will be just 50, in what year of Christ were they severally born; the question being proposed anno 1806?. (51) A. born 445 years before the year 1733, died anno 1362; B. born 37 years ago, will die 18 years hence; C. born 256 years ago, died 197 years since; D. born anno 1578, lived till within 75 years of the said 1733. The length of these people's lives is severally required. (52) A. born anno 1441, lived till B. was seven years of age, which was 23 years before the Reformation in 1517: B. survived this remarkable æra just 49 years; C. born 9 years after the death of A. lived but till B. was 36 years of age. The sum of the ages of these three persons is required. (53) A. born anno 1438, died at 48 years of age: B. died anno 1502, aged threescore and seventeen; C. in the year 1577, was 22 years of age, and survived that time 54 years; D., anno 1616, had lived just half his time, and died in 1648; E. was 13 years old at the death of D. and 14 years after that was father to F. who was 31 when his son G. was born, who at his grandsire's death was 7 years of age. The years of Christ, wherein these men were born, and the years wherein the first five of them died, are severally réquired. (54) A. born 17 years after C. and 13 before B. died 42 years before King George the Second's inauguration in 1727, aged 47 years: C. died anno 1712, and B. exactly 6 years before him; D. born 23 years before C. died at 64; E. born 11 years after B.'s death, died 12 years after the year 1733; and F. born just in the midway of the interval between the births of A. and D. did not reach the time of E.'s death by 14 years. What is the sum of all their ages, and which of them lived longest? Case 1. When the Multiplier consists of the same Figures in all the places, (i. e.) all 9's or all 7's, &c. then, for each Figure in the Multiplier, annex a cipher to the Multiplicand, and, from the line thus produced, subtract the Multiplicand; and if the repeating Figure is 9, the Remainder will be the Product required; but if any other figure, multiply it into the ninth part of the Remainder; or, for the figure 3, take the third part of the Remainder; and for six, multiply the third part by 2, which will give the required number. In many cases the work may be performed with more ease, likewise more concisely, than is usually practised. IX. COMPOUND MULTIPLICATION TEACHETH to multiply, by one common Multiplier, any sum or number consisting of different denominations. Case 1. When the given quantity doth not exceed 12. RULE. 1. Write the Multiplier, or given quantity, under the lowest denomination of the Multiplicand. 2. Multiply the number of the lowest denomination by the Multiplier, and divide that Product by as many of that as make one of the next higher denomination, the same which you stopped at in Addition; set down the remainder underneath its own place, and add the quotient to the next superior denomination, as you multiply; in this manner proceed with all the other denominations to the highest. s. d. 6 4 9. (1) Multiply 14 17 11 (2) 140 100 (3) 17 (4) 4 Yards of cloth, at 17s. 6d. per yard. (5) 5 Cwt. of cheese, at 31. Os. 6d, per cwt. (6) 7 Ells of Holland, at 7s. 10d. per ell. (7) 8 Pounds of tea, at 18s. 9 d. per lb. (8) 9 Gallons of wine, at 12s. 8d. per gallon. (9) 10 Ankers of brandy, at 21. 6s. 4d. per anker. (10) 11 Barrels of small beer, at 12s. 7d. per barrel. (11) 12 Firkins of butter, at 11. 17s. 6d. per firkin. Case 2. When the given quantity exceeds 12, and is such a number that any two figures in the Multiplication Table, being multiplied together, will produce it. RULE. Multiply the given price by one of those numbers, and the product by the other, which will give the answer. EXAMPLES. (12) 14 Ounces of silver, at 6s. 74d. per oz. (13) 18 lb. of sugar, at 104d. per ib. (14) 27 Quarters of wheat, at 21. 9s. 6d. per quarter. (16) 36 Stone of wool, at 10s. 8d. per stone. (17) 45 Yards of tape, at 24d. per yard. (18) 50 Moidores, at 27s. each. (19) 56 Yards of shalloon, at 2s. 74d. per yard. (24) 96 Yards of Indian dimity, at 1s. 104d. per yard. (29) 144 lb. of tobacco, at 1s. 74d. per lb. Case 3. When the given quantity cannot be produced by the multiplication of two small numbers. RULE. Find the nearest number to its less, by which multiply as before; then, for what is wanting, multiply the price by that number, and add it to the last Product, and the Total will be the Answer. EXAMPLES. (30) 17 Cwt. of Malaga raisins, at 11. 4s. 101d. per cwt. (33) 30 Dozen pair of stockings, at 21. 17s. 6d. per doz. Case 4. When the given quantity consists of 4,, or, RULE. 1 Divide the upper line (the price of one) by 4 for 4, by 2 for; and for, by 2 first for, then divide that Quotient by 2, for; add them to the Product, and the Sum will be the Answer required. EXAMPLES. (40) 35+ Tons of hay, at 31. 6d. per ton. (41) 764 Dozen of red port, at 11. 12s. 10d. per dozen. (42) 17 Barrels of ale, at 36s. 64d. per barrel. (43) 8 Butts of beer, at 41. 6s. 7d. per butt. (44) 100 Acres of land, at 26l. 17s. 6d. per acre. This method of finding the value of any quantity of goods under 100, at any price per yd. lb. &c. is of excellent use to such as buy or sell by retail. But for great quantities, there are other methods much better. (See PRACTICE.) Case 5. Sometimes it may so happen, that your given quantity, though considerably great, may be wrought by the continual product of three numbers, as the following: EXAMPLES. (45) 112 Bushels of oats, at 1s. 104d. per bushel. OF WEIGHTS and MEASURES. (1) Multiply 14 lb. 10 oz. O dwts. 21 grs. by 4. 17 tons, 17 cwt. O qr. 24 lb. by 2. (2) (3) 14 cwt. O qr. 21 lb. O oz. 14 drs. by 7. (16) 74 lasts, 7 qrs. 4 bu. 1 p. by 7. (17)-365 d. 5 h. 48 m. 57 sec. by 12. APPPLICATION. (1) What number, taken from the square of 54, will leave 19 times 46? (2) Suppose 50 men to take a prize, and each man's share comes to 1451., what is the value of the prize ? (3) What is the difference, and what the sum, of six dozen dozen, and half a dozen dozen? (4) A certain island contains 52 counties, every county 42 parishes, every parish 246 houses, and every house 10 persons. I demand the number of parishes, houses, and persons, that are in the whole island? (5) What difference is there between twice eight and twenty and twice twenty-eight: as also, between twice five and fifty, and twice fifty-five? |