What will be the price of 5 loads of cider, each load containing 7 barrels, at 4 dollars a barrel ? Now 5 loads, each containing 7 barrels, are 35 barrels. 35 barrels, at 4 dollars a barrel, amount to 140 dollars. . Or we may say one load comes to 28 dollars, and 5 loads will come to 140 dollars. Or lastly 1 barrel from each load will come to 20 dollars, and 7 times 20 are 140. Thus 7 Or 7 Or 5 5 4 140 140 What is the price of 23 loads of hay, at 34 dolls. aload ? 34 2 It is easy to see that we may multiply by any other number in the same manner. This operation may be expressed as follows. To multiply by a composite number : Find two or more numbers, which being multiplied together, will produce the multiplier ; multiply the multiplicand by one of these numbers, and then that product by another, and so on, until you have multiplied by all the factors, into which you had divided the multiplier, and the last product will be the product required.,7 If the multiplier be not a composite number, or if it cannot be divided into convenient factors : Find a composite number as near as possible to the multiplier, but smaller, and multiply by it according to the above rule, and then add as many times the multiplicand, as this number falls short of the multiplier. I V. I have shown how to multiply any number by a single figure; and when the multiplier consists of several figures, how to decompose it into such numbers as shall contain but one figure. It remains to show how to mulply by any number of figures; for the above processes will not always be found convenient. The most simple numbers consisting of more than one figure are 10, 100, 1000, &c. It will be very easy to multiply by these numbers, if we recollect that any figure written in the second place from the right signifies ten times as many as it does when it stands alone, and in the third place, one hundred times as many, and so on. If a zero be annexed at the right of a figure or any number of figures, it is evident that they will all be removed one place towards the left, and consequently become ten times as great; if two zero's be annexed they will be removed two places, and will be one hundred times as great, &c. Hence, to multiply by any number consisting of 1, with any number of zeros at the right of it, it is sufficient to annex the zeros to the multiplicand. men VI. When the multiplier is 20, 30, 40, 200, 300, 2000, 4000, &c. These are composite numbers, of which 10, or 100, or 1000, &c. is one of the factors. Thus 20 = 2 x 10; 30 = 3 x 10; 300 = 3 x 100; &c. In the saine manner 387000 = 387 X 1000. How much will 30 hogsheads of wine come to, at 87 dollars per hogshead ? Operation. 87 3 261 dolls. price of 3 hhds. 10 2610 dolls. price of 30 hhds. More simply thus 87 30 2610 dolls. price of 30 hhds. It appears that it is sufficient in this example to multiply by 3 and then annex a zero to the product. If the number of hogsheads had been 300, or 3000, two or three zeros must have been annexed. It is plain also that, if there are zeros on the right of the multiplicand, they may be omitted until the multiplication has been performed, and then annexed to the producto VII. A man bought 26 pipes of wine, at 143 dollars a pipe ; how much did they come to ? 26 = 20 + 6. The operation may be performed thus: 143 6 858 dolls. price of 6 pipes. 143 2860 dolls. price of 20 pipes + 858 dolls. price of 6 pipes = 3718 dolls. price of 26 pipes The operation may be performed more simply thus : 143 2860 dolls. price of 20 pipes + 858 dolls. price of 6 pipes = 3718 dolls. price of 26 pipes 143 858 dolls. price of 6 pipes + 2860 dolls. price of 20 pipes = 3718 dolls. price of 26 pipes If the wages of 1 man be 438 dollars for 1 year, what will be the wages of 234 men, at the same rate ? Operation. 438 87600 dolls. wages of 200 men + 13140 do. wages of 30 men + 1752 do. wages of 4 men 102492 dolls. wages of 234 med Or thus, 438 1752 dolls. wages of 4 men of 13140 do. wages of 30 mnen + 87600 do. wages of 200 men = 102492 dolls. wages of 234 men When we multiply by the 30 and the 200, we need not annex the zeros at all, if we are careful, when multiplying by the tens, to set the first figure of the product in the tens' place, and when multiplying by hundreds, to set the first figure in the hundreds' place, &c. Operation. 438 1752 1314. 876.. 102,492 If we compare this operation with the last, we shall find that the figures stand precisely the same in the two. We may show by another process of reasoning, that when we multiply units by tens, the first figure of the product should stand in the tens' place, &c.; for units multiplied by tens ought to produce tens, and units multiplied by hundreds, ought to produce hundreds, in the same manner as tens multiplied by units produce tens, &ck If it take 853 dollars to support a family one year, how many dollars will it take to support 207 such families the same time? Operation. 853 In this example I multiply first by the 7 207 units, and write the result in its proper place; then there being no tens, I multiply 5971 next by the 2 hundreds, and write the first 1706 figure of this product under the hundreds of the first product; and then add the results 176571 in the order in which they stand. |