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NUMERATION TABLE.

Those words at the head of the table are applicable to any sum or number, and must be committed perfectly to memory, so as to be readily applied on any occasion.

Hundreds of Millions.
Tens of Millions.
Hundreds of Thousands.
Tens of Thousands.
Millions.
Thousands.
Hundreds.
Tens.
Units.

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Of these characters, 1, 2, 3, 4, 5,

6, 7, 8, 9, 0, the nine first are some8 6 times called significant figures, or 4 3 2 digits, in distinction from the last,

3 .70 54 which, of itself, is of no value, yet,

8 6 200 placed at the right hand of another 90 O 3 mg 1 figure, it increases the value of 5 0 8 6 0 0 0 that figure in the same tenfold pro1 0 3 0 2 0 70 portion as if it had been followed by 806 1 0 5 4 0 9 any one of the significant figures.

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Note. Should the pupil find any difficulty in reading the following numbers, let him first transcribe them, and point them off into periods. 5768 52831209

286297314013 34120 175264013

5203845761204 701602 3456720834

13478120673019 6539285

25037026531 341246801734526 The expressing of numbers, (as now shown,) by figures, is called Notation. The reading of any number set down in figures, is called Numeration.

After being able to read correctly all the numbers in the foregoing table, the pupil may proceed to express the following numbers by figures :

1. Seventy-six.
2. Eight hundred and seven.

3. Twelve hundred, (that is, one thousand and two hundred.)

4. Eighteen hundred. 5. Twenty-seven hundred and nineteen. 6. Forty-nine hundred and sixty. 7. Ninety-two thousand and forty-five. S. One hundred thousaud. 9. Two millions, eighty thousands, and seven hundreds. 10. One hundred millions, one hundred thousand, one hundred and one.

11. Fifty-two millions, six thousand, and twenty.

12. Six billions, seven millions, eight thousand, and nine hundred.

13. Ninety-four billions, eighteen thousand, one hundred and seventeen.

14. One hundred thirty-two billions, two hundred millions, and nine.

15. Five trillions, sixty billions, twelve millions, and ten thousand.

16. Şeven hundred trillions, eighty-six billions, and seveu: millions.

ADDITION
OF SIMPLE NUMBERS.

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1 4. 1. James had 5 peaches, his mother gave him 3 peaches more; how many peaches had he then?

2. John bought a slate for 25 cents, and a book for eight cents; how many cents did he give for both ?

3. Peter bought a waggon for 36 cents, and sold it so as to gain 9 cents; how many cents did he get for it?

9 4. Frank gave 15 walnuts to one boy, 8 to another, and had 7 left; how many walnuts had he at first ?

5. A man bought a chaise for 54 dollars; he expended s dollars in repairs, and then sold it so as to gain 5 dollars ; how many dollars did he get for the chaise ?

6. A man bought 3 cows; for the first he gave 9 dollars, for the second he gave 12 dollars, and for the other he gave 10 dollars; how many dollars did he give for all the cows?

7. Samuel bought an orange for 8 cents, a book for 17 cents, a knife for 20 cents, and some walnuts for 4. cente ; how many cents did he spend ?

8. A man had 3 calves worth 2 dollars each, 4 valves worth 3 Jollars each, and 7 calves worth 5 dollars cach; bow many

calves had he? 9. · A man sold a cow for 16 dollars, some corn for 20 dollars, wheat for 25 dollars, and butter for 5 dollars; how many dollars must he receive ?

The putting together two or more numbers, (as in the foregoing examples,) so as to make one whole number, is called Addition, and the whole number is called the sum, or amount.

10. One man owes me 5 dollars, another owes me 6 dollars, another 8 dollars, another 14 dollars, and another 3 dollars; what is the amount due to me?

11. What is the amount of 4, 3, 7, 2, 8, and 9 doilars ?

12. In a certain school 9 study grammar, 15 study arithmetic, 20 attend to writing, and 12 study geography; what is the whole number of scholars?

SIGNs. A cross, t, che line horizontal and the other perpendicular, is the sign of addition. It shows that numbers, with this sign between them, are to be added together. It is sorzetimes read plus, which is a Latin word signifying

Two parallel, horizontal lines, =, are the sign of equality. It signifies that the number before it is equal to the number after it. Thus, 5 + 3 = 8 is read 5 and 3 are 8; or, 5 plus (that is, more) 3 is equal to 8.

In this manner let the pupil be iustructed to commit the following

more.

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ADDITION TABLE.

2+0= 2 3+0=

3 4 +0= 4 2+1:- 3 3-1 4 4+1= 5 2 + 2 = 4 3 +2=

5 4 4-2 6 2+3 = 5 3+3 6 4-4- 7 2 + + 6 3+4 71 4+ 8 2 +5 = 7 3 + 5 = 8 4 to 9 2 +6 8 3 + 6 = 9 4-5 2 +7= 9 3-67 = 10 4+7= !1 2+8=10 3 ; &:- 11 4 +3= 12 2+9=11 3+9=124 2

3+9 = 12 14.9=13 B

5+0 5 5+15. 6 5+ horny 5+ - 8 5

9 5+ 10 5 + 6 = 11 5+7= 12 5 +8=13 5 4-9 = 14

=10

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ADDITION TABLE-CONTINUED. 6 +0= 617+0 18+0= 8 9+0= 9 6 + 1 n

7 + 1

8 8+1= 9 9+1=10 6+ 8 7+2 = 9 8 +2=109+2=11 6+ 9 2+3= 10 8+3=11 9 +3=12 6 + 4 7+4=11 8+4

= 12

9 +4=13 6 +5=11 7+5 = 12 8 +5 13 9+5 = 14 6 + 6 = 127 +6= 13 8 + 6 = 14 9 +6 = 15 6+7= 137+7= 14 8+7=15 9+7= 16 6 +8=

-14 7 + 8 = 15 8+8= 16 9+8=17 6+9 = 15 7+9 = 16 8 +9 17 9+9= 18

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5 +9= how many ?
8+7= how many?
4+3+2= how many?
6+4+5= how many?
2+0+4+6= how many?

+1+0+8= how many?
3+0+9+5 = how many ?
97-2+6+4 +5= how many?
1+3+5+7 +8= how many?
1+2+3+4+5+6 = how many?
8+9+0+.2-4-4 4-5= how many?
6+2 +5+0+8+3=how many?

T 5. When the numbers to be added are small, the add1tion is readily performed in the mind; but it will frequently be more convenient, and even necessary, to write the numbers down before adding them.

13. Harry had 43 cents, his father gave him 25 cents more; how many cents had he then?

One of these numbers contains 4 tens and 3 units. The other number contains 2 tens and 5 units. To unite these two numbers together into one, write them down one under the other, placing the units of one number directly ander units of the other, and the tens of one number directly under tens of ibe cher, thus :

43 cents. Having written the numbers in this man25 cents. ner, draw a line underneath.

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43 cents.

We then begin at the right hand, and add

the 5 units of the lower number to the 3 25 cents.

units of the upper number, making 8 units, 8 which we set down in unit's place.

We then proceed to the next column, and 43 cents. add the 2 tens of the lower number to the 25 cents. 4 tens of the upper number, making 6 tens,

or 60, which we set down in ten's place, Ans. 68 cents. and the work is done.

It now appears that Harry's whole number of cents is 6 tens and 8 units, or 68 cents; that is, 43 +25= 68.

14. A farmer bought a chaise for 210 dollars, a horse for 70 dollars, and à saddle for 9 dollars; what was the whole amount:

Write the numbers as before directed, with units under units, tens under tens, &c.

OPERATION. Chaise, 210 dollars, Add as before. The units will Horse,

70 dollars. be 9, the tens 8, and the hundreds Saddle, 9 dollars. 2; that is, 210 + 70 +9=289. Answer, 289 dollars.

After the same manner are performed the following exannples:

15. A man had 15 sheep in one pasture, 20 in another pasture, ar.d 143 in another; how many sheep had he in the three pastures? . 15 + 29 + 143 = how many?

16. A man has three farms, one containing 500 acres, another 213 acres, and another 76 acres; how many acres in the three farms ? 500+213 +76= how many?

17. Bought a farm for 2316 dollars, and afterwards sold it so as to gain 550 dollars; what did I sell the farm for? 2316 + 550 = how many ?

Hitherto the amount of any one column, when added up, has not exceeded 9; consequently has been expressed by a single figure. But it will frequently happen that the amount of a single column will exceed 9, requiring two or more figures to express it. 18. There are three bags of money.

The first contain's 876 dollars, the second, 653 dollars, the third, 524 dollars, what is the amount contained in all the bags ?

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