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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. (2). 4)8 (5). 4)4884

(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

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DIVISION.

109

2. How many times is 7 contained in 56? 3. How many times is 9 contained in 639? 4. How many times is 5 contained in 405? 5. How many times is 4 contained in 3248? . 6. How many times is 3 contained in 1569? 7. If 4 horses are required to draw 1 wagon, how many wagons might be drawn by 168 horses?

8. How many yards of broad-cloth, that is sold at 6 dollars a yard, can be bought for 492 dollars?

9. If a man can travel 5 miles an hour, how many hours will it take him to travel 205 miles?

10. Suppose 69 to be a dividend, and 3 a divisor; what is the quotient?

11. Suppose 128 to be a dividend, and 4 a divisor, what is the quotient?

12. Suppose 486 to be a dividend, and 6 a divisor; what is the quotient?

13. How many times is 4 contained in 872?

4)872

218

4 in 8, 2 times; 4 in 7, 1 time, and there is 3 over; (we join this 3 with the 2, making 32,) then 4 in 32, 8 times. 14. How many times is 6 contained in 726? 15. How many times is 8 contained in 896? 16. How many times is 5 contained in 1605? 17. How many times is 7 contained in 924? 18. How many times is 4 contained in 6732? 19. Suppose 1585 to be a dividend and 5 the divisor; what is the quotient?

20. Suppose 4518 to be a dividend and 6 the divisor; what is the quotient?

21. How many times is 7 contained in 742?

7)742

The divisor not being contained once in the ten's place of the dividend we write a 106 0 in the ten's place of the quotient. 22. How many times is 3 contained in 609? 23. How many times is 8 contained in 1624? 24. How many times is 5 contained in 4015? 25. How many times is 9 contained in 2880? 26. How many times is 7 contained in 10500?

K

What will 3 books cost, at 31 cents apiece? What will 4 slates cost, at 24 cents apiece? 8. What will 5 baskets cost, at 17 cents apiece? 9. What will 6 cows cost, at 25 dollars apiece? 10. What will 7 horses cost, at 115 dollars apiece? 11. How many are 8 times 9? 12. How many are 9 times 16? 13. How many are 5 times 342 ? 14. How many are 7 times 6453? 15 How many are 3 times 42 908 ? 16. How many are 6 times 704 370?

17. Multiply 251 by 8,- that is, find 8 times 251.
18. Multiply 475 by 4.

19. Multiply 3086 by 6.
20. Multiply 15 350 by 8.
21. Multiply 430 039 by 7.
22. Multiply 7 000 005 by 9.
23. Multiply 42 862 000 by 5.
24. Multiply 928 064 309 by 4.

25. Suppose 8 to be a multiplicand, and 6 the multiplier; how much will be the product?

26. Suppose 35 to be a multiplicand, and 7 the multiplier; how much will be the product?

27. Suppose 491 to be a multiplicand, and 5 the multiplier; how much will be the product?

SECTION 3.

1. Multiply 657 by 24.

657
24

2628 1314

15768

We first multiply by the 4 units. Then
we multiply by the 2 tens, and since this
product must be ten times greater than it
would be if the 2 were 2 units, we set the
product one place to the left. At last, we
add the two products together, and the sum
is the whole product of 657 by 24.

2. Multiply 75 by 16.
3 Multiply 634 by 45.
4. Multiply 3291 by 63.
5. Multiply 71 538 by 77.
6. Multiply 428 601 by 81.

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RULE FOR MULTIPLICATION.

Write the multiplier un

der the multiplicand, placing units under units, &c. When there is but one figure in the multiplier, begin with the units, multiply each figure in the multiplicand separately, and place each product under the figure in the multiplicand from which it arose; observing to carry the tens to the left as in addition.

When there is more than one figure in the multiplier, multiply by each figure separately, and write its product in a separate line, placing the right hand figure of each line under the figure by which you multiply; and finally, add together the several products. The sum will be

the whole product.

7. Suppose 5476 208 to be a multiplicand, and 3942 the multiplier; how much will be the product?

5476208
3942

10952416

21904832

49285872

16428624

21587211936

8. Suppose 73 054 to be a multiplicand, and 548 the multiplier; how much will be the product?

9. Suppose 295 to be a multiplicand, and 486 the multiplier; what will be the product?

10. What is the product of 9351 by 765 ? 11. What is the product of 3008 by 254 ? 12. What is the product of 5603 by 6448 ? 13. How many are 74 times 6580 ?

14. How many are 236 times 3759 ?

15. There is an orchard containing 9 rows of trees, and there are 57 trees in each row.

are there in the orchard?

How many trees

16. A merchant bought 75 pipes of wine, at 145 dollars a pipe. What did the whole cost?

17. A merchant bought 37 mules, for shipping, at 52 dollars per head. What did the whole cost?

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?

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