18. A man travelled 26 days, travelling 47 miles a day. How far did he travel in the whole time?

19. A merchant sold 342 tons of iron, at 142 dollars per ton. What was the price of the whole?

20. If a coach wheel turn round 346 times in 1 mile, how many times will it turn round in the distance from New York to Philadelphia, it being 95 miles?

21. A prize was divided among 47 men, and each man received 25 dollars. How much was the prize? 22. What sum of money must be divided among 45 men, so that each man shall receive 59 dollars?

23. A merchant bought 7 bales of cloth, each bale containing 11 pieces, and each piece, 29 yards. How many pieces, and how many yards were there?

24. A trader bought 9 pieces of cloth, each piece containing 42 yards, at 6 dollars a yard. How many yards were there, and what did the whole cost?

25. If hats are worth 7 dollars apiece, what are 15 boxes of hats worth, each box containing 24 hats?

How

26. The distance from Washington to Boston is 436 miles; and in each mile there are 320 rods. many rods is it from Washington to Boston?

27. The distance from Washington to New-Orleans is 1255 miles. How many rods is it?

28. What is the value of the hay, that is produced on 16 farms; allowing each farm to produce 62 tons, and allowing the hay to be worth 12 dollars a ton?

29. There are 24 hours in a day, and 365 days in a year. If a ship sail 7 miles in an hour, how many miles will she sail in a year?

30. How many days' work can 9 men do in 24 days? 31. How many days will it take 1 man to perform a piece of work, that 9 men will perform in 24 days?

32. How many days will it take 1 man to build a piece of road, that 13 men can build in 47 days?

33. How many men must be employed to do a piece of work in 1 day, that 11 men can perform in 18 days? 34. Suppose that a ship's crew of 13 men will drink 82 gallons of water in 14 days, how long would the same quantity of water last 1 man?

SECTION 4.

ABBREVIATIONS.

When there are ciphers standing between figures, in the multiplier, they may be disregarded.

1. What is the product of 12318

multiplied by 7004?

12318

7004

49272

86226

86275272

2. What is the product of 9651 multiplied by 304 ? 3. How many are 1001 times 57 906?

4. How many are 905 times 820 437 ?

Ciphers on the right hand of the multiplier or multiplicand may be disregarded till the multiplication is performed, and then placed on the right hand of the product

5. What is the product of 5763 multiplied by 3600 ?

5763

3600

34578

17289

20746800

6. What is the product of 158 multiplied by 350 ? 7. How many are 800 times 369 ?

8. How many are 40 times 4728 ?

Ciphers on the right hand of the multiplier and mul tiplicand both, may all be disregarded in multiplying and finally placed on the right hand of the product.

9. What is the product of 46000 multiplied by 340.

46000

340

184

138

15640000

10. What is the product of 8370 multiplied by 240?

11. How many are 90 times 761000?

12. How many are 5700 times 6800?

When the multiplier is 10, 100, 1000, &c. merely place the ciphers of the multiplier on the right hand of the multiplicand, and it becomes the product.

13. What is the product of 5 multiplied by 10? 14. What is the product of 17 multiplied by 100? 15. What is the product of 49 multiplied by 1000 ? 16. In 1 dollar there are 100 cents. How many cents are there in 6 dollars?

17. How many cents are there in 25 dollars?

18. If 1 box of lemons cost 7 dollars, how many cents will it take to pay for 10 boxes?

When the multiplier is a number, that can be produced by multiplying two smaller numbers together, multiply the multiplicand first by one of the smaller numbers, and the product thence arising by the other.

19. Find the price of 32 horses, at 96 aollars apiece. 96 price of 1 horse.

8

768 price of 8 horses.

4

3072 price of 4 times 8 horses, or 32 horses. Observe in the above example, that 32 can be produced by multiplying 4 and 8 together. The 4 and the 8 are called the factors of 32.

20. A merchant bought 24 hogsheads of molasses at 19 dollars a hogshead. What did the whole cost?

In this example we consider 24 to be the multiplier. For 24, we can find several different sets of factors; viz. 3, 8; also, 4, 6; also, 2, 3, 4; also, 2, 2, 6. Either set of these factors may be used.

21. If a ship sail at the rate of 129 miles a day, how many miles will she sail in 72 days?

22. If 1 man can dig 41 bushels of potatoes in a day, how many bushels can 28 men dig?

23. Multiply 425 by 36, using the factors of 36. 24. How many are 63 times 540?

25. How many are 45 times 2807 ?

Questions to be answered Orally.

(1) What is meant by multiplicand?— what by multiplier?-and what by product? (2) When we say, 5 times 8 are 40, which of these numbers is the multiplicand?-which the multiplier ?- and which the product? (3) Can you obtain the product of any two numbers, by means of addition? (4) Recite the rule for multiplication. (5) When there are ciphers between figures in the multiplier, what may be done? (6) When there are ciphers on the right of the multiplier, or multiplicand, or on the right of both, what may be done with them? (7) In what manner can you multiply by 10, by 100, by 1000, &c.? (8) What is meant by the factors of a number? (9) Name two factors of 24, (10) Name three factors of 24. (11) Name two factors of 36. (12) Name three factors of 36.

Perform the following examples by either of the foregoing methods, which may be found convenient.

26. What is the value of a farm consisting of 200 acres of land, at 40 dollars an acre?

27. Suppose à book to contain 235 pages, 45 lines in each page, and 50 letters in each line; how many letters are there in the book?

28. Suppose an orchard to consist of 109 rows, 126 trees in a row, and 1007 apples on a tree;- how many trees, and how many apples are there?

29. Suppose a crew of fifty men have provision for 30 days, allowing each man 20 ounces a day;- how many days would it last, if each man ate 1 ounce a day?

30. Suppose a crew of fifty men have provision for 30 days, allowing each man 20 ounces a day;-how many men would it serve for the same time, if each man ate one ounce a day?

31. How many fishes would be caught by 14 boats, employed for 30 days, each boat drawing a net 15 times a day, and taking 13 fishes each draught?

32. What is the product of 90042 multiplied by 9009 ›

CHAP. V.

DIVISION.

SECTION 1.

1. How many yards of cloth, at 3 dollars a yard, can be bought for 396 dollars?

Here we must find how many times 3 dollars there are in 396 dollars: that is, we must divide 396 by 3.

3)396

We first divide the 3 hundreds, then the. 132 9 tens, and then the 6 units; thus, 3 in 3, once; 3 in 9, 3 times; 3 in 6, 2 times.

Observe in the above example, that the 3 which we first divide, means 3 hundred; and the 1 which we place under it means 1 hundred, showing that 3 is contained in 300, 100 times. The 9 means 9 tens, and the 3 which we place under it means 3 tens, showing, that 3 is contained in 90, 30 times.

A Dividend is a number which is to be divided; such is the number 396 in the above example. A Divisor is a number by which we divide; such is the number 3 in the above example. The Quotient is the number of times which the divisor is contained in the dividend; such is the number 132 in the above example.

Find the quotient in each of the following examples. (5). 4)4884

(2). 4)8

(3). 2)46

(4). 3)936

6. A man laid out 69 dollars for sheep, paying 3 dollars a head for them. How many did he buy?

7. If 4 bushels of wheat will pay for 1 barrel of flour, how many barrels will 848 bushels pay for?

SECTION 2.

1. How many times is 4 contained in 3684 ?

4)3684

921

In this example we find that 4 is not contained in 3, therefore we join the 3 with the 6, and say, 4 in 36, 9 times.