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under the divided figure. The remainder, if there be any, carry to the next figure, calling it so many tens.

Find how many times the divisor is contained in this dividend, and set it down as before; and so continue to do until the figures in the dividend are all divided.

EXAMPLES.

1. Paid 150 dollars for 6 tons of hay. How much was it a ton? Answer, 25 dollars. 2. In a certain town there are 1280 inhabitants. average number in each family is S. are there?

3. How many yards of cloth can dollars, at 7 dollars per yard?

The

How many families
Answer, 160.

be bought for 1155 Answer, 165 yards.

4. If a man labour one month for 12 dollars, how many months will he labour for 1008 dollars? and how many years, allowing 12 months to a year?

Answer, 84 months-7 years.

5. If 15 horses consume 2550 bushels of oats in one year, how many will one horse consume?

Operation.
5)2550

3)510

It will be seen that 15 is a composite number, produced by the multiplication of 5 and 3, thus: 5×3=15. As Division is the reverse of Multiplication, it is evident, that when the divisor is a composite number, we may divide, first by one of the component parts, and that quotient by the other. For example: Suppose 30 apples to be divided equally between 15 boys. In the first place, we divide the whole number by 5. If there were only 5 boys, they would receive 6 apples each; but, as there are 3 times 5 boys, they can have only one third as many as 5 boys would have.

6. How many days would it take a Boston to New-York, travelling at the day, the distance being 240 miles?

7. If a horse travel 2184 miles in miles will he travel in one day?

8. If 112 barrels of flour cost 672 barrel cost?

170 Ans.

man to travel from rate of 30 miles a Answer, 8 days. 42 days, how many Answer, 52 miles. dollars, what will I Answer, 6 dollars.

QUESTIONS. 10. When the divisor is a composite number, how may you proceed? 11. What is the first step in the 5th example? Second step?

LONG DIVISION.

1. If 2624 bushels of corn be divided equally among 41 men, how many bushels will each receive?

As 41 is greater than 12, and not a composite number, the operation must be performed by the whole divisor at once. To carry on the computation in the mind would be difficult; we must, therefore, institute a different mode from that in which the preceding questions have been performed.

Operation.
41)2624(64

246

164

164

Setting down the numbers as before directed, and taking 41 for the divisor, we find that it is not contained in the 1st figure, nor in the 1st and 2d taken together, but it is contained in the first three figures, 6 times; that is, 41 is contained in 262 tens, 60 times and something over. To find what this remainder is, we find the product of 6 times 41, which we place under the three figures employed in the dividend, and subtracting it therefrom, we find the remainder to be 16, which is 16 tens. We next bring down the 4 units of the dividend, and place them at the right hand of the 16 tens, which make 164 to be divided by 41, which is contained in it 4 times. The answer, then, is 64.

By examining the work of the last question, it will be seen, that it is the same as Short Division, only that the operation is all set down, instead of being carried on in the mind. For example-divide 868 by 7, Long Division. Operation. 7)868(124 7

16

14

28

By Short Division, we say, 7 in 8 once, and 1 over; 7 in 16, twice, and 2 over; 7 in 28, 4 times, and no remainder.

In Long Division, we say-7 in 8 once, and place 1 for the first figure in the quotient; multiply 7 by this quotient

QUESTIONS. 12. What is the difference between Long and Short Division?

figure, and place the result under the 8, and subtracting it we find the difference to be 1, to which we bring down the next figure for a new dividend, and proceed as before.

From the preceding explanations, the following RULE is deduced.

Place the divisor at the left hand of the dividend. Draw a line at the right and left of the dividend, and find how many times the divisor is contained in as many figures as will contain it once or more. Place the number of times at the right hand of the dividend, for the first figure of the quotient. Multiply the divisor by this quotient figure, and place the result under the divided figures; find the difference between them, by subtraction, and to this difference bring down the next figure of the dividend, and divide as before; so continue to do until all the figures of the dividend are brought down. Should it be necessary to bring down more than one figure to contain the divisor, a cipher must be added to the quotient.

EXAMPLES.

1. A man raised 6996 bushels of potatoes on 33 acres. How many did he raise per acre? Answer, 212 bushels. 2. How many years in 32485 days, if 365 days make a year? Answer, 89 years. 3. A legacy of 15808 dollars was left to a certain number of men, giving them 832 dollars each. How many men were there?

Answer, 19 men.

4. How many pounds in 11520 farthings, there being 960 farthings in one pound?

Answer, 12 pounds.

5. How many hogsheads in 49896 pints, if 504 pints make one hogshead?

6. There are 8 furlongs in one

in 123 furlongs?

Answer, 99 hogsheads.
mile; how many miles
Operation.
8)123

153 Answer.

By dividing 123 by 8, we find the quotient to be 15 miles, and there is a remainder of 3 furlongs. As it takes 8 furlongs to make a mile, it is evident that 1 furlong is of a mile, and 3 furlongs are of a mile, and 8 furlongs are 8, equal one mile. The answer, then, is 15 miles and

QUESTIONS. 13. Rule for Long Division?

, which we place at the right hand of the quotient. We have, then, this rule, when there is a remainder in Division Place it at the right hand of the quotient, as the numerator of a fraction, and under it place the divisor, as a denominator. A number like this is called a mixed number: Thus, 153 is a mixed number. To prove this last question, we multiply the quotient by the divisor, and add to the product the numerator of the fraction, or the re

mainder, thus:

15

123

7. What is the quotient of 1832 divided by 16?

8. There are 320 rods in a mile. 66327 rods?

Answer, 1148. How many miles in Answer, 207870.

9. How many miles from Boston to Providence, the distance being 12800 rods?

Answer, 40 miles.

10. If 10 shares in a factory be worth 2220 dollars, what is 1 share worth? Answer, 222 dollars.

To divide by 10, 100, 1000, or any number of ciphers, cut off as many figures from the right hand Operation. of the dividend as there are ciphers at the 10)2220 right hand of the divisor. The figures cut off on the left of the dividend, will be the quotient, and those on the right hand will be the remainder.

11. Divide 18986421 by 10000. Operation.

12. Divide 342871 by 7000.

10000)1898 6421

Answer, 1898,6421
Operation.
7000 342 871

Answer, 48,6871

In this example, cut off the ciphers and figures of the dividend, as before, and divide by 7; to the right hand of the remainder bring down the figures which are cut off from the dividend.

13. What is the quotient of 421998 divided by 8400 ?

QUESTIONS. 14. When there is a remainder, after dividing, what is to be done with it? 15. What is a number like 15 3-8 called? 16. When there are ciphers at the right hand of the divisor, how may you proceed? 17. How must the figures cut off from the right hand of the dividend, be placed?

SUPPLEMENT TO

MULTIPLICATION AND DIVISION.

MULTIPLICATION.

DIVISION.

1. What will 1574 yards of 2. If 1574 yards of cloth cloth cost, at 12 dollars per cost 18888 dollars, what will yard? yard cost? 3. How many inches in 56541 feet?

5. If a man travel 38 miles in a day, how many will he travel in 16 days?

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4. How many feet in 678492 inches, if 12 inches make 1 foot?

6. If a man travel 608 miles in 16 days, how many will he travel in one day?

7. If 60 minutes make 1 8. How many hours in hour, how many minutes in 784201560 minutes?

13070026 hours?

9. How many hours in 336 days?

10. In S064 hours, how many days?

11. The quotient of two 12. The product of two numnumbers is 46, and the divi-bers is 644, the multiplier 14; sor 14; what is the dividend? what is the multiplicand? 13. The quotient of two 14. The product of two numbers is 72, the divisor 84 ; numbers is 6048, the multiwhat is the dividend? plicand 84; what is the multiplier?

15. How many pounds of 16. A man has 125440 flour may be put into 640 pounds of flour, to be put into barrels, containing each 196 barrels containing 196 each. pounds? How many barrels must he have?

17. What will 24 oxen cost at 46 dollars each?

18. If 24 oxen cost 1104 dollars, what do they cost apiece?

19. A carriage wheel that 20. If a carriage wheel will turn 340 times in a mile, turn round 81600 times behow many times will it turn tween Boston and New-York, in going from Boston to New- and turn 340 times in a mile, York, it being 240 miles? what is the distance?

21. If 33 men do a piece

22. If 1 man do a piece of of work in 24 days, in what work in 792 days, in what time will one man do it? time will 33 men do it?

23. In 7894 feet, how many barley-corns?

24. How many feet in 284184 barley-corns?

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