Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

NOTE. WHEN THE DIVISOR is the product of two numbers, neither of which exceeds 12, short division may be employed, by first dividing the given sum by the one number, and the quotient. thus obtained, by the other: the last quotient is the answer.

Example.-Divide £376, 11s. 1d. by 63.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]

III. WHEN THE DIVISOR Is 10, 100, 1000, OR 1 WITH ANY OTHER

NUMBER OF NOTHINGS ANNEXED.

RULE.-Point off as many figures from the right of the highest denomination of the dividend, as there are nothings in the divisor; the remaining figures are the quotient of the denomination divided: reduce the figures pointed off to the next lower denomination, and add any of the same denomination in the given sum; then point off as before for a further quotient, and reduce the figures pointed off to the next lower denomination; and so on. The figures that remain at each stage, after the pointing off, form the answer required.

Example.-Divide £3642, 15s. 6d. by 100.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

IV. WHEN THE DIVISOR CONTAINS A FRACTION-AS 33.

RULE.-Multiply the integer or whole number of the divisor, by the under figure of the fraction, adding the upper figure to the product multiply the dividend also by the under figure of the fraction: then divide the one product by the other.

Example.-Divide £82, 15s. 8d. by 52d.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][ocr errors][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small]

V. WHEN THE DIVISOR IS A COMPOUND NUMBER.

RULE.-Reduce both divisor and dividend to the lowest denomination that is in the one or the other; thus, if the lowest denomination in either be pence, reduce both to pence. Having now two simple numbers, proceed by long or short division, as the case may require.

Example.-Divide £58, 18s. 84d. by £2, 6s. 3d.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small]

Miscellaneous Exercises in Compound Division.

1. A gentleman gives £10, 10s. to be equally divided among 30 poor people. What is the share of each?

Ans. 7s.

2. A captain of a vessel receives £276, 15s. 8d. to be equally divided among his crew, consisting of 45 man's share?

men. What is each
Ans. £6, 3s. 02d. 23
What is the price
Ans. 2s. 7d.

[ocr errors]

3. Paid £3, 17s. 6d. for 30 yards of linen. per yard? 4. What is the price of sugar per lb. when it is 77s. per cwt.?. Ans. 84d.

5. If the distance between Edinburgh and Newcastle, which is 118 miles 6 fur. 25 poles, be divided into 12 stages of equal length, what is the length of each stage? Ans. 9 miles 7 fur. 83 poles. 6. How many parcels of coffee, of 7 lbs. each, may be made out of a cask containing 3 cwts. 1 qr. 14 lbs. ? 7. How many yards of cloth, at 9s. 4d. £12, 12s.? 8. 1 dozen silver table-spoons weighed 1 lb. 10 oz. 12 dwts. What is the weight of each?

9. 25 bales of cotton weighed 82 the average weight of each bale?

Ans. 54 parcels. may be bought for Ans. 27 yards.

[ocr errors]

Ans. 1 oz. 17 dwts. 16 grains. cwts. 3 qrs. 15 lbs. What is Ans. 3 cwts. 1 qr. 7

[ocr errors]

10. How many shirts may be made each shirt requiring 3 yds. 2 qrs.?

lbs. out of 136 yds. 2 qrs. linen, Ans. 39 shirts. What is the price per Ans. 14s. 41d. 1

11. 26 yards of cloth cost £18, 14s. yard?

12. What is the price of 1 yard of linen, when a piece containing 25 yards cost £3, 8s. 9d.?.

.

13. When iron is £6, 16s. 10d. per ton, what

[merged small][ocr errors]

14. What is the price of an article per lb. £5, 2s. 8d. per cwt.?

15. What is the price of a bushel of wheat, £3, 18s. 8d. per quarter?

16. Among how many persons may £576, to give each £3, 13s. 6d. ?

17. A farm containing 237 acres is let much does it pay per acre?

18. If a pound of gold is coined into 47 weight of each sovereign?

[ocr errors]

Ans. 2s. 84d. 17
is the value of
Ans. 6s. 10gd.
at the rate of
Ans. 11d.

[ocr errors]

at the rate of

Ans. 9s. 10d. 19s. 6d. be divided,

Ans. 157 persons. for £325, 15s. How Ans. £1, 7s. 52d. 117 sovereigns, what is the Ans. 5 dwts. How much may he Ans. £2, 18s. 031

19. A tradesman's yearly income is £176. spend weekly, in order to save £25 per year?

[ocr errors]
[ocr errors]

20. The sum of £738, 15s. is to be made up by 463 persons. How much must each pay? Ans. £1, 11s. 102d. 243 21. If 112 ingots of gold are worth £77878, 5s. 4d., what is the value of one? · Ans. £695, 6s. 10d. 22. Prize-money to the amount of £683, 5s. 4d. is to be equally divided among 83 seamen, how much will each receive?

[ocr errors]
[ocr errors]

Ans. £8, 4s. 74d. 39

Miscellaneous Exercises in Compound Addition, Subtraction, Multiplication, and Division.

1. A purchases from B a hogshead of sugar, of which the value was £73, 10s.; a box of tea, £54, 16s. 8d.; and a pipe of wine, £93, 5s. In return, B receives from A £50 in money, and 3 pieces of cloth valued at £67, 15s. How much does A still owe B?

Ans. £103, 16s. 8d. 2. A lady went to market with £5, 3s. 11d., and laid out on groceries 18s. 44d.; on bread, 12s. 54d.; on beef, £1, 6s. 3d.; and on various other articles, 4s. 11d. How much money should she have remaining? Ans. £2, 1s. 114d. 3. A gentleman's income is £1200 a year, and he spends on an average, £1, 17s. 5d. every day. How much does he save in a year-a week-a day? Ans. Yearly, £516, 0s. 14d.; Weekly, £9, 18s. 51d. 1; Daily, £1, 8s. 34d. 365. 4. A gentleman's income is £460 a year; he wishes to save £53, 19s. 6d. annually. How much may he spend a week?-per day? Ans. Weekly, £7, 16s. 13d. 44; Daily, £1, 2s. 2 d. 328. 5. A farmer sold 39 quarters of wheat, at £2, 16s. 11d. per quarter, and 23 quarters, at £2, 4s. 73d. How much money did he receive?-and what was the average price per quarter?

[ocr errors]

Ans. £162, 6s. 74d.; average price, £2, 12s. 44d. 31. 6. A manufacturer sold 739 yards of calico, at 53d. per yard; 69 yards of tartan, at 4s. 74d. per yard; 73 yards of carpeting, at 3s. 9d. per yard. How much money did he draw?

[ocr errors]
[ocr errors]
[ocr errors]

Ans. £47, 6s. 11ąd. 7. A bricklayer's wages are 3s. 10d. per day; he requires to save £23 for house-rent and clothes. How much may he spend per day? Ans. 2s. 74d. 183. 8. If a workman gain 23s. 7d. per week, and spend 18s. 3d. per week, how much does he save in a year? Ans. £13, 15s. 2d. 9. A gentleman's annual income is £1000, and his daily expenses are £1, 17s. 31d. How much does he save in 9 years? Ans. £2874, 16s. 101d. 10. If 1869 sovereigns are coined from forty troy pounds of gold, what is the weight of a sovereign ? Ans. 5 dwts. 3

gr. 11. A purse contains £95, 14 crowns, 23 half-crowns, 19 shillings, 15 sixpences, and 11 fourpenny-pieces, and the money is equally divided among 12 individuals. How much does each receive? Ans. £8, 11s. 5d. 1.

[ocr errors]

12. A tradesman being insolvent, called all his creditors together, and found he owed to A £53, 7s. 6d. ; to B, £105, 10s.; to C, £34, 5s. 2d.; to D, £28, 16s. 5d.; to E, £14, 15s. 8d.; to F, £112, 9s.; to G, £143, 12s. 9d. The value of his stock was £212, 6s.; the debts due to him amounted to £112, 8s. 3d., besides £21, 10s. 5d. money in hand. How much would his creditors lose by taking the whole of his effects? Ans. £146, 11s. 10d.

[ocr errors]

SIMPLE PROPORTION.

PROPORTION is the method of finding an unknown number, by means of certain other given numbers to which it bears a proportion.

Simple Proportion is where three numbers, or terms, as they are called, are given in order to find a fourth; hence it is also called the RULE OF THREE.

Compound Proportion, as afterwards explained, is where more than three numbers or terms (usually five) are given to find out the unknown quantity.

In Simple Proportion, two out of the three given numbers are always of the same kind-as, for instance, 9 yards and 18 yards; and the third is the same in kind as the fourth number soughtthus, if the third were pounds, the fourth would also be pounds.

RULES.

I. RULE FOR STATING.*-1. Write down as the third of the three terms (which are all to be placed in one line) that term which is of the same kind as the answer sought.

2. Consider, from the nature of the question, whether the answer should be greater or less than the third term: if greater, place the greater of the other two terms second; if less, place the less second; and the remaining term in each case, first. Two dots, thus [] are placed between the first and second term, and four dots [::] between the second and the third; the three terms when stated appear thus-3: 6 :: 12.

II. RULE FOR WORKING.-1. Reduce the first and second terms, if compound, to the same simple denomination: reduce also the third term, if compound, to its lowest given denomination.

2. Multiply the second and third terms together, and divide their product by the first. The quotient will be the answer sought, and is always of the same kind as the third term. In multiplying, the second is placed under the third term, or the third under the second, according to convenience.

3. Convert the answer, when necessary, into its highest denomination; thus, if the answer were in pence, it must be converted into pounds.

NOTE. When the second term does not exceed 12, it will be more convenient to multiply the third term as in Compound Multiplication, than to reduce it to its lowest denomination, before multiplying. See Example 1, page 58.

For an explanation of the reason of the rule, see page 63.

*SEE ANOTHER MODE OF STATING THE RULE, PAGE 59.

« ΠροηγούμενηΣυνέχεια »