DIVISION OF DENOMINATE NUMBERS.

§ 101. A denominate number may be divided into any number of equal parts by dividing each of its denominations by the divisor.

RULE.

I. Set down the number to be divided in the order of its denominations from the highest to the lowest, and write the divisor on the left.

II. Find how often the divisor is contained in the figures of the highest denomination.

III. Reduce the remainder, if there be any, to the next lower denomination, and add the figures of the dividend expressing that denomination, and then divide the sum by the divisor.

IV. Proceed in the same way for all the denominatrons, to the last, and if there be a remainder place the divisor under it, as in division of simple numbers. Each of the quotients will be of the same denomination as its dividend, and the several quotients connected together will be the entire quotient sought.

PROOF OF MULTIPLICATION.

§ 102. Divide the product by the multiplier, and if the quotient is equal to the multiplicand, the work may be considered right.

PROOF OF DIVISION

103. Multiply the quotient by the divisor, and if the product is equal to the dividend, the work may be considered right.

QUESTIONS.

§ 101. How may a denominate number be d do you set down the number to be divided?

then divide? When there is a remainder what do you do with it? Of what denomination will each of the quotients be? § 102. How do you prove multiplication?

103. How do you prove division?

Ex. 1. Divide £25 15s 10d into 8 equal parts.

In this example we find that 8 is contained in £25, 3 times and £1 over. Now this £1 has yet to be divided by 8, as well as the 15s and 10d. Therefore by multiplying the £1 by 20 and adding the 15s gives 35s, which contains 8, 4 times and 3s over. Multiplying the 3s by 12 and adding in the 10d, gives 46d, which contains 8, 5 times and 6d over. The 6d being reduced, gives 24 farthings which contains 8, 3 times. Therefore each of

8)£25 15s 10d(£3

24

£1

20
8)35s(4s
32

3s

12

8)46(5d
40

6d

4

8)24far (3far.

the denominations has been divided by 8, and the

reason of the rule is plain.

2. Divide 36bu. 3pk. 7qt. by 7.

Ans. £3 4s 5ąd.

7)26bu. 3pk. 7qt.(5bu.

35

1

4

7

In this example we find that 7 is contained in 36 bushels 5 times and 1 bushel over. Reducing this to pecks, and adding 3 pecks 7)7pk.(1pk. gives 7 pecks, which contains 7, 1 time and no remainder. Multipying 0 by 8 quarts and adding, gives 7 quarts to be divided by 7.

0

8

7)7(1gt.

Ans. 5bu. 1pk. 1qt.

NOTE.-When the divisor does not exceed 12 the division may be made after the manner of short division in simple numbers.

Thus in the first example,

8) £25 15s 4d

£ 3 4s 5d

£1 or 20s over. Then after adding the 15s, we say, 8 into 35, 4 times and 3s over. Then reducing the 3s to pence and adding in the 4d, we say 8 into 40, 5 times.

3. Divide £821 17s 93d by 4.

Ans. £205 9s 5d 13far.

4. Divide £55 14s 3d by 7.

Ans. £7 19s 1d 34 far.

5. Divide 16cwt. 3qr. 271b. 6oz. by 7.

Ans. 2cwt. 1gr. 19lb. 144oz.

NOTE 2. When the divisor is a composite number, and exceeds 12, the work may be shortened by dividing by the factors, in succession, as in division of simple numbers.

Ex. 1. Divide £28 2s 4d by the composite number 21. Here the factors are 3 and 7.

7)£28 2s 4d

£4 Os 4d

3)£4 Os 4 d
£1 6s 91d

Hence the answer sought is £1 6s 9}d.

2. Divide £57 3s 4d by 35=5×7.

1. Bought 65 yards of cloth for which I paid £72 14s 44d: what did it cost per yard?

Ans. £1 2s 41d. 2. Bought 64 gallons of brandy for £30 8s: what did it cost per gallon?

Ans. 9s 6d.

3. Bought 144 reams of paper for £96: what did it cost me per ream?

Ans. 13s 4d.

4. Sixty three barrels of sugar contain 7T. 16cut. 3qr. 211b: how much is there in each barrel? Ans. 2cwt. 1qr. 27lb.

5. A farmer has a granary containing 232 bushels 3 pecks 7 quarts of wheat, and he wishes to put it in 105 bags: how much will each bag contain? Ans. 2bu. 7qt.

6. One hundred and seventy six men consumed in a week 13cwt. 3qr. 1lb. 6oz. of bread: how much did each man consume? Ans. 8lb. 12oz. 2dr.

APPLICATIONS IN THE FOUR KULES.

Albany, July 1, 1833.

Mr. James Sears

Bought of Albert Titus.

3lb. of green tea at 7s 6d per pound.
27yd. of muslin at 1s 6d per yard.
4cwt. of sugar at £2 2s 8d per cwt.
2hhd. of molasses at 2s 6d per gallon.
67b. of raisins at 1s 7d per pound.

Received payment, £27 18s 2d.
Albert Titus.

2. A gentleman purchased of a silversmith, 2 dozen silver spoons each weighing 3oz. 4pwt. 1gr.; 2 dozen of tea spoons, each weighing 15pwt. 16gr.; 3 tankards each weighing 22oz. 14pwt.; he sold him old silver to the amount of 67b. 10oz. 3pwt.: How much remained to be paid for?

Ans. 6lb. 9oz. 12pwt. 3. What will be the cost of 22 tons of hay, at £2 1s 10d per ton?

Ans. $46 0s 4d.

4. If two hogsheads of wine cost £67,4s; what does it cost per gallon?

Ans. 10s 8d. 5. If 4cwt. of sugar cost £14; what is it per pound?

Ans. 74d.

6. A man paid £67 4s for a pile of wood containing 64 cords he sold 30 cords for £29 16s: for how much must he sell the remainder per cord so as not to lose?

7. If 78cwt. 3qr. 10lb. of sugar be equally divided among 5 men, what will be each one's share?

Ans. 15cwt. 3qr.