RULE II.

§ 20. To write in Figures any given Number.

Place proper figures from left to right, to denote the number in each of the descending orders of units, from the highest in the given number down to simple units; observing to fill each vicant place with a 0. (§ 17.)

EXAMPLE.

To write in figures the number

Three millions, twenty-five thousand, and thirty.

The descending orders of units in this number, are

3 millions, 2 tens of thous., 5 thousands, and 3 tens.

3025030;

in which the vacant places of hundreds of thousands, hundreds, and units, are filled with Os.

EXERCISES.

Write in figures each of the following numbers:

19. Twelve thousand and ten. 31. Nine hundred and one thou20. Twenty thousand and nine. [sand, one hundred and nine.

143. One hundred millions.

32. One million. 33. Five millions, five hundred 44. Three hundred millions, thousand. one hundred thousand. 34. Nineteen millions, two hun-45. Five hundred and thirtydred and forty-seven thous. four millions, nine hundred. 35. Thirty millions, one hun- 46. Six hundred and nine mildred and fifty thousand, seven

hundred.

36. Seventy-five millions, eight 47. hundred and sixty-four thousand, nine hund. and twelve.

lions, fifty thousand, one hundred and twenty-five.

Nine hundred and seventeen millions, five hundred thous.,four hundred and sixty.

ty thousand, three hundred and four.

37. Eleven millions, seven hun- 48. Five hundred millions, sixdred and fourteen thousand. 38. Twenty-nine millions, four hundred and one thousand, 49. two hundred and ten. 39. Thirty millions, nine hundred and twenty thousand.

Seven hundred and ten millions, one hundred thousand, five hundred and ninety-one.

40. Seven millions, eighty-five 50. Three hundred and one milthousand, six hundred and forty-nine.

41. Eighty-five millions, eighty-
seven thousand, four hundred
and ninety seven.
42. Ninety-nine millions, one
hundred and eleven thousand,
one hundred and one.

lions, seven hundred and ten. 51. Eight hundred and six millions, nine hundred and nineteen thousand, one hundred. 52. Nine hundred and ninetynine millions, nine hundred and ninety-nine thousand, nine hund. and ninety-nine.

French and English Numeration.

§ 21. In the French system of Numeration, which prevails in continental Europe, and in America, a thousand millions make one billion, a thousand billions make one trillion, and so on (§ 9 and § 12).

In the English system, a million millions make one billion, a million billions make one trillion, and so on.

Hence, in this system, after hundreds of millions, the ascending order of units are, thousands of millions, tens of thousands of millions, hundreds of thousands of millions, billions; and in like manner after hundreds of billions, &c.

For example, the number 3 840 930 670 820, in the French system, is 3 trillions, 840 billions, 930 millions, 670 thousand, eight hundred and twenty.

In the English, it is 3 billions, 840930 millions, 670820.

§ 22. ADDITION consists in finding the sum or aggregate amount of two or more numbers.

Thus the sum of 4 and 5 is 9; or 5 added to 4 makes 9.

What is the sum of 7 and 3? Of 6 and 4? Of 8 and 5?

The Sum found may be regarded as a whole, of which the given numbers are the parts.

What is the sum of 4, 6 and 8? Then what is the whole, and what are its parts? What is the sum of 10, 4, and 3? Then what is the whole, and what are its parts?

§ 23. The whole is equal to the sum of all its parts.

Recite the elementary sums of numbers; thus 1 and 1 are 2; 1 and 2 are 3; &c.-2 and I are 3; 2 and 2 are 4; &c., as given from left to right in the

Addition Table.

81

6 and are 72 are

73 are 8 are 95 are 106 are 11|7
83. are 94 are 105 are 116 are

1 and 1 are 22 are 33 are 44 are 55 are 66 are 77 are 88 are 99 are 10 2 and are 32 are 43 are 54 are 65 are 76 are 87 are 98 are 109 are 11 3 and 1 are 42 are 53 are 64 are 75 are 86 are 97 are 10| 8 are 119 are 12 4 and 1 are 52 a are 63 are 74 are 8 85 are 96 are 107 5 and are 62 are

are 118 are 129 are 13

are 128 are 13 9 are 14

12/7

are 13 8 are 14 9 are 15

7 and are 82 are

933 are 104 are 11 5 are 126 are 137 are 14|8 are 159 are 16

8 and 1 are 92 are 10|3 are 11|4 are 12|5 are 13|6 are 14|7 are 158 are 16|9 are 17 9 and 1 are 10 2 are 11 3 are 124 are 135 are 14|6 are 157 are 168 are 179 are 18 :0 and|1 are 11|2 are 12/3 are 134 are 14/5 are 15|6 are 16|7 are 178 are 189 are 19 |11 and 1 are 12/2 are 1334 3 are 14 4 are 15 5 are 166 are 177 are 188 are 199 are 20 12 and 1 are 132 are 14 3 are 15|4 are 16 5 are 176 are 187 are 19 3 are 20|9 are 21

Sign of Addition.

$ 24. The sign +, called plus, placed between numbers, signifies that the numbers are to be added together.

Thus 5+4, 5 plus 4, signifies 5 and 4 added together.

What is the sum of 4+3+2? Of 6+4+8?

Sum of Concrete Numbers.

Of 7+3+4+6?

$ 25. The sum of similar concrete numbers, is a concrete number of the same kind.

Thus, the sum of 5 cents and 4 cents is 9 cents.

What is the sum of 6 pounds +5 pounds? Of 7 days + 3 days + 5 days? Of 10 miles 9 miles? Of 12 pints + 6 pints+2 pints? § 2. Dissimilar concrete numbers cannot be united in one number.

Thus we cannot add 5 cents and 3 days together.

RULE III.

$27. To Add two or more Numbers together.

1. Set the numbers one under another, with units under units, tens under tens, &c.

2. Proceeding from right to left, add up each column of figures, and under each set its amount, if less than 10.

3. If the amount be 10 or more, set down its right hand figure, and add the left figure or figures to the next column. Set down the whole amount of the last column.

EXAMPLE.

To find the Sum of 930+6754+8621

930

6754

8621

16305

Having set units under units, tens under tens, &c., we say 1 and 4 are 5, and set 5 under the units' column.

Then, 2 and 5 are 7, and 3 are 10. We set the 0 under the tens' column, and add or carry the 1 to the next column; thus 1 and 6 are 7, and 7 are 14, and 9 are 23. We set 3 under that column. and say 2 and 8 are 10, and 6 are 16.

The left hand figure in the amount of any column, denotes the number of tens in that amount; and these tens are so many units when carried to the next column on the left. (§ 11.)

In the preceding example, the amount of the tens' column is 10 tens. But 10 tens being 1 hundred, we set down no tens, and add I to the hundreds' column,-which makes 23 hundreds, or 2 thousands and 3 hundreds. The 3 is put in the hundreds' place, and the 2 is added to the thousands' column, making 16 thousands.

By thus carrying one for every ten, from right to left, we find the numnber belonging to each distinct order of units in the sum of the several numbers. The whole is equal to the sum of all its parts.

The Operation Proved.

§ 28. Addition may be verified or proved, by adding the several columns of figures downwards; the Sum must be the same as when they are added upwards.

Thus to prove the operation in the preceding example, we begin at the top, and say 4 and 1 are 5; then 3 and 5 are 8, and 2 are 10. Setting down the 0, and carrying the 1, we say 1 and 9 are 10, and 7 are 17, and 6 are 23; then 2 and 6 are 8, and 8 are 16.

The Sum found is the same as before.

EXERCISES.

1. John has 95 chestnuts, Thomas has 180, and Charles 270; what number have they all together?

The whole number of chestnuts will be found by adding together 95, 180, and 270. Answer, 545 chestnuts.

2. A farmer being asked how many sheep he had, replied: "in one field I have 410, in another 500, in another 602." How many had he? Ans. 1512 sheep.

3. A merchant bought cloth for 375 dollars, linen for 83 dollars, silk for 234 dollars, and calico for 75 dollars. What sum did he expend for the whole ? Ans. 767 dollars.

4. A gentleman bought a carriage for 350 dollars, a pair of horses for 240 dollars, and a set of harness for 100 dollars. What did the whole amount to? Ans. 690 dollars.

5. Going out to collect money, I received from one person 13 dollars, from another 124 dollars, from another 89 dollars, and from another 20 dollars. What was the whole sum collected? Ans. 246 dollars.