11. 10. 1002003004.00 98087076065 10000006 APPLICATION. 1. From 360418 tons, take 293752. 2. From 100046 acres, take 10009. 3. What is the difference between 1735 and 1897348 hours? 4. How much do 540312 days exceed 7953? 5. How much are 30491 gallons less than 57321469 ? 6. If the distance from Hallowell to Savannah, through Washington, be 1268 miles, and that from Washington to Savannah, 658 miles; how far is Washington from Hallowell? 7. From Hallowell to the city of New-York is 383 miles. Now, if a man should travel 10 days from Hallowell towards New-York, at the rate of thirty-six miles each day; how far would he then be from that city? 8. If a farmer kills six hogs, which weigh two hundred and fifty-four, one hundred and ninety-seven, two hundred and sixteen, two hundred and forty-nine, three hundred and twelve, and three hundred and sixty-three, and markets one thousand weight of pork; what quantity does he reserve for his own use? SIMPLE MULTIPLICATION. MULTIPLICATION is finding the amount of any given number, by repeating it any proposed number of times; as, 4 times 7 are 28. The number to be multiplied is called the multiplicand. The number which multiplies is called the multiplier. The number arising from the operation is called the product. The multiplicand and multiplier are called factors; and if these are of one denomination it is called Simple Mul tiplication. 714 21 28 35|42|49|56| 63 70 77 84 10 20 30 40 50 50 70 80 9010010120 |24|33|44|55|66|77|88| 99|110|121|132| 12|24|36|48 60|72|84|96|108||20|13|144 USE of the Table in Multiplication. Find the multiplier in the left hand column, and the multiplicand in the uppermost line; and the product is in the common angle of meeting, or against the multiplier, and under the multiplicand. To use the above Table in Division, seek your divisor in the left hand column; then run your eye along the line, to the right hand, till you come to your dividend; and the figure in the top line, of the same column, will be the quotient, or number of times the divisor is contained in the dividend. CASE I-When the multiplier is not more than twelve. RULE.-Multiply each figure in the multiplicand by the multiplier, beginning at the right hand side, and setting down the whole of such products as are less than ten; but for such as are just equal to a certain number of tens, write down 0, and carry 1 for each ten to the next product; and for such as exceed a certain number of tens, set down the excess, and carry for the tens as before. EXAMPLES. 1. What number is equal to 4 times 365? CASE II.-When the multiplier consists of several figures. RULE.-Set the multiplier under the multiplicand, so that units may be under units, tens under tens, &c. then find the product for each figure in it, as in the first case, not regarding in what order the lines are found, provided the first figure in each stand straight below its respective multiplier. Add all the lines of products together in the same order as they stand, and the sum will be the whole product required. PROOF.-Make the former multiplicand the multiplier, and the multiplier the multiplicand, and proceed as before; and the new product will be the same as before, when the work in both is right. Or, add together the figures first of one factor, and then of the other, casting out all the nines in the sums of each, as often as they amount to 9. Multiply the two remainders, if any, together, and the nines cast out of their product, will leave the same remainder as the nines cast out of the answer, when the work is right. The first remainder may be set at the left side of a cross or X; the second at the right; that arising from their product at the top; and that arising from the answer at the bottom; if the answer be right, the top and bottom figures will be alike. CONTRACTIONS IN MULTIPLICATION. CASE I. When there are ciphers at the right hand of one or both of the factors. RULE.-Proceed as before, neglecting the ciphers, and to the right hand of the product, place as many ciphers as are in both the numbers. CASE II.-When the multiplier is the product of two or more numbers. RULE.-Multiply once successively by each of those numbers instead of using the whole multiplier at once. 1. What will 87 horses for shipping come to, at 52 dollars per head? Ans. 1924 dols. 2. What will 587 firkins of butter come to, at 7 dollars per firkin? Ans. 4109 dols. 3. What will 367 acres of land cost, at 13 dollars per acre? Ans. 4771 dols. 4. If a barrel of pork cost 18 dollars what will 857 barrels be worth? Ans. 15426 dols. 5. What will be the worth of 924 tons of potash, if one ton sell for 95 dollars? Ans. 87780 dols. 6. A merchant having traded ten years, found he was worth 13000 pounds. His books showed that the last three years he had cleared 873 pounds a year; the three preceding but 586 pounds a year; and before that but 364 pounds a year. With what sum did he begin busiAns. 7167 pounds. ness? 7. Trajan's bridge over the Danube is said to have had twenty piers to support the arches, every pier being 60 fet thick, and some of them 150 feet above the bed of the river; they were also 170 feet asunder. Pray, how wide was the river in that place? and how much did this bridge exceed in length that at Westminister, in England, which is about 1200 feet from shore to shore, and is supported by 11 piers, making the number of arches 12? 4770 feet wide, and 3570 feet longer than Westminster bridge. Aus. |