7. A person bought 45 shares in the Edinburgh and Glasgow Railway, at £73, 10s. 6d. per share, and was afterwards obliged to sell out when the price per share was £65, 17s. 9d. How much did he lose? Ans. £343, 13s. 9d.

8. A vessel came into Leith harbour with 67 tons of guano; 10 tons were disposed of at £7, 6s. 3d. per ton, 8 tons at £7, 1s. 9 d. per ton, 17 tons at £6, 15s. per ton, 23 tons at £6, 11s. 4 d. per ton, and the remainder at £5, 18s. 7d. per ton. Required the value of the cargo, and the average price per ton, Ans. Value of cargo, £449, 0s. 84d.; average price, £6, 14s. 04d. §3. 9. A manufacturer sold 739 yards of calico at 5d. 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?

Ans. £47, 6s. 11ąd. 10. A gentleman's income is £160 a year; his house-rent amounts to £19, 10s.; his taxes are £5, 3s. 74d.; his grocer's account, £15, 11s. 3d.; his baker's account, £7, 17s. 5d.; his butcher's, £14, 1s. 33d.; his shoemaker's, £6, 5s. 9d.; his tailor's, £8, 1s. 54d.; his draper's, £5, 13s. 11ąd.; his income-tax, £4, 13s. 4d.; and his miscellaneous expenses are £46, 14s. 10d. How much money may he save annually? Ans. £26, 7s.

11. What is the value of 39 boxes of oranges at £5, 3s. 11d. per box? Ans. £202, 12s. 9d. 12. A man's daily wages are 3s. 10d.; he requires to save £23 for house-rent and clothes. How much may he spend per day? Ans. 28. 74d. 183.

13. A merchant's clerk being sent to collect payment of accounts, took £5, 3s. 6d. in his pocket; at York he received £49, 13s. 9d., his expenses there were 15s. 34d.; at Sunderland he received £51, 11s. 54d., his expenses there were £2, 5s. 9d.; at Durham he received £179, 13s. 102d., his expenses there were £2, 10s. 6d.; at Newcastle he received £91, 7s. 94d., his expenses there were £1, 3s. 9d.; and at Carlisle he received £275, 10s. 111⁄2d., and his expenses there were £3, 6s. 4d. How much money does he have at Carlisle ? Ans. £642, 19s. 83d. 14. A grocer gave his boy £50 to pay a debt of £34, 11s. 5d. How much money must he get back? Ans. £15, 8s. 7d.

15. A purse contains £95, 14 crowns, 23 half-crowns, 19 shillings, 14 sixpences, and 12 fourpenny-pieces, and the money is equally divided among 12 individuals. How much does each receive? Ans. £8, 11s. 51d.

16. If a workman gain 23s. 7d. per week, and spend 18s. 3 d. per week, how much does he save in 52 weeks? Ans. £13, 15s. 2d. 17. A gentleman's annual income is £1000, and his daily expenses are £1, 17s. 3d. How much does he save in 9 years? Ans. £2874, 16s. 101d. 18. If 1869 sovereigns are coined from forty troy pounds of gold, what is the weight of a sovereign? Ans. 5 dwt. 3 l gr.

INVOICES.

AN INVOICE is a list or account of the particulars and prices of goods, &c., that have been sold on a certain day by one person to another. The following is an example:

24 lb. of fine green tea, at 12s. 11 d. per lb.

18 dozen of sherry wine, at 39s. 11d. per doz.

3.

MR WILLIAM PANTON,

GLASGOW, August 14, 1846.

Bought of ADAM ROBINSON.

36 yards of superfine cloth, at 23s. 4 d. per yd.

100 " of cassimere,

49 pair of Eng. blankets,

65 " of Scotch

" 8 71

"

"

" 8 3

4. Edinburgh, June 3, 1846.-Adam Black, Esq. bought of Cowan & Co. 24 ream of demy at 52s. 6d. per ream, 75 ream of wove post at 40s., 27 ream of crown at 33s., 13 ream of hot-pressed at 43s., 52 ream of foolscap at 25s. 6d., 70 ream of thin post at 28s. 9d. Write out, and find the amount of this bill,

Ans. £452, 8s. 6d.

5. London, February 4, 1847.-Mrs George Scott bought of John Duncan 73 yards of silk at 14s. 3d. per yard, 25 yards of lawn at 2s. 6d., 31 yards of cambric at 5s. 31d., 86 yards of velvet at £1, 4s. 93d., 75 yards of lace at 12s. 34d., and 19 yards of brocade at 16s. 9d. Write out, and find the amount of this bill, Ans. £232, Os. 94d.

6. Liverpool, March 21, 1847.-Mr William Moffat bought of Peter Johnston 57 feet of wainscot sashes at 10d. per foot, 560 feet of ash at 34d., 79 cubic feet of oak at 4s. 2d., 136 feet of framed deal at 3s. 9d., 95 feet of mahogany at 5s. 6d., and 9 men's labour for 17 days at 4s. 9d. each per day. What is the amount of this bill? Ans. £115, 1s. 7 d.

7. Dublin, February 28, 1847.-Mr John Veitch bought of Walter Watson 36 yards of Italian crape at 1s. 10d. per yard, 17 yards of silk velvet at 12s. 43d., 19 yards of Irish tabinet at 3s. 3d., 29 yards scarlet cloth at 19s. 4d., 31 yards French cambric at 18s. 3 d., and 18 Indian shawls at £8, 10s. 6d. each. Write out the bill, and calculate its amount, Ans. £226, 17s. 5ąd.

8. Sheffield, March 13, 1847.-Mr David Reid bought of Alexander Roger 7 dozen razors at 1s. 44d. each, 5 dozen ditto at 1s. 1d., 2 dozen ditto at 83d., 6 dozen knives and forks at £1, 4s. 10d. per dozen, 3 dozen ditto at 18s. 6d., 8 dozen scissors at 7s. 2d. per dozen, and 12 cases of lancets at 17s. 33d. per case. Required a copy of the bill and its amount, Ans. £33, 7s. 7d.

F

THE GREATEST COMMON MEASURE.

A MEASURE or FACTOR of any number is a number that divides it exactly without a remainder: thus, 3 is a measure of 24.

A COMMON MEASURE of two or more numbers is any number that will divide each of them without a remainder : thus, 4 is a common measure of 16 and 24.

THE GREATEST COMMON MEASURE of two or more numbers is the greatest number that measures each of them : thus, 5 is the greatest common measure of 15, 20, and 25.

A Prime number is one that can be divided without a remainder only by itself or by 1: thus, 1, 2, 3, 5, 7, 29, are prime numbers. They are sometimes called Primes.

A Composite number is one which is the product of two or more factors: thus, 32, 40, 64, are composite numbers.

A Number that measures two other numbers, measures also their sum and difference.

Thus, since 4 measures 36 and 28, it also will measure 36 +28, or 64, and 36 — 28, or 8.

=

+ 4 × 7 4 x 16 64; that is, 4 taken 7 times in addition, is equal to

For 36+ 28 = 4 × 9 taken 9 times, and then 4 taken 16 times at once. And 36-28 4 x 9 4 X 7 = 4 x 2 = 8; that is, 4 taken 9 times, diminished by 4 taken 7 times, is equal to 4 taken 2 times at once.

A Number that measures any other number, measures also any multiple of that other number.

Thus, since 3 measures 6, it will also measure 12, 18, 24, or any other multiple of 6.

For 12 = 6 × 2 = 3 × 2 x 2 = 3 × 4; that is, 12, which is a multiple of 6, is also a multiple of 3, and is therefore measured by 3.

THE GREATEST COMMON MEASURE OF TWO

TO FIND
NUMBERS.

RULE.-Divide the greater number by the less; then the divisor by the remainder, if any; and so on, continually dividing the preceding divisor by the last remainder, till nothing remains. The last divisor will be the greatest

common measure.

Example.-Find the greatest common measure of 696 and

1305.

696)1305(1
696

609)696(1
609
87)609(7
609

Pupil. I first divide 1305 by 696; the quotient is 1, and the remainder 609. I next divide 696, the last divisor, by 609; the quotient is 1, and the remainder 87. Í next divide 609, the last divisor, by 87; the quotient is 7, and the remainder nothing; therefore, 87 is the greatest common measure.

REASON OF THE RULE.-Referring to the foregoing example, it is obvious that the greatest common measure cannot exceed 696; we therefore try if 696 is the measure sought. 1305 divided by 696 leaves a remainder of 609; therefore, 696 is not the greatest common measure.

Now, the greatest common measure of 696 and 1305 must measure the remainder 609, therefore, the greatest common measure cannot exceed 609; we therefore try if 609 is the measure sought. 696 divided by 609 leaves a remainder of 87; therefore, 609 is not the greatest common measure.

Now, since the greatest common measure of 696 and 1305 is also the greatest common measure of 609 and 696, therefore, the measure sought cannot exceed their difference, 87; we therefore try if 87 measures 609. 609 divided by 87 leaves no remainder; therefore, 87 is the greatest common measure required.

Exercises.

1. Find the greatest common measure of 252 and 348,

Ans. 12.