Ans. 6 miles 5 fur. 39 poles. rod. Ans. 3 yds. 9 inc. 6. From 83 yards take 1 Ans. 30 gallons 1 quart. of a hundred weight take of a pound. 8. From 94 Ans. 2qrs. 27 lbs. 4 oz. MULTIPLICATION OF VULGAR FRACTIONS. RULE. Reduce whole and mixed numbers to improper fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator; and if it be an improper fraction, bring it to a mixed one. 1. Multiply by . EXAMPLES. Ans. 8 13 DIVISION OF VULGAR FRACTIONS. RULE. Prepare the fractions as before; then invert the divisor, and proceed exactly as in multiplication. 1. Divide by t EXAMPLES. Thus, x=2 Ans. RULE OF THREE IN VULGAR FRACTIONS. RULE. Prepare the fractions as before taught; then state your question, and invert the first term in the proportion. Then multiply the three numerators together for a new numerator, and all the denominators together for a new denominator, and that will be the answer in the same name with the second term. EXAMPLES. 1. If of a yard of muslin cost 37 cents, how much will 42 yards cost, at that rate? Ans. 23 dolls. 81 cts. dollars; what is the value 2. Bought of a ship for 940 of the whole ship, at that rate? Ans. 1567 dollars 913 cents. Ans. 3 cents. 3. Sold 33 tons of iron for 152,8 dollars; how much will 1 pounds cost, at that rate? 4. At of a dollar a yard, how much will 80 yards come Ans. 60 dollars. to ? 5. If I paid 1 cents for 13 herrings, how many can I get for 11 cents? Ans. 11 herrings. 6. Bought 3 hhds. of tobacco, each weighing 73 cwt. at the rate of 74 cents a pound. How much does the tobacco Ans. 195, dollars. 7. If of a ship be worth 1000 dollars, what part of her may be purchased for 800 dollars ? Ans. . come to ? RULE OF THREE INVERSE IN VULGAR FRACTIONS. RULE. Prepare the fractions, and state the question for inverse proportion; then invert the third term, which is your divisor, and multiply the three numerators together for a new numerator, and the denominators together for a new denominator, and that will be the answer. 1. How much cloth, that is of a yard wide, will line 58 yards, that is 2 yards wide? yda. yds. yd. As 12:51: Thus, × ×=335=16,1 Ans. 2. If a man performs a journey in 3 days, when the days are 12 hours long, in how many days the days are 94 hours long? 3. When the days are 94 hours long, journey in 45 days. In how many when the days are 124 hours long? 50 117 will he do it, when 4. If a man performs a journey in 3 are 124 hours long, how long must the days be, when he will perform the same journey in 4,50 days? 117 Ans. 93 hours. 117 5. When a man performs a journey in 4,50 days, when the days are 93 hours long, how long must the days be, when he will perform the same journey in 3 days? Ans. * 124 hours. 6. If the 4 of 6 be 3, how much will be the of 20? (Direct Proportion.) Ans. 71. SECTION IV. PRACTICE. RULE. Practice is a contraction of the Rule of Three Direct, when the first number is 1, or a unit, and is a concise method of calculating most questions that occur in business, where sterling money is reckoned; and for which reason it was, and is called Practice. But in this country, this Rule is almost useless; for which reason, I will not give many questions in it. Multiply the whole numbers of the given numbers together, and take aliquot parts for the rest. 1. What is the amount of 146 yards of cloth, at 1 dollar 50 cents per yard? When the price is the fractional part of a dollar, or a cent. RULE. Multiply the given number by the numerator, and divide the product by the denominator, and the quo tient will be the answer. EXAMPLES. 1. What will 240 yards of cloth come to, at of a dollar per yard ? 240 720-4-180 dollars. Ans. 2. What will 3 cwt. 2 qrs. 14 lbs. of sugar come to, at of a dollar per pound? Ans. 25 dolls. 37 cts. lar 3. What is the price of 4 cwt. and 16 lbs. of butter, at of a dollar a pound? Ans. 58 dollars. 4. What is the cost of 18 cwt. 3 qrs. of hay, at of a dolper cwt. ? Ans. 3 dolls. 75 cts. 5. What is the amount of 23 cwt. 1 qr. 21 lbs. of iron, at 4 dollars per cwt.? Ans. 101 dolls. 564 cts. 6. Bought three barrels of salt, each containing 5 bushels 2 pecks, at of a dollar per bushel. What does the salt amount to? Ans. 10 dolls. 31 cts. 7. Bought four boxes of tobacco pipes, the first two boxes contained each 73 gross, and the other two contained each 14 score 1 dozen and 4, at the rate of 3 of a cent for every two tobacco pipes. What is the whole amount? Ans. 10 dolls. 82 cts. 8. Sold 17 cwt. 3 qrs. 19 lbs. of sugar, at 10 dolls. 94 cts. per 112 lbs. How much is the amount? Ans. 196 dollars 4 cents. 9. Bought six hampers of cheeses, each hamper contained eight cheeses, and each cheese weighed 123 lbs. at 6 dolls. the 112 lbs. How much is the amount of the cheese? Ans. 36 dollars. 10. What is the amount of 324 barrels of flour, each weighing 186 lbs. at 23 dollars per 112 lbs.? Ans. 127740 dollars. 11. How much is the amount of 19 tons 19 cwt. 3 qrs. 27 lbs. at 9 eagles 9 dollars 9 dimes 9 cents 94 mills the ton? Ans. 199 eag. 9 dolls. 9 dim. 6 cts. 78088 mills. TARE AND TRET Tare and Tret are practical Rules for deducting certain allowances, which are made by merchants, in buying and selling goods, &c. by weight; and in which are noticed the following. |