25. The ROMAN NOTATION employs seven capital letters to express numbers, viz.:

All other numbers may be expressed by combining and repeating these letters.

26. The Roman Notation is based on the following principles :

1st. When two or more letters of equal value are united, or when one of less value follows one of greater, the sum of the values is indicated; thus, XX stands for 20, XXX for 30, LXV for 65, DC for 600, MDCCLXVIII for 1768.

2d. When a letter of less value is placed before one of greater, the difference of their values is indicated; thus, IV stands for 4, IX for 9, XL for 40, XC for 90.

3d. When a letter of less value stands between two of greater value, the less is to be taken from the sum of the other two; thus, XIV stands for 14, XIX for 19, CXL for 140.

TABLE OF ROMAN NUMERALS.

25. How many and what characters are employed in the Roman Notation? Value of each? How may other numbers be expressed?

26. What is the first principle in the Roman Notation? Second? Third?

EXERCISES IN ROMAN NOTATION.

27. Express the following numbers by letters:

1. Nine.

2. Fifteen.

Ans. IX. Ans. XV.

3. Eighteen.
4. Twenty-four.
5. Twenty-six.

6. Thirty-nine.

7. Forty.

8. Sixty.

9. One hundred and eighty-four.

10. One hundred and ninety-six.

11. One thousand six hundred and forty-six. 12. The present year, A. D.

28. Besides the Arabic and Roman figures, there are various marks used to indicate certain relations between numbers and operations to be performed on them, as, for example, the sign of equality, ; the sign of addition, +; the sign of subtraction,

•; etc.

These signs will be given, and their uses explained hereafter, when their aid is needed.

23. What characters are used in Arithmetic besides the Arabic and Roman figures? For what?

ADDITION.

29. Three apples and four apples are how many apples ? Ans. Three apples and four apples are seven apples.

This is a question in addition.

30. ADDITION is the process of finding how many units there are in two or more numbers of the same kind taken together. The result of the addition is called the sum or amount.

ADDITION TABLE.

2 and 1 are 3 3 and 1 are 4 4 and 1 are 5 5 and 1 are 6

2 2 2 2 N N N 2 2 2

66

66

2

66

3 " 8

63"

4 "

74"

4 "

85"

66 73 66 5 "

84"

5 "

95"

5" 10

66

66

93

3

"123

2 66

2 66

"8

66

"10

"10

11 3

6 and 1 are 7 7 and 1 are 8 8

83 66

6"

94"

6" 10 5 "

6 "11

30. What is Addition? What is the result called?

MENTAL EXERCISES.

Ex. 1. Robert has 5 cents in one hand, and 3 cents in the other; how many cents has ǹe in both hands? Ans. 8.

2. John bought a pencil for 6 cents, and some paper for 5 cents; how many cents did he pay for both?

3. George has 7 chickens and David has 8; how many have both?

Ans. 15.

4. Mary has 6 tulips and 9 roses; how many blossoms has she?

5. Daniel caught 9 fishes, Abel caught 6, and James caught 5; how many did they all catch?

6. A farmer had 6 cows in one pasture, 8 in another, and 7 in another; how many cows had he in the three pastures?

7. I paid 9 dollars for a barrel of flour, 8 dollars for a box of sugar, and 5 dollars for a cheese; how many dollars did I pay for all? Ans. 22.

8. A man bought a ton of coal for 8 dollars, a cord of wood for 6 dollars, and a stove for 9 dollars; what did he pay for all?

9. Charles has 5 marbles, Albert has 7, and Edward has 9; how many have they all?

10. A farmer has 8 sheep in one pen, 9 in another, and as many in a third pen as in both the others; how many has he in the third pen? Ans. 17.

11. A gardener raised 3 bushels of cherries, 2 bushels of currants, 5 bushels of peaches, and 8 bushels of pears; how many bushels of fruit did he raise?

12. George paid 10 cents for a writing-book, 8 cents for a pen-holder, 2 cents for pens, and 6 cents for ink; how much did he pay for all?

31. A SIGN is a mark which indicates an operation to be performed, or which is used to shorten some expression.

32. This mark, $, is often used as a sign of the word dollar or dollars; thus, $1 stands for one dollar, $6 stands for six dollars.

NOTE. It is customary to separate dollars and cents by a period; thus, $4.25 stands for four dollars and twenty-five cents.

33. The sign of equality, =, signifies that the quantities between which it stands are equal to each other; thus, $1 = 100 cents; that is, one dollar equals one hundred cents.

34. The sign of addition, +, called plus or and, denotes that the quantities between which it stands are to be added together; thus, 3+25; that is, three plus two equal five, or, three and two are five.

Ex. 12.

13.

14.

How many are 3 +5+4? Ans. 12.
How many are 2 + 6 + 5?

3+8+4?
How many are 5+3+6? 9+2+6?
How many are 8+ 6 + 5?
16. How many are 7+9+ 4?

15.

9+3+7?

6+9+8?

31. What is a sign? 32. Make the sign of dollars on the black-board. How are dollars and cents separated? Give an example. Another.

33. Make the sign of equality. What does it mean? Illustrate. 34. Make the sign of addition. What is it called? What does it mean?