10. A butcher gives 41 dollars a piece for 9 oxen ; what does he give for them all? Ans. 369 dollars. NOTE 1.-When the product of two figures is more than 9, and an exact number of tens, set a cipher under the figure multiplied, and add as many ones to the next product, as there were tens; but if the product be not an exact number of tens, set down the right hand figure, and carry the tens as before. 11. What is the product of 9766, multiplied by 2? Operation. 976 6 2 1953 2 of the same. Illustration.The reason for carrying the tens to the left hand product, is founded in the nature of simple numbers; for 1 in any column, except the right hand one, is equal to 10 in the column to the right hand 12. If the multiplicand be 16705, and the multiplier 6, what is the product? Operation. 6 1 0 0 2 3 0 Explanation. When we have tens to add to the next product, if the next be occupied by a cipher, the tens must be placed directly beneath it, as in this question. 13. Multiply ten thousand, six hundred and twenty-five by 8. Prod. 85'000. 14. Multiply one hundred and sixteen thousand, nine hundred and sixty-nine by seven. Prod. 818'783. 15. A certain army was composed of nine battalions; each battalion consisted of six hundred and fifty-three men; how many men were there in the army? Ans. 5'877. Two lines crossing each other thus X, are used as a sign of Multiplication; and signify that the number before it is to be multiplied by the number after it; thus, 62 x2=124; which is read 62 multiplied by 2 is equal to 124. The sign of multiplication is frequently expressed by the word into; thus, 53 into 4 212, and is read, 53 into 4 equals 212. EXAMPLES. 16. 396 X 3=1188. 17. 2408 X 5=12040. 18. 7034 into 6=42204. 19. 1928 into 7=13496. The pupil may ascertain whether he has worked the 8 last examples correctly, by adding up his products, the sum of which must equal 2'249'318. 28. A boy buys 15 lemons for 4 cents each; what does he give for them all? Ans. 60 cents. 29. A merchant sells a roll of riband, measuring 28 yards, for 8 cents a yard; what does he obtain for the roll? Ans. 224 cents. 30. What will 256 pounds of nails come to, at 6 cents a pound? Ans. 1536 cents. Note 2.-100 cents make 1 dollar, therefore there will always be as many dollars in any number of cents as there are hundreds. Separate the two right hand figures from the others by a comma; those to the left will signify dollars, and those to the right, cents. This sign is used to denote dollars. All the figures after the sign of dollars, to the comma, denote dollars, and those to the right of the comma, cents, if no more than two places; but if no comma is inserted, all the figures represent dollars. 31. A merchant sells 671 yards of tow cloth at 9 cents a yard; what is the price of the whole? Ans. $60,39. 32. What will 6 hogsheads of rum come to, at 4555 cents a hogshead? Ans. $273,30. 33. What will 89 pounds of beef cents a pound? 34. What will 101 boxes of sugar dollars a box? come to at 7 Ans. $6,23. come to, at 9 Ans. $909. When the multiplier consists of several figures. RULE. Place the multiplier under the multiplicand, units under units, tens under tens, hundreds under hundreds, &c. Multiply the multiplicand by each sig nificant figure in the multiplier, beginning with the figure in units' place, and write the first figure of each product directly under the figure by which you multiply. Add the several products together, their sum will be the product of the multiplicand multiplied by all the figures in the multiplier. 35. What is the product of 26412, multiplied by 32 ? Operation. 2 64 12 32 5 2 8 2 4 product of 2. 8 4 5 1 8 4 product of 32. 36. What is the product of 90821, multiplied by 432? Operation. 9082-1 432 18 1 6 4 2 product of 2. 2 7 2 4 6 3 3 6 3 2 8 4 product of 3 tens, or 30. product of 4 hundred. 3 92 3 4 6 7 2 product of 432. 37. What is the product of 8765401, multiplied by 5432? Ans. 47'613'658'232. 38. Let the multiplicand be seven hundred sixtyfive thousand, four hundred and two, and the multiplier 263; what is the product? Ans. 201'300'726. Illustration of the last rule.-The product of the unit figure in the multiplier, is found in the same manner as was shown in the illustration of the first rule. Each 1 in the place of tens, denotes 10 units, and the multiplicand must be brought into the product once for every single unit contained in any figure standing in tens' place. When we multiply the unit figure of the multiplicand by the tens in the multiplier, we make use of the same expressions as though the multiplier were in units' place; but by removing the product of the unit figure of the multiplicand into tens' place in the product, it signifies ten times as many as it would, if it stood in units' place. By removing the product of any other figure, when multiplied by the figure standing in tens' place in the multiplier, it denotes ten times as many as it would, if it stood directly under that figure of the multiplicand; consequently the product of any figure standing in tens' place in the multiplier, will express ten times as many as it would, if it stood one place further to the right hand. In multiplying by a figure standing in hundreds' place, we place the product of every figure in the multiplicand, two places further to the left, than we should if the figure by which we multiply, had stood in units' place; therefore the product must represent one hundred times as many as it would, if it were removed two places further to the right. The same might be shown of the product of a figure standing in any other place; therefore, by adding the several products together we obtain a number which is made up of the multiplicand, taken as many times as the multiplier contains an unit. Let it be required to multiply 54321, by 321. Operation. 5 4 3 2 1 1 7 4 3 7 0 4 1 When we multiply by the 2 in the multiplier, we say, twice 1 are 2; but as the 2 is 2 tens, our meaning is, that 20 times 1 are 20, and we obtain 20 by setting the We 2 in tens' place. also say, 2 times 2 are 4, but by setting the 4 in hundreds' place, the result is, that 20 times 20 are 4 hundred. In like manner, we say, 3 times 1 are 3, but the 3 is 3 hundred, and the product becomes the same by placing it in the third place. The operation of this example may be performed by separating the multiplier into 3 parts, as follows: 5 4 3 2 1 1 54321 1.0 8 6 4 20 1 6 2 9 6 3 0 0 1 6 2 9 6 3 0 0 is 3 hundred times 54321. 1 0 8 6 4 2 0 is 20 times 54321. 5 4 3 2 1 is once 54321. 1 7 4 3 7 0 4 1 the product 54321, multiplied by 321. 39. A gentleman has a field of corn consisting of 196 rows, each row has 219 hills. the field? How many hills in Ans. 42'924. Explanation. The number of hills in each row must be taken as many times as there are rows. 40. What is the product of 612'813, multiplied by eleven thousand, one hundred and twelve? Ans. 6'809'578'056. 41. A merchant sells 309 bales of cotton at 41 dollars a bale; how many dollars does he receive for the whole ? Ans. 12'669. 42. If one hundred and twenty-five men receive each one hundred and fifteen dollars for one year's labour, how much do they all receive. Ans. $14'375. 43. If a man spend 65 cents a day, what will be his expense for one year, it being 365 days? Ans. $237,25. PROOF. Multiply the multiplier by the multiplicand, and if the product be the same number as the product |