21. James has 125 nuts, and William has 5 times as many; how many nuts has William? Ans. 625 nuts. 22. A merchant has 9 boxes of raisins, each containing 15 pounds; how many pounds do all the boxes contain? Ans. 135 pounds. 23. A farmer sold 426 pounds of cheese at 7 cents a pound; how many cents did he receive for the whole? Ans. 2982 cents. 24. If you pay 7 dollars for one yard of broadcloth; how many dollars must you pay for 6 yards? Ans. 42 dollars. 25. If the wages of one man for a year be 132 dollars; what will the wages of 12 men be? Ans. 1584 dollars. 26. There are 24 hours in a day, and 7 days in a week; how many hours are there in one week? Ans. 168 hours. 27. A teacher had 6 classes in his school, and 8 scholars in each class; how many scholars had he in all? Ans. 48 scholars. 28. A farmer bought 626 acres of land at 3 dollars an acre; how many dollars did he pay for the whole? Ans. 1878 dollars. 29. A lady bought 9 yards of cambrick at 56 cents a yard: how many cents did she pay for the whole? Ans. 504 cents. 30. Jane bought 17 yards of riband at 5 cents a yard; how many cents did she pay for the whole? Ans. 85 cents. 31. A merchant bought 55 firkins of butter at 12 dollars a firkin; how many dollars did he pay for the whole? Ans. 660 dollars. Q. When the multiplier exceeds 12, how must it be placed? A. It must be placed under the right hand figures of the multiplicand, with units directly under units, tens under tens, hundreds under hundreds, &c. Q. Where must you begin to multiply? A. At the right hand figure of the multiplier, and multiply by each figure of the multiplier separately. Q. Where must the first figure of each product be placed? A. It must be placed directly under its multiplier, or the figure multiplied by. Q. How do you find the total product of the several products? A. The several products must be added together according to the rules of Addition, in the same order as they stand, and their sum will be the total product. EXAMPLES For Exercise on a Slate. 1. There are in a hogshead 63 gallons; how many gallons are there in 24 hogsheads? Ans. 1512 gallons. EXPLANATIONS. You must begin with the figure 4 in the multiplier, and say, 4 times 3 are twelve, that is, twelve units, set down 2 in the place of units and carry one: thus, 4 63 multiplicand. 252 four times 63. 126 twenty times 63. 1512 twenty-four times 63. times 6 are twenty-four, and the one ten carried makes twenty-five, that is, twenty-five tens; set down 5 in the place of tens, and 2 in the place of hundreds. You will then see that the product of 4 times 63 is 252. Beginning with the 2, the next figure in the multiplier, you must say, 2 times 3 are six, set down the 6 directly under the 2, in the place of tens, for it is not six units but six tens; as you will readily perceive, the 2, by which you multiplied, being in the place of tens, and not units, as the figure 4, the first figure of the multiplier is. It is, therefore, twenty times 3, which is sixty, as the 2 stands in the place of tens, and, consequently, represents twenty. As there are 6 tens and no hundreds, there is nothing to be carried to the next figure, so you must begin anew, and say, 2 times 6 are twelve, that is, twelve hundreds; for the 2 in the multiplier, and the 6 in the multiplicand, are both in the place of tens; it is, therefore, twenty times sixty, which, as I have just told you, make twelve hundreds. You must set down 2 in the place of hundreds, and carry one to the place of thousands; or, rather, set down the whole amount 12, as there are no more figures to multiply. You will then see that the product of 20 times 63 is 1260. The two products added together make 1512, which is the total product of 24 times 63. In order to have you fully understand the principles of this operation, I have worked out the sum at length, that you may be enabled to work any sum of this description without difficulty. Thus, beginming with the figure 4, as before, you must say, 4 times 3 are twelve, that is, twelve units; set down the 2 in the place of units, and the 1 in the place of tens; and then say, 4 times 60, as the 6 is in the 63 multiplicand. 12 four times 3. 60 twenty times 3. 1200 twenty times 60. place of tens, are 240, that is, 24 tens; set down 4 in the place of tens, 2 in the place of hundreds, and a cipher in the place of units; and proceeding to the next figure, the 2, in the multiplier, you must 1512 twenty-four times 63. say, 20 times 3, as the 2 is in the place of tens, are 60, that is, 6 tens; set down 6 in the place of tens, and a cipher in the place of units; and then say, 20 times 60, as the 2 and 6 are both in the place of tens, are 1200, that is,. 12 hundreds; set down 1 in the place of thousands, and 2 in the place of hundreds, a cipher in the place of tens, and a cipher in the place of units. Then add these several products together, and you will have 1512, the total product as before. I think you will now be able to understand why the first figure of each product is placed directly under the figure by which you multiply; and you will also be convinced of the importance and advantage of "CARRYING ONE FOR EVERY TEN,' as in Addition; this last operation being much more tedious and longer than the first. PROOF. When the multiplier exceeds 12, you may prove multiplication by making the multiplicand the multiplier. Thus, as in the present case, place 24 for the multiplicand, and 63 for the multiplier; and proceed as be 24 multiplicand. 63 multiplier. 72 144 1512 fore, placing the first figure of the product directly under its multiplier, and then add the products together; and if the total product be the same as before, the work is right; for it is evident, that 63 times 24 are the same as 24 times 63. 2. Multiply 3164251 by 327. EXPLANATIONS. Ans. 1034710077. 3164251 multiplicand. 327 multiplier. 22149757 6328502 9492753 Beginning with the 7 at the right hand, as in the former example, you must proceed with that and the 2 in the place of tens as before; and proceeding to the 3, in the place of hundreds, you 1034710077 product. must say, 3 times 1 are 3, that is, three hundreds, as the three is in the place of hundreds, it is three hundred times one unit; and, therefore, you perceive you must set down the 3 under the 3 in the place of hundreds; and proceeding with the next figure, you must say, 3 times 5 are fifteen, that is, fifteen thousands, as the 5 is in the place of tens, and the 3 in the place of hundreds, it is three hundred times fifty, or five tens; and, therefore, you perceive you must set down the 5 in the place of thousands, and carry one to the place of tens of thousands; and so you must proceed with each figure of the multiplicand. It is very important that you observe the method pursued in ranging these lines of products; and, indeed, it is the only thing of any importance to be learned in this rule. Thus, in the preceding example, if you had placed the product of the 2 and the 3 directly under the product of the first figure, the 7, |
