51. Two thousand eight hundred and four. 52. Four thousand and twenty- 53. Six thousand and six. 55. Eighty thousand, two hun dred and one. 56. Ninety thousand and one. 58. Four hundred and ten 61. Five hundred thousand and 62. One hundred thousand and ten. 63. Nine hundred and nine 64. One hundred million, ten 66. Seventy million and four. 68. One billion, one million and forty. 69. Forty billions, two hundred thousand and five. 70. Seven hundred and twentysix billions, fifty millions, one thousand, two hundred and forty-three. ROMAN NOTATION. ART. 16. The common method of representing num bers, 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 hundred; 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 taken from the greater; if placed after it, the value of the greater is increased: thus, IV denotes four, while VI denotes six. REVIEW.-15. What is Notation? What is the Rule? 16. What is the common method of Notation termed? 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 effect of repeating a letter? 16. What the effect of placing a letter of less value before one of greater value? After one of greater value? What of placing a line over a letter? 3. A line over a letter increases its value a thousand times. Thus, V denotes 5000, M denotes one million. 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. 3D. By letters, termed the Roman method. II. ADDITION. 1. If you have 2 cents and find 3 cents, how many you then have? will 2. I spent 12 cents for a slate, and 5 book: how many cents did I spend? Ans. 5 cents. cents for a copy Ans. 17 cents. 3. John gave 6 cents for an orange, 7 cents for pencils, and 9 cents for a ball: how many cents did they all cost? Ans. 22 cents. ART. 18. The process of uniting two or more numbers into one number, is termed Addition. The number obtained by addition, is the Sum or Amount. REMARK. When the numbers to be added are of the same denomination, that is, all cents, or all yards, &c., the operation is called Simple Addition. 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. 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 easily added. SOLUTION. Write the numbers as in the margin; then say 5 units and 3 units are 8 units, which write in units' place; 3 tens and 6 tens are 9 tens, which write in tens' place. The sum is 9 tens and 8 units, or 98 cents. tens. units. 63 cents. 35 cents. Ans. 98 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 unit 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 240 acres 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: 132 acres. 25 acres. 397 acres. Lastly, 1 hundred and 2 hundreds are 3 hundreds, which write in hundreds' place, and the work is complete. 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 sign is used for the word dollars? 4. I owe one man $210, another $142, $35 what is the amount of the debts? 5. Find the sum of 4321, 1254, 3120. 6. The sum of 50230, 3105, 423. and another Ans. $387.` Ans. 8695. 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 express it. To explain the method, TAKE THIS EXAMPLE. 1. James bought a reader for 74 cents, an atlas for 37 cents, a slate for 25 cents: how much did all cost? 1ST SOLUTION. By adding the figures in the first column, the sum is 16, which is 1 ten and 6 units. Write the 6 units in the order of units, and the 1 ten in the order of tens. The sum of the figures in the tens' column is 12 tens, which is 1 hundred and 2 tens. Write the 2 tens in the order of tens, and the 1 hundred in the order of hundreds. T. U. Reader 74 cents. Atlas 37 cents. Slate 25 cents. 16 12 Ans. 136 cents. Lastly, unite the figures in the column of tens. The sum is 1 hundred, 3 tens, and 6 units, or 136 cents. 2D SOLUTION. The preceding example is usually performed thus: 5 units 7 units and 4 units are 16 units, which is 1 ten and 6 units. Write the 6 units in units' place, and carry the 1 ten to tens' place. 74 37 25 136 Then, 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 units' column? 22. What is the rule for addition? The proof? |