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51. Two thousand eight hun- , 62. One hundred thousand and dred and four,

ten. 52. Four thousand and twenty- | 63. Nine hundred and nine nine.

million and ninety thou53. Six thousand and sis.

sand. 54. Twenty-two thousand seven 64. One hundred million, ten hundred and sixty-five.

thousand and one. 55. Eighty thousand, two hun- | 65. Ninety-one million, seven dred and one.

thousand and sixty. 56. Ninety thousand and one. 66. Seventy million and four. 57. Thirty thousand and thirty. | 67. Soven hundred millions, 58. Four hundred and ten

ten thousand and one. thousand, two hundred and 63. One billion, one million five.

and forty. 59. Eight hundred thousand, 69. Forty billions, two hundred

six hundred and sisty-nine. thousand and five. 60. Nine hundred thousand 70. Seven hundred and twentyand one.

six billions, fifty millions, 61. Five hundred thousand and one thousand, two hundred fifty.

and forty-three.

ROMAN NOTATION. ART. 16. The common method of representing numbers, by figures, is termed the Arabic. Another method, by means of letters, is termed the Roman.

The letter I stands for one; V, five; X, ten; L, fifty; C, one hundred; D, five hundrel; and M, one thousand. Numbers are represented on the following principles : 1. Every time a letter is repeated, its value is repeated :

thus, II denotes two, XX denotes twenty. 2. When a letter of less value is placed before one of greater value, the less is takoil from the greater ; if placed after it, the value of the greater is increased :

thus, IV dcnotes four, while VI denotes six.

Review.-15. What is Notation? What is the Rulc? 16. What is the cominon mothod of Notation termod? What other method ? What number is represented by the letter I ? By V? By X? By L? By C? by D? By M? What is the effe:t of repeating a letter ?

16. What the effect of placing a letter of less value before one of greater valuo? After one of greater valuo? Wbat of placing a line over a letter ?

3. A line over a letter increascs its valuo a thousand times. Thus, V denotes 5000, M denotes one million.

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ART. 17. The preceding illustrations show the three methods of expressing numbers :

1st. By words, or ordinary language.
2D. By figures, termed the Arabic method.
30. By letters, termed the Roman method.

II. ADDITION. 1. If you have 2 cents and find 3 cents, how many will you then have?

Ans. 5 cents. 2. I spent 12 cents for a slate, and 5 cents for a copy book : how many cents did I spend ? Ans. 17 cents.

3. John gave 6 cents for an orange, 7 cents for pencils, and I cents for a ball: how many cents did they all cost ?

Ans. 22 cents.

Art. 18. The process of uniting two or more numbers inta one number, is termed Addition.

The number obtained by addition, is the Sum or Amount,

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REMARK. When the numbers to be added are of the same de nomination, that is, all cents, or all yards, &c., the operation is called Simple Addition.

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ART. 19. OF THE SIGNS. The Sign +, called plus, means more. When between two numbers, it shows that they are to be added; thus, 4+ 2 means that 4 and 2 are to be added together.

The sign of equality, =, denotes that the quantities between which it stands equal each other.

The expression 4+2=6, means that the sum of 4 and 2 is 6; read, 4 and 2 are 6, or 4 plus 2 equals 6.

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REVIEW.-17. What are the three methods of expressing numbers ? 18. What is Addition ? What the sum or amount? Rem. What is Simple Addition? 19. What does the sign plus mean? What does it show? What does the sign of equality denote? Give an example.

ART. 20. 1. James had 63 cents, and his father gave him 35 cents : how many cents had he then ?

Place the units and the tens of one number under the units and the tens of the other, that figures of the same unit value may be more casily added.

SOLUTION.-Write the numbers as in the margin; then say 5 units and 3 units are 8

63 cents. units, which write in units' place; 3 tons and 6 tens are 9 tens, which write in tens' place. The sum is 9 tens and 8 units, or 98 cents. Ans. 98.cents.

units.

35 cents,

In this example, units are added to units, and tens to tens, since only numbers of the same kind, that is, having the same unii value, can be added. Thus,

3 units and 2 tens make neither 5 units nor 5 tens; as, 3 apples and 2 plums are neither 5 apples nor 5 plums.

2. I own 3 tracts of land: the first contains 240 acres ; the second, 132 acres; the third, 25 acres : how many acres in all ?

Since units of different orders can not be added together, place units under units, tens under tens, &c., that figures to be added may be in the most convenient position.

SOLUTION. Begin at the right, and say 5 units and 2 units are 7 units, which write in units’ place; 2 tens and 3 tens and 4 tens are 9 tens, which write in tens' place : Lastly, 1 hundred and 2 hundrea's are 3 hun

397 acres. dreds, which write in hundreds' place, and the work is complete.

240 acres. 132 acres.

25 acres.

Questions to be solved and explained as above. The sign $ stands for the word dollars, and when used is placed before the figures.

3. There are 43 sheep in one pasture, 21 in another, and 14 in another: how many sheep in all? Ans. 78.

Review.–20. Why are units placed under units, and tens under tens ? Can numbers of different unit values be added? Why not? Give an example. What siga is tused for the word dollars?

4. I owc one man $210, another $142, and another $35 : what is the amount of the debts ? Ans. $387.

5. Find the sum of 4321, 1234, 3120. Ans. 8695. 6. The sum of 50230, 3105, 423. Ans. 53758.

ART. 21. Where the sum of the figures in a column does not exceed 9, it is written under the column added.

When the sum of the figures exceeds 9, two or more figures are required to cxpress it. To explain the method,

TAKE THIS EXAMPLE.

T. U.

1. James bought a reader for 74 cents, an atlas for 37 cents, a slate for 25 cents : how much did all cost ? ist Solution.—By adding the figures in

Reader 7 4 cents. the first column, the sum is 16, which is 1

Atlas 37 cents. ten and 6 units. Write the 6 units in the

Slato 25 cents. order of units, and the 1 ten in the order of tens.

16 The sum of the figures in the tens' column

12 is 12 tens, which is 1 hundred and 2 tens. Write the 2 tens in the order of tens, and

Ans, 136 cents. the 1 hundred ir the order of hundreds.

Lastly, unite the figures in the column of tens. The sum is 1 hundred, 3 tens, and 6 units, or 136 cents. 20 Solution. The preceding example is usually per

74 formed thus: 5 units 7 units and 4 units are 16 units, 37 which is 1 ten and 6 units. Write the 6 units in units' place, and carry the 1 ten to tens' place.

25

136 Chen, 1 ten 2 tens 3 tens and 7 tens are 13 tens, which is 1 hundred and 3 tens; write the 3 tens in tens' place, the 1 hundred in hundreds' place, and the work is completed.

The 1 ten derived from the sum of the figures in the 1st column, and added to the 2d, is said to be carried.

REVIEW.-21. When the sum of a column does not exceed 9, where is it written? If greater than 9 ? What is understood by carrying the tens? In what does it consist ? Why does the addition begin with the inits' column? 22. What is the rule for addition ? The proof?

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