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DIVISION OF DENOMINATE NUMBERS.
1. Charles has 3s. and wishes to divide it equally be. tween himself and two brothers : how much must he give to each? If he divides 2s. 6d., how much? If he di. vides 2s., how much ? If he divides 1s. 6d., how much ? If he divides 1s., how much?
2. John has a bushel of nuts and wishes to divide them equally among himself and three brothers : how much will each have ?
3. If James divides 3pk. of corn among 4 persons, how much will each have ? If he divides 2pk. 4qt. ? If he divides 1pk. ? If he divides 2qt. ? If he divides lqı. ?
4. William has 8 eagles, 5 dollars, 6 dimes, 9 cents, and 5 mills, and wishes to divide them equally among five of his schoolmates : how many of each kind will each boy receive ?
EXAMPLE ILLUSTRATING PRINCIPLES.
Divide £25 158. 10d. equally among 8 persons.
OPERATION. 8 is contained in £25, 3 times 8) £25 158. 10d.(£3 and £1 over. Now this £1
24 has yet to be divided by 8, as £ 1 well as the 15s. and 10d. Then
20 multiplying the £1 by 20 and adding in the 158. gives 358.,
8)358.(4s. which contains 8, 4 times and 3s. over. Multiplying the 3s.
12 by 12 and adding in the 10d. gives 46d., which contains 8, 8)46(5d. 5 times and 6d. over. The 6d.
40 being reduced, gives 24 far
6d. things, which contains 8, 3
4 times. Therefore, each of the
8)24far.(3far. denominations has been divi. ded by 8.
Ans. £3 4s. 5d.
101. Therefore, a denominate number may be divided into any number of equal parts, by dividing each of its denoininations by the divisor.
1. 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, and 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.
III. Proceed in the same way for all the denominations 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 quntients connected together will be the en. tire quotient sought.
EXAMPLES ILLUSTRATING PRINCIPLES.
102. When the divisor does not exceed 12, the division may be made afier the manner of short division in sim. ple numbers.
Ex. 1. Divide £25 158. 4d. by 8.
We first say 8 into 25, 3 times OPERATION and £1 or 20s. over. Then after 8)£25 158. 4d. adding the 15s. we say, 8 into 35, 4 £3 4s. 5d. times and 3s. over. Then reducing the 3s. to pence and adding in the 4d., we say 8 into 40, 5 times. 2. Divide £16 8s. 9d. by 5.
Ans. £3 5s. 9d. 3. Divide £27 19s. 6d. by 9. Ans. £3 2s. 2d.
101. How may a denominate number be divided? How do you set down the number to be divided? How do you then divide ? When there is a remainder, what do you do with it? Of what donomination will each of the quotients be?
102. When the divisor does not exceed 12, how may the division be performed?
4. Divide 36bu. 3pk. 7qt. by 7.
In this example we find 7)36bu. 3pk. 7qt.(5bu. that 7 is contained in 36 35 bushels 5 times and i bushel
1 over. Reducing this to pecks 4 and adding 3 pecks, gives 7
. pecks, which contains 7, 1
7 time and no remainder. Mul.
0 tiplying 0 by 8 quarts and
8 adding, gives 7 quarts to be divided by 7.
Ans. 5bu. 1pk. 1qt. 5. Divide £821 178. 9 d. hv 4.
dns. £205 9s. 5d. 1 far. 6. Divide £55 14s. d. by 7.
Ans. £7 19s. 1d. 34 far. 7. Divide 16cwt. 3qr. 271b. 6oz. by 7.
Ans. Acut. Iqr. 181b. 340%. 8. Divide 49yd. 3qr. 3na. by 9.
Ans. 9. Divide 131 A. IR. by 12. Ans. 10A. 3R. 30P.
103. 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 28. 4d. by the composite number 21. Here the factors are 3 and 7.
7)£28 2s. 4d.
3)£4 0s. 4d. £4 Os. 4d.
£i 6s. 9 d. Hence, the answer sought is £1 6s. 9fd. 2. Divide £57 3s. 4d. by 35=5x7. A. £1 12s. 8d. 3. Divide £85 4s. by 72.
Ans. 4. Divide £31 2s. 10 d. by 99. Ans. 6s. 31d. 103. When the divisor is a composite number, how may the divi. sion be performed ?
PROOF OF MULTIPLICATION. 104. Divide the product by the multiplier, and if the quotient is equal to the multiplicand, the work may be considered right.
PROOF OF DIVISION.
105. Multiply the quotient by the divisor, and if the product is equal to the dividend, the work may be considered right.
1. Divide £1138 12s. 4d. by 53. Ans. £21 9s. 8d. 2. Divide 1417cwt. 7lb. by 79. A. 17cut. 3qr. 189916. 3. Divide £23 15s. 7 d. by 37.
Ans. 4. Divide £199 3s. 10d. by 53. Ans. £3 15s. 2d.
1. Bought 65 yards of cloth for which I paid £72 14s. 44d.: what did it cost per yard ? Ans. £i 2s. 4 d.
2. Bought 64 gallons of brandy for £30 88.: 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. 4. Sixty-three barrels of sugar contain 7T. 16cwt. 3qr. 121b.: how much is there in each barrel ?
Ans. 2cwt. Iqr. 2416. 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.
6. One hundred and seventy-six men consumed in a week 13cwt. 2qr. 1516.6oz. of bread : how much did each man consume ?
Ans. 776. 12oz. 2dr. 7. If 62 yards of velvet cost £2 18s. 8d., what will one yard cost ?
Ans. 11d. 14. far. 8. If 92 yards of broadcloth cost £71 14s. Od., what is the value of 1 yard ?
104. How do you prove multiplication ?
9. If 90 hogsheads of sugar weigh 567. 14cut. 3qr. 15lb., what is the weight of i hogshead ?
Ans. 12cwt. 2qr. 11lb. 10. When 192 shares of a certain stock are valued at £1290 4s. Od., what would be the cost of 1 share ?
11. If the earth revolve 15° on its axis in 1 hour, how far does it revolve in 1 minute ?
Ans. 15'. 12. If 106 tons of iron cost £1001 9s. 7d., what is the value of 1 ton ?
Ans. 13. If 57 gallons of wine cost £23 11s. 544., what is the cost of one gallon ?
Ans. 8s: 31d. 14. If 59 casks contain 44hhd. 53gal. 2qt. Ipt. of wine, what are the contents of one cask ?
Ans. 15. When 175gal. 2qt. of beer are drank in 52 weeks, how much is consumed in one week ?
Ans. 3gal. Iqt. 1 pt. 16. A rich man divided 168bu. 1pk. 6qt. among 35 poor men: how much did each receive ? Ans.
17. Suppose a man had 981b. 202. 19pwt. 5gr. of sil. ver: how much would he give 1 man if he gave an equal amount to 7 men ?
Ans. 1416. Spwt. 11gr. 18. Divide 9hhd. 28gal. 2qt. by 12. Ans.
19. What will be the share of 1 man, if 810T. 11cwt. 2016. 130%, 4dr. be divided equally among 346 men ?
Ans. 2T. 6cwt. 3qr. 10lb. 50%. 12dr. 20. What will be the quotient of 65bu. 1pk. 3qt. divi. ded by 12?
Ans. 21. Sold 8lb. of indigo for £19 13s. 8d. : how much Was it a pound?
Ans, £2 98. 2 d. 22. I gave
68 68. 2d. 2far. for 10 dozen of combs : how much did I pay for 1 dozen ?
Ans. 23. If I pay £12 14s. 5d. 3far, for 35 bushels of wheat, how much is it per bushel ? . Ans. 7s. 3d. ifar.
24. If a merchant pays £23 12s. 6d. for 84 yards of cloth, how much did he pay a yard ? Ans.
25. Suppose a man has 246mi. 6fur. 36rd. to travel in 12 days: how far will that be in a day?
Ans. 20mi. 4fur. 23rd.