and then have added the products, you would have only repeated the multiplicand twelve times, instead of 327 times; for when you multiply by 7, the first figure of the multiplier, you repeat the multiplicand seven times; and if you multiply by the 2, and place the product directly under the product of the first figure of the multiplier, you repeat it two times; and, again, if you multiply by the 3, and place the product directly under the product of the first figure of the multiplier also, you repeat the multiplicand three times; and 7 times repeated, 2 times repeated, and 3 times repeated, make twelve times repeated, which is the amount of the 7, 2, and 3, the figures of the multiplier added together.

To make this perfectly clear to you, I have worked it out below, thus:

Having now, as I trust, fully explained this part of Multiplication, I shall give you a few more examples, and pass to the next part of the subject.

Note.-TO TEACHERS. The preceding EXPLANATIONS are of great importance to the scholar, and they should be read by him with more than usual care and attention.

17. A merchant bought 526 barrels of flour at 13 dollars a barrel; how many dollars did he pay for the whole? Ans. 6838 dollars.

18. A merchant had 28 chests of tea, each weighing 96 pounds; how many pounds were there in all? Ans. 2688 pounds.

19. A farmer had 25 acres of wheat, each acre of which produced 22 bushels of wheat; how many bushels had he in all? Ans. 550 bushels.

20. If a steam-boat run 15 miles in one hour, how many miles can it run in 24 hours? Ans. 360 miles. 21. A farmer sold to a drover 24 cows at 18 dollars apiece; how many dollars did he receive for them? Ans. 432 dollars.

22. A merchant bought 446 pieces of linen, each

piece containing 24 yards; how many yards were there in all? Ans. 10704 yards.

23. To the Senate of the United States each of the 24 states sends 2 members; how many members are there in the Senate of the United States? Ans.

48 members.

24. A drover bought 125 horses at 115 dollars each; how many dollars did he pay for the whole? Ans. 14375 dollars.

25. A merchant bought 432 barrels of beef at 15 dollars a barrel; how many dollars did he pay for the whole? Ans. 6480 dollars.

Q. When the multiplier is a composite number, that is, when any two numbers in the multiplication table, being multiplied together, will produce a number exactly equal to the multiplier, how must you multiply?

A. Multiply first by one of those numbers or component parts; then multiply that product by the other number, and the last product will be the total product.

EXAMPLES

For Exercise on a Slate.

1. A farmer sold his farm, containing 325 acres, at 21 dollars an acre; how many dollars did he receive for the whole? Ans. 6825 dollars.

EXPLANATIONS.

Here, in this example, 3 and 7 are the component parts of 21; for 3 times 7 are 21. You must first

325 acres.

3 an acre.

975 price at 3 dls. an acre.

multiply by the 3, which will repeat the multiplicand three times; that is, it shows the price of the land at 3 dollars an acre; and you must then multiply this product, 6825 price at 21 dls. an acre. 975, by the 7, which will repeat it seven times; that is, it shows a number seven times as large as the first product of the 325, repeated three times; and, therefore, it shows the price of the land at twenty-one dollars, as 3 times 7 are 21.

In order to make this operation perfectly plain to you, I have multiplied the 325 by 21 directly; and you will thus be enabled to perceive that the same result is produced.

(4.) 842534

325

21

6825

42

8. A drover bought 28 cows of a farmer at 16 dollars each; how many dollars did he pay for all? Ans. 448 dollars.

9. There are 365 days in a year, and 24 hours in each day; how many hours are there in a year? Ans. 8760 hours.

10. A lady bought 35 yards of cambrick at 49 cents a yard; how many cents did she pay for the whole? Ans. 1715 cents.

11. A gentleman bought 27 yards of camlet at 81 cents a yard; how many cents did he pay for the whole? Ans. 2187 cents.

12. A farmer bought 275 acres of land at 28 dollars an acre; how many dollars did he pay for the whole? Ans. 7700 dollars.

Q. When there are ciphers at the right hand of either the multiplier or multiplicand, or both, how must you multiply?

A. The significant figures must be placed as if there were no ciphers at the right hand, and must be multiplied without any regard to the ciphers.

Q. What must be done with the ciphers in the final product?

A. There must be as many ciphers added at the right hand of the total product, as there are ciphers at the right hand in the multiplier and multiplicand.

EXAMPLES

For Exercise on a Slate.

1. A merchant bought 123 penknives at 20 cents apiece; how many cents did he pay for the whole?

Ans. 2460 cents.

EXPLANATIONS.

You must first place the 2, of the multiplier, under the 5, the right hand figure of the multiplicand, and multiply as before directed. You will thus repeat