123 20 the multiplicand only two times; but as the cipher is at the right hand of the product, it gives the product of the 2 its local value; that is, it places it in the place of tens, which 2460 is ten times more than its simple value; and ten times the simple value of two is twenty; and, therefore, the multiplicand is repeated twenty times. 2. There are in one square mile 640 acres; how many acres are there in 400 square miles? Ans. 256000 acres. EXPLANATIONS. 640 400 Place, as before directed, the first significant figure of the multiplier directly under the first figure of the multiplicand, and multiply; then to the product add as 256000 many ciphers as there are in the multiplicand and multiplier, and then the work is done. You will readily perceive that, in the preceding example, you do not simply multiply by 4, but by 4000, as the 4 is, by its location, with three ciphers on the right, placed in the place of thousands; the product is, therefore, 4000 times 64, and not simply 4 times 64. 6. A gentleman owns 20 houses, for the rent of each of which he receives 300 dollars; how many dollars does he receive a year for the rent of all of them? Ans. 6000 dollars. 7. A merchant bought 150 tuns of pearlash at 120 dollars a tun; how many dollars did he pay for all? Ans. 18000 dollars. Q. When ciphers are intermixed with the figures of the multiplier, how must you multiply? A. The ciphers must be omitted, and the first figure of each product must be placed directly under its respective multiplier. EXAMPLES For Exercise on a Slate. 1. A merchant bought 106 hogsheads of wine at 204 dollars a hogshead; how many dollars did he pay for the whole? Ans. 21624 dollars. EXPLANATIONS. Beginning, you must multiply by the 4; and, omitting the cipher, you must multiply by the 2, and place the product directly under the 2; for the 2, in the multiplier, is in the place of hundreds, and the product must, therefore, be in the place of hundreds. (2.) 120013 106 204 424 212 21624 408 960104 480052 48965304 (3.) 374957 2009 3374613 749914 753288613 Q. When the multiplier is 10, 100, 1000, or 1, with any number of ciphers annexed to it, how must you multiply? A. There must be as many ciphers annexed to the multiplicand as there are ciphers in the multiplier, and the multiplicand so increased will be the product required. EXAMPLES For Exercise on a Slate. 1. A merchant bought 76 barrels of flour at 10 dollars a barrel; how many dollars did he pay for the whole? Ans. 760 dollars. EXPLANATIONS. 76 multiplicand. 10 multiplier. 760 product. Here, in this example, you merely add a cipher to the 76, the multiplicand, and the work is done; for you will remember, that any figure, when it is removed one place toward the left hand, is increased in value tenfold; therefore, if you wish to multiply any number by 10, you need only write a cipher at the right hand of it: thus, 10 times 76 are 760; for the 6, which was units before, is now made tens by the addition of the cipher, being removed one place toward the left hand; and the 7, which was tens before, is now made hun dreds; also, if any figure be removed two places toward the left hand, it is increased in value 100 times; if three places it is increased 1000 times, &c.; consequently, when the multiplier is 10, 100, 1000, &c., you must annex as many ciphers to the multiplicand as there are ciphers in the multiplier, and the multiplicand so increased will be the required product. 7. A farmer sold 84 bushels of wheat at 100 cents a bushel; how many cents did he receive for all? Ans. 8400 cents. 8. A general paid 1000 soldiers 132 dollars each; how many dollars did he pay in all? Ans. 132000 dollars. 9. A drover bought 75 horses at 100 dollars each: how many dollars did he pay in all? Ans. 7500 dollars. Note.-To TEACHERS. The learner should be exercised in a variety of examples, until he has become accustomed to every operation, and is able to multiply any sum without errour; and the teacher should endeavour to convince the scholar, that multiplication, by a number of places of figures, is a mere repetition of the operation with which he is already acquainted, and only requires a little more attention, and more accuracy in placing the figures. |