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Practical Questions on the foregoing.

1. A boy, having 18 apples, gave them to his companions, as follows; to William 4, to Rufus 6, and to Thomas 5: how many did he give away in all, and how many had he left?

2. Thomas gave to one of his companions 6 peaches, to another 3, to another 2, and sold 3: how many had he at first? 3. A man bought a wagon for 17 dollars, and gave 5 dollars to have it repaired, then sold it for 26 dollars; how much did he make by the bargain?

4. A man bought a horse for 25 dollars, and, to pay for it, gave 6 bushels of rye, worth 6 dollars, and the rest in money; how much money did he pay?

5. Rufus, having 20 cents, bought a book for 12 cents, and a knife for 6 cents; how much more did the book cost than the knife? and how many cents had he left?

6. What is the cost of 5 yards of cloth, at 4 dollars a yard? At 3 dollars? At 7 dollars? At 2 dollars? At 8 dollars? At 9 dollars? At 12 dollars?

7. If 1 lemon be worth 3 apples, how many lemons are 6 apples worth? Are 12 apples worth? Are 18 apples worth? Are 24 apples worth? Ave 36 apples worth?

8. 11ow many barrels of flour, at 8 dollars a barrel, can you buy for 16 dollars? For 48 dol'ars? For 96 dollars? For 80 dollars?

Are 4, 2, and 6? Art. Are 10, 8; and 2? Are 5,

9. Ilow many are 2, 3, and 5? 8, 3, and 2? Are 9, 3, and 4?

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Are 7, 6, 3, and 2? Are

G times 4? 6 times 7?

4, 3, and 2?
8. 9. and 10?
10.
7 times 8? 9 times 7? 12 times 7? 9 times 5? 8 times 7?
7 times 6? 7 times 9? 12 times 11 8 times 5? 3 times
72 12 times 12?

Are 12, 11, 10, and 9?
How many are 6 times 3?

11. How many times 2 in 12? 2 in 18? 2 in 24? 3 in 62 3 in 12? 3 in 36? 4 in 20? 4 in 32? 4 in 48? 5 in 253 5 in 352 5 in 602 6 in 36? 6 in 489 6 in 72? 7 in 14? 7 in 56? 7 in 84? 8 in 40? 8 in 96? 36? 9 in 108? 11 in 22? 11 in 55? 11 in 132? 12 in 144?

9 in

Note.-Younger pupils should be required to review and dwell on the preceding questions for illustration, and the tables, till their solutions be made perfectly familiar.

NUMERATION.

TV. Q. When I say to you, "Give me that book," do I mean one book, or more than one?

Q. When we speak of a single thing, then, what is it called? . A unit, or one.

Q. What are one unit and one more, or one and one, called? Q. What are two units and one more, or two and one, called? Q. What are three units and one more, or three and one, called? Q. What are four units and one more, or four and one, called? Q. What are five units and one more, or five and one, called? Q. What are six units and one more, or six and one, called! Q What are seven units and oue more, or seven and one, called ? Q Wat are eight units and one more, or eight and one, called? QW are mine units and one more, or nine and one, called? Q. Now to be obliged always to write these numbers out in words, would be very troublesome: to prevent this, how do we sometimes ex press the numbers one, two, &c. up to thousands, millions, &c.? A. By letters.

Q. What does the letter I stand for?

A. One.

Q. What does the letter V stand for?
A. Five.

Q. What does the letter X stand for?
A. Ten.

Q. What does the letter L stand for 1
A. Fifty.

Q. What does the letter C stand for 1
A. One hundred.

Q. What does the letter D stand for !
A. Five hundred.

Q. What does the letter M stand for 1
A. One thousand.

Q. You said that V stands for five suppose you place the letter before the V, thus, IV, what will both these letters stand for them? A. Only four.

Q. What, then, may be considered as a rule for determining the value of these letters ?

A. A letter standing for a smaller number, and before a larger, takes out its value from the larger. Q. One X stands for ten; what do two X's stand for?

A. Twenty.

Q. What, then, is the value of a letter repeated?

A. It repeats the value as often as it is used.
Q. How many letters do we use for expressing numbers 1
A. Seven.

Q. Will you name them?

A. I, V, X, L, C, D, M.

Q. What is this method of expressing numbers by letters called P A. The Roman method.

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1 VI. We have a shorter method still, which is in very general Bee, as will appear by observing what follows:

A unit, or one, is written....................................

Two,...

Three,

Four,..

Five,

.1.

.2.

.3.

.4

.5.

.5.

Six,

Seven,
Eight,
Niue,

Q. What are these characters called?

A. Figures.

Q. By what other name are they sometimes called !
A. The 9 digits.

Q. What is this method of expressing numbers called !
A. The Arabic method.

Q. Why so called !

A. Because the Arabs are supposed to have in

vented it.

Let me see you write down on the slate, in Agures, the numbem one, two, three, four, five, six, seven, eight, wine.

Q. To express seu, as we have no ane chwarter that will do it what two characters do we make use of to represent this number !

A. The first character, 1, and 0 or cipher's thus, 10.

Q. What place does the 0, or cipher, in this case take?
A. The units' place.

Q. What place does the figure 1 take?

A. A new place.

Q. What is this new place called ?

A. The tens' place.

Q. Write down in figures, on the slate, the number ten, now take away the 1, and what will be left ?

A. Nothing but 0, or cipher.

Q. What is the value of this 0, or cipher, thus standing alone f
A. No value.

Q. Now place the 0 at the right of the figure 1, and what will it becomes

Q. How was it obtained from the Arabs?

A. The Moots communicated it to the Spaniards, and John of Basingstoke Archdeacon of Leicester, introduced it into England; hence its introductiei into our own country

Q. About what time was it introduced into England?

A. About the middle of the eleventh century.

Q. How extensively is it now used?

4. All over the civilized world

A. Ten, (10.)

Q. How many times is the figure I increased by the 0 or cipher 1 A. Ten times.

Q. What effect, then, has a cipher, in all cases, when placed at the eight of figures?

A. It increases the value ten times.

Q. In what proportion is this increase said to be?
A. Tenfold proportion.

As you have probably learned by this time how to write down ten In figures, by the help of a cipher, and learned also the value of thie eipher, we will now proceed to higher numbers; and to begin: let me sec you write down in figures, on the slate, the following numbers, viz. One ten and one unit, or eleven,...........

...

Que ten and two

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One ten and three

Oue ten and four

One ten and five

units, or twelve,.....
units, or thirteen,....
units, or fourteen,

12

13

14

units, or fifteen.............
units, or sixteen,.......

....15

16

....17

18

....19

....

....20

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One ten and six
One ten and seven units, or seventeen,..
One ten and eight units, or eighteen,
One ten aud nine units, or nineteen,
Two tens,.
......................................or twenty,
Three tens,.............or thirty,
Four tens...............or forty,....
Five tens...............or fifty,.
Six tens............................................or sixty......................................................60

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Seven eus,.............or seventy,
Eight tens,.............or eighty,..
Nine tens,..............or ninet 7,

.....

Ten tenis,...............or que hundred, ..........................100

Q. Here we see the value of the cipher again; for, by placing a eipher at the right of ten, it becomes one hundred, (100,) that is; ten teus: should we place another cipher still at the right of the 100, (thus, 1000,) what would it become?

A. One thousand, (1000.)

Q. From what you have now seen of the value of figures, what may and 5 be made to stand for?

A. 25 or 52.

Q. What is this different value called, which arises from the figuret being placed or located differently?

A. Their local value.

Q. What would be the value of the five written alone?

A. Simply 5.

Q. What is the value, then, of a figure standing alone 1
A. The simple value.

Q. How many values do figures appear to have 7

A. Two.

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