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TXXXIII. 1. William had 2 qts. 1 pt. of wuinuts, which he wished to divide equally among his tww little brothers; how many must he give each?

2. James bought 2 books for 2 s. 6 d. ; how much did hae pay apiece?

3. If you pay 1 s. 6 d. for 2 inkstands, how many shillings. would that be apiece ?

4. A man bought 4 lambs for 6 shillings ; how many pence did he pay apiece?

5. William has 3 pks. 4 qts. of walnuts, which he wishes to put into 4 little baskets, each of which will hold 7 qts.; will his baskets hold all his walnuts, or not? and inform me how you do it.

6. 3 men have 4 gals. 2 qts. of cider allowed them every day; how much is that apiece?

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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, hy which we find how many mmes one number is contained in another of different denominations ? 4. Compound Division.

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

Q. How do you get the 7£in the

answer? 2012

A. I begin as in Short Division of £ s. d. 2) 15 3

whole numbers, and say, 2 is con8

tained in 15£, ? (£) times, and 1£

over, writing down the 7 times. Ans. £7 11 10

Q. What do you do with the 1£

| over? 4. 1£= 20 s. which I join or carry to the 3 s., making 23 s. Q. How ao you proceed then, to get the 11 s. ?

Ă. I say, 2 in 23, 11 times, and 1 8. over, writing down the 11 s. underneath.

Q. How do you get the 10 d. ?

Ă. 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 hand 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 numbe s.

Proof. Q. What is the proof?
A. The same as in Simple Division.

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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 to of a dollar, a yard ?-200. At 12 cents, or f of a dollar?-400. At 25 cents, or of a dollar?-800. A. $1400.

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

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

7. At 4 cents å 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 roda 10. How many dollars in 300£? In 900£? A. $4000. 11. Reduce 58 17 s. 6 d. to farthings. A. 5640 farthings.

12. How many pounds in 5640 farthings ? A. 5€ 17 s. 6 d. 13. Multiply 3600 by 254. A. 90600.

14. What will 1 ton of clover-seed cost, at 5 mills an ounou 3. $179.-20.

15. At 2 cents an inch, what will 1 yard of cloth cost? 4. 72 cents.

16. Reduce 1 tun to gills. A. 8064 gills.
17. Reduce 20 bushels to pints. A. 1280 pinte.
18. Reduce 4 tons to drams. n. 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 oliek at the usual rate of 60 times in a minute ? A, 031103000.

21. A father left legacies to his children as follows: to Thom. as 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 227.23 s. 6 d., Mary 12£ 12 s. 5 d., Susan 294 £ 16 s. 9 d.

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I XXXIV. 1. If one third (!) 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 cents ? 50 cents ? 100 cents ?

3. If you pay 3 cents for one fifth (1) 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? Înto 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. T'hree sixths. Three eighths. Eight twelfths.

Q. What arc 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 paris called ?

A. Fractions.
Q. Why called fractions ?
A. Because fraction signifies broken.

Q. You have seen, that, when any whole thing is divided into : parts, these parts are called thirds; into 4 parts, called fourths : what ihen, 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 ß) called ?
A. The denominator.
Q. Why so called ?

A. Because it gives the name or denomination to the parts.

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