7. flow many pence is of 1s.? of 2s.? } of 3s.?

of I s. 6 d.

of 1 s. 3 d.?

of 1 d.?

of 1 d. 2 qrs.?

of 1 s. 6d.? of 2 s. 6 d.?

Q. What is this, which you have now been doing, called?
A. Compound Division.

Q. Wherein does it differ from Simple?

A. Simple consists of only one denomination; Compound, of more than one.

Q. What, then, is the process called, by which we find how many mes one number is contained in another of different denominations!

A. Compound Division.

Operation by Slate illustrated.

1. A man bought 2 loads of hay for 15£3 s. 8d.; how much was that a load?

OPERATION.

20 12 £ S. d.

2) 15 3 8

Ans. £7 11 10.

Q. How do you get the 7£ in the

answer?

A. I begin as in Short Division of whole numbers, and say, 2 is contained in 15, 7 (£) times, and 1£ over, writing down the 7 times.

Q. What do you do with the 1£

over?

A. 1£20 s. which I join or carry to the 3 s., making 23 s. Q. How do you proceed then, to get the 11 s.?

A. I say,

2 in 23, 11 times, and I s. over, writing down the 11 s. underneath.

Q. How do you get the 10 d.?

A. The 1 s. over being equal to 12 d., I join or carry it to 8 d., making 20 d.; then, 2 in 20, 10 times.

From these illustrations we derive the following

RULE.

Q. At which band do you begin to divide, and how do you proceed? A. With the highest denomination, and divide as in Simple Division.

Q. If you have a remainder, how do you proceed?

A. Find how many of the next lower denomination this remainder is equal to, which add to the next denomination; after which divide as in whole numbers.

PROOF. Q. What is the proof?

A. The same as in Simple Division.

More Exercises for the Slate.

2. If 8 tons of hay cost 40€ 14 s. 8 d., what will 1 ton cost? A. 5£ 1 s. 10 d.

3. If 11 gals. of brandy cost 5£ 16 s. 5 d., what will 1 gallon cost? A. 10 s. 7 d.

4. If a man spend 60£ 13 s. 4 d. a week, how much is that a day? A. 8£ 13 s. 4 d.

5. If 1 cwt. of rice cost 2£ 6 s. 8 d., what will 1 lb. cost? A. 0£0 s. 5 d.

6. You have 31 £ 9 s. 6 d. to be divided equally among 2 men: how much would it be apiece ?-15-14-9. How much would it be apiece to be divided among 3?-10-9-10. Among 6?-5-4-11. A. 31£ 9 s. 6 d.

7. Will you divide 2 gals, 2 qts. by 4?-0-2-1. By 5?-0-2. By 10-0-1. By 2?-1-1. A. 2 gals. 2 qts. 1 pt.

8. Will you divide 96 acres, 2 roods, 16 rods, by 7?-13-3-8. By 8-12 0-12. By 12?-8-0-8. A. 33 acres, 3 roods, 28 rods.

Questions to exercise the foregoing Rules.

1. What is the sum of the following numbers, viz. one, two thousand, thirty thousand, four millions, twenty thousand, nineteen, four hundred millions? A. 404052020.

2. Bought a coat for 15 dollars, a vest for 1 dollar 37 cents, a pair of boots for 6 dollars 12§; what did the whole cost me ? A. $22,50.

3. Bought a horse for $75, and sold him for 37 cents less than he cost me; what did I get for him? A. $74,62,5.

4. What will 3200 yards of tape come to, at 64 cents, or of a dollar, a yard?-200. At 12 cents, or of a dollar?-400. At 25 cents, or of a dollar?-800. A. $1400.

5. How many yards in 31557600 rods? A. 173566800.

6. How many years in 31557600 seconds, allowing the year to contain 365 days? A. 1 year.

7. At 4 cents a gill, what will 1 tun of wine cost? A $322,56.

8. How much wine can be bought for $322,56, at 4 cents a gill? A. 1 tun.

9. How many rods in 1100 yds.? In 3300 yds.? A. 800 rods 10. How many dollars in 300£? In 900£? A. $4000. 11. Reduce 5£ 17 s. 6 d. to farthings. A. 5640 farthings

12. How many pounds in 5640 farthings? A. 5£ 17 s. 6d. 13. Multiply 3600 by 25. A. 90600.

14. What will 1 ton of clover-seed cost, at 5 mills an ounce? A. $179,20.

15. At 2 cents an inch, what will 1 yard of cloth cost? A.

72 cents.

16. Reduce 1 tun to gills. A. 8064 gills.

17. Reduce 20 bushels to pints. A. 1280 pints.

18. Reduce 4 tons to drams. A. 2293760.

19. How many barley corns will reach across the Atlantie Ocean, allowing it to be 3000 miles. 4. 570240000.

20. How many times will a watch click in 20 years, if it click at the usual rate of 60 times in a minute? A. 631152000.

21. A father left legacies to his children as follows: to Thomas 75£ 14 s. 6 d., to William 3 times as much as Thomas, to his daughter Mary as much as Thomas, and to Susan, his youngest child, as much as all the rest, lacking 20£ 13 s. 8d.: how much did each receive? A. William 227£ 3 s. 6 d., Mary 12£ 12 s. 5 d., Susan 294£ 16 s. 9 d.

¶ XXXIV.

FRACTIONS.

1. If one third (1) of an apple cost 2 cents, what will a whole apple cost?

2. If one third cost 3 cents, what will a whole one cost? If one third cost 4 cents, what will one whole apple cost? If one third cost 6 cents? 8 cents? 9 cents? 20 ce 50 cents? 100 cents?

3 If you pay 3 cents for one fifth (†) of an orange, what will a whole orange cost?

4. If you pay 2 dollars for one eighth (3) of a ticket, what will a whole ticket cost?

Q. How many halves to an apple, or any thing?

Q. How many thirds? Fifths? Eighths? Sixteenths? Q. When an apple, or any thing, is divided into two equal parts, would you call one of these parts a half or a third? Into 3 equal parts, what is one part called?

Q. Into 4 parts, what is 1 part called?
Q. Into 5 parts, what is 1 part called?
Q. Into 8 parts, what is 1 part called?
Q. Into 8 parts, what are 2 parts called?
Q. Into 8 parts, what are 5 parts called?

Q. When an apple, or any thing, is divided into two equal parts, how would you express one part, on the slate, in figures. A. I set the 1 down, and draw a line under it; then write the 2 under the line.

Let me see you write down in this manner, on the slate, One half. One third. One fourth. One fifth. One sixth. Two sixths. Three sixths. Three eighths. Eight twelfths.

Q. What are such expressions as these called?

A. Fractions.

Q. When, then, any whole thing, as an apple, a unit, &c. is broken or divided into equal parts, what are these parts called?

A. Fractions.

Q. Why called fractions?

A. Because fraction signifies broken.

Q. You have seen, that, when any whole thing is divided into 3 parts, these parts are called thirds; into 4 parts, called fourths: what. then, does the fraction take its name or denomination from?

A. From the number of parts into which any thing is divided.

Q. When an apple is divided into 6 parts, and you are desirous of giving away 5 parts, how would you express these parts?

A. §.

Q. What is the 6 (in §) called?

A. The denominator.

Q. Why so called?

A. Because it gives the name or denomination

the parts.

Q. What is the 5 (in §) called?

A. Numerator.

Q. Why so called?

A. Because it numerates or numbers the parts Q. Which is the numerator, then?

A. The number above the line.

Q. Which is the denominator?

A. The number below the line.

Q What, then, does the denominator show?

A. The number of parts a unit, or any thing, is divided into.

Q. What does the numerator show?

A. How many parts are taken, or used.

7

Q. In the expressions 3, 16, 12, 50, which are the numerators,

and which are the denominators!

Q. If you own 28 of a vessel, how many parts is the vessel supposed to be divided into? and how many parts do you own? A. 40 parts, and I own 28 parts.

Q. Is of an apple more than of it?

Q. What fraction, then, is greater than? Than? Than ? Than Than? What fraction is less than? Than Thar ? Than ?

Q. From these remarks, what appears to be a correct definition of fractions?

A. They are broken parts of a whole number. Q. How are they represented?

A. By one number placed above another, with a line drawn between them.

Q. In Simple Division, you recollect, that the remainder was represented in like manner; what, then, may justly be considered the origin of fractions?

A. Division.

Q. What may the numerator be considered?

A. The dividend.

Q. What may the denominator be considered?

A. The divisor.

Q. What, then, is the value of a fraction?

A. The quotient of the numerator divided by

the denominator.

Q. What is the quotient of 1 dollar divided among 2 men?
A. .

Q. What is the quotient of 7 divided by 8 ?