12 there are, therefore 12 bushels will last 36 days. At of a dollar a bushel, how many bushels of corn may be bought for 15 dollars? First find how many bushels might be bought at of a dollar a bushel. It is evident, that each dollar would buy 5 bushels; therefore 15 dollars would buy 15 times 5, that is, 75 bushels. But since it is instead of of a dollar a bushel, it will buy only as much, that is, 25 bushels. This question is to find how many times of a dollar are contained in 15 dollars. It is evident, that 15 must be reduced to 5ths, and then divided by 3. 15 75 75 (3 25 bushels. The above question is on the same principle as the following. How much corn, at 5 shillings a bushel, may be bought for 23 dollars? The dollars in this example must be reduced to shillings, before we can find how many times 5 shillings are contained in them; that is, they must be reduced to 6ths, before we can find how many times are contained in them. 23 138 (5 Ans. 273 bushels. 23 138 and are contained 273 times in 13. If 13 yds. of cloth will make 1 suit of clothes, how many suits will 48 yards make? If the question was given in yards and quarters, it is evident both numbers must be reduced to quarters. In this instance then, they must be reduced to Sths. In the three last examples, the purpose is to find how many times a fraction is contained in a whole number. This is dividing a whole number by a fraction, for which we find the following rule: Reduce the dividend to the same denomination as the divisor, and then divide by the numerator of the fraction. Note. If the divisor is à mixed number, it must be reduced to an improper fraction. N. B. The above rule amounts to this; multiply the dividend by the denominator of the divisor, and then divide it by the numerator. At of a dollar a bushel, how many bushels of potatoes may be bought for & of a dollar? is contained in as many times as 1 is contained in 3. Ans. 3 bushels. If of a ton of a hay will keep a horse 1 month, how many horses will of a ton keep, the same time? 3 are contained in as many times as 3 are contained in 9. Ans. 3 horses. At of a dollar a pound, how many pounds of figs be bought for of a dollar? may 5ths and 4ths are different denominations; before one can be divided by the other, they must be reduced to the same denomination; that is, reduced to a common denominator. 15 and are contained in as many times as 4 are contained in 15. Ans. 3 lbs. At 7 dolls. a yard, how many yards of cloth may be bought for 57% dollars? 7338 and 57461. 5ths and 8ths are different denominations; they must, therefore, be reduced to a common denominator. From the above examples we deduce the following for dividing one fraction by another: rule If the fractions are of the same denomination, divide the numerator of the dividend by the numerator of the divisor. If the fractions are of different denominations, they must first be reduced to a common denominator. If either or both of the numbers are mixed numbers, they must first be reduced to improper fractions. Note. As the common denominator itself is not used in the operation, it is not necessary actually to find it, but only to multiply the numerators by the proper numbers to reduce them. By examining the above examples, it will be found that this purpose is effected, by multiplying the numerator of the dividend, by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor. Thus in the third example; multiplying the numerator of by 5 and the denominator by 1, it becomes 5, which reduced is 33 pounds, as before. XXIV. A owned of a ticket, which drew a prize. A's share of money was 567 dollars. What was the whole prize? of a number make the whole number. Therefore the whole prize was 5 times A's share. 567 Ans. 2835 dollars. A man bought of a ton of iron for 135 dollars; what was it a ton? make the whole, therefore the whole ton cost 7 times 13. 13 7 Ans. 953 dolls. A man bought of a ton of iron for 40 dollars; what was it a ton? 5 12 2 are 5 times as much as. If cost 40 dollars, Tmust cost of 40. Ans. 96 dolls. of 40 is 8, and 8 is of 96. A man bought of a ton of hay for 17 dollars; what was it a ton? are 3 times as much as . Since cost 17 dollars, must cost of 17, and must cost of 17. If 42 firkins of butter cost 33 dollars, what is that a. firkin? 1 4층 22 2. First we must find what costs.is part of, therefore will cost of 33 dollars, and will cost of 33 dollars. 5 22 22 The six last examples are evidently of the same kind. In all of them a part or several parts of a number were given to find the whole number. They are exactly the reverse of the examples in Art. XVI. If we examine them still farther, we shall find them to be division. In the last example, if 4 firkins instead 43 had been given, it would evidently be division; as it is, the principle is the same. It is therefore dividing a whole number by a fraction; the general rule is, to find the value of one part, and then of the whole. To find the value of one part, divide the dividend by the numerator of the divisor; and then to find the whole number, multiply the part by the denominator. Or, according to the two last examples, multiply the dividend by the denominator of the divisor, and divide by the numerator. N. B. This last rule is the same as that in Art. XXIII. This also shows this operation to be division. Note. If the divisor is a mixed number, reduce it to an improper fraction. If of a yard of cloth cost of a dollar, what will a yard cost? It is evident that the whole which is 20 2 dollars. If of a yard of cloth cost a yard? If cost,must cost 24 2 yard will cost 5 times, of a dollar, what is that of; of iss being, 7 times or = 11 dollars must be the price of a yard. If 35 barrels of flour cost 234 dollars, what is that a burrel? 3 16 2 and 23 143. If 2 of a barrel cost 163 of a dollar, of a barrel will cost of 193.1 of 183 is 183 183 being of the price of 1 barrel, 8 times 163 will be the price of a barrel. 8 times 163 60 dollars. Ans. 6 dollars per barrel. 20ཏུ་ 203 20 203 = 1304 203 = The three last examples are of the same kind as those which precede them; the only difference is, that in these, the part which is given, or the dividend, is a fraction or mixed number. In this case the dividend, if a mixed number, must be reduced to an improper fraction; then in order to |