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EXAMPLES IN EXPRESSING NUMBERS BY FIGURES.

1. Write four in figures.

Ans. 4. 2. Write-four tens or forty.

Ans. 3. Write four hundred.

Ans. 400. 4. Write four thousand.

Ans. 5. Write forty thousand.

Ans. 40,000. 6. Write four hundred thousand.

Ans. 7. Write four millions.

Ans. 4,000,000. These examples show us very clearly that the same significant figure will have different values according to the place which it occupies.

8. Write six hundred and seventy-nine. Ans. 679. 9. Write six thousand and twenty-one, 10. Write two thousand and forty. 11. Write one hundred and five thousand and seven. 12. Write three billions. 13. Write ninety-five quadrillions.

14. Write one hundred and six trillions, four thousand and two.

15. Write fifty-nine trillions, fifty-nine billions, fiftynine millions, fifty-nine thousands, fifty-nine hundreds, and fifty-nine.

16. Write eleven thousand, eleven hundred and eleven. 17. Write nine billions and sixty-five.

18. Write three hundred and four trillions, one mil. lion, three hundred and twenty-one thousand, nine hundred and forty-one.

19. Write nine trillions, six hundred and forty billions, with 7 units of the ninth order, 6 of the seventh order, 8 of the fifth, 2 of the third, 1 of the second, and 3 of the first.

20. Write three hundred and five trillions, one hundred and four billions, one million, with 4 units of the 5th order, 5 of the 4th, 7 of the 2d, and 4 of the first.

21. Write three hundred and one billions, six millions, four thousand, with 8 units of the 14th order, 6 of the 3d, and 2 of the second.

22. Write nine hundred and four trillions six hundred and six, with four units of the 18th order, five of the 16th, four of the 12th, seven of the 9th, and 6 of the 5th.

11. There is another method of expressing numbers, called the Roman. In this method the numbers are represented by letters. The letter I stands for one ; V, five; X, ten; L, fifty ; C, one hundred; D, five hun. dred, &c.

ROMAN TABLE.

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1.
One
LXX.

Seventy
II.
Two
LXXX.

Eighty
III.
Three
XC.

Ninety
IV.
Four
C.

One hundred
V.
Five
CC..

Two hundred VI. Six CCC.

Three hundred VII. Seven CCCC.

Four hundred VIII. Eight D.

Five hundred IX. Nine DC.

Six hundred X. Ten DCC.

Seven hundred XX. Twenty DCCC.

Eight hundred XXX. Thirty DCCCC.

Nine hundred XL. Forty M.

One thousand L. Fifty MM.

Two thousand LX. Sixty MMD.

2500. 12. We see, that there are three methods of expressing numbers: 1st, by words or common language ; 2d, by figures, called the Arabic method ; and 3d, by letters, called the Roman method.

.

EXAMPLES.

1. Write 1847 in common language : also in the Ro. man notation.

2. Write MDCCC in figures, and also in common language.

3. Write 2675 in common language: also in the Roman.

4. Write 98447096 in common language.

5. Write MMMDCCIV in common language, also in figures.

11. What characters are used in the Roman notation? What does X stand for? What does D stand for?

12. How many methods are there of expressing numbers? What are they? What is the the by means of figures called? The one by letters ?

ADDITION OF SIMPLE NUMBERS.

13. John has three apples and Charles two: how many apples have both of them? Every boy will answer five.

Here a single apple is the unit, and the number five contains as many units as the two numbers three and two. The operation by which this result is obtained is called Addition. Hence,

ADDITION is the process of uniting together two or more numbers, in such a way, that all the units which they contain may be expressed by a single number.

Such single number is called the sum or sum total of the numbers added. Thus, five is the sum of the apples possessed by John and Charles.

What is the sum of 2 and 4? Of 3 and 5? Of 6 and 3 ? Of 4, 3 and 1 ? Of 2, 3 and 4? Of 1, 2, 3, and 4 ? Of 5 and 7 ?' How many units in 4 and 6 ?

OF THE SIGNS.

14. The sign +, is called plus, which signifies more. When placed between two numbers it denotes that they are to be added together.

The sign =, is called the sign of equality. When placed between two numbers it denotes that they are equal to each other; that is, that they contain the same number of units. Thus, 3+2=5.

When the numbers are small we generally read them, by saying, 3 and 2 are 5.

Before adding large numbers the pupil should be able to add, in his mind, any two of the ten figures. Let him commit to memory the following table, which is read, two and 0 are two; two and one are three ; &c.

13. What is addition? What is the single number called which expresses all the units of the numbers added? How many units in 3 and 2? What is 5 called?

14. What is the sign of addition ? What is it called? What does it signify? Express the sign of equality. When placed between two numbers what does it show?. When are two numbers equal to each nther? Give an example.

2+0= 2 2+1= 3 2+2= 4 2+3= 5 2+4= 6 2+5= 7 2+6= 8 2+7= 9 2+8=10 2+9=11

ADDITION TABLE.
3+0= 3 4+0=4
3+1= 4 4+1= 5
3+2= 5 4+2= 6
3+3= 6 4+3= 7
3+4= 7 4+4= 8
3+5= 8

4+5= 9
3+6= 9 4+6=10
3+7=10 4+7=11
3+8=11 4+8=12
3+9=12 4+9=13

5+0= 5 5+1= 6 5+2= 7 5+3= 8 5+4= 9 5+5=10 5+6=11 5+7=12 5+8=13 5+9=14

6+0= 6 6+1=7 6+2= 8 6+3= 9' 6+4=10 6+5=11 6+6=12 6+7=13 6+8=14 6+9=15

7+0= 7
7+1= 8
7+2= 9
7+3=10
7+4=11
7+5=12
7+6=13
7+7=14
7+8=15
7+9=16

8+0= 8 8+1= 9 8+2=10 8+3=11 8+4=12 8+5=13 8+6=14 8+7=15 8+8=16 8+9=17

9+0= 9 9+1=10 9+2=11 9+3=12 9+4=13 9+5=14 9+6=15 9+7=16 9+8=17 9+9=18

2+3= how many ? 1+2+4= how many ? 2+3+5+1= how many ?

6+7+2+3= how many ?

1+0+7+2+3= how many ? 1+2+3+4+5+6+7+8+9 how many ? 1. What is the sum of 3 and 3 tens? Ans. 2. What is the sum of 8 téns and 9 ? Ans. 89. 3. What is the sum of 4, 5, and 4 tens ? Ans. 4. What is the sum of 1, 2, 3, 4, and 9 tens ? 5. What is the sum of 1, 2, 3, 4, 5, and 6 tens ? 6. What is the sum of 1, 4, 9, and' 5 tens? Ans. 64. 7. What is the sum of 4, 8, 3, and 7 tens ? 8. What is the sum of 1, 2, 4, and one hundred ?

9. What is the sum of 1, 3, 4, and 4 units of the second order ?

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10. What is the sum of 4 and 5, and 4 units of the third order ?

11. What is the sum of 6 and 2, and 5 units of the third order?

12. James has 14 cents, and John gives him 21 : how many will he then have ?

14 Having written the numbers, as at the 21 right of the page, draw a line beneath them.

35

!

The first number contains 4 units and 1 ten, the second 1 unit and 2 tens. We write the units under the units, and the tens under the tens.

We then begin at the right hand, and say 1 and 4 are. 5, which we set down below the line in the units' place. We then proceed to the next column, and add the tens, by saying 2 and 1 are 3, which we write in the tens? place. Hence, the sum is 35: that is, James will have 35 cents.

13. John has 24 cents, and William 62: how many have both of them ?

We write the numbers as before, and 24 draw a line beneath them. We then add 62 the units to the units, and the tens to the 86 tens.

14. A farmer has 160 sheep, 20 cows, and 16 young cattle: how many in all ? We write the numbers so that units shall

160 stand under units, tens under tens, and hun."

20 dreds under hundreds. By adding, we find

16 the sum of the units to be 6, the sum of the tens 9, and the sum of the hundreds 1 : and

196
the entire sum 196.
Add together the following numbers:
(1)
(2)
(3)

(4)
328
304
891

3607
171
273
104

4082
499

7689

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