3. Three hundred and eighty-five.

4. Two thousand six hundred and ten.

5. Sixty-four thousand, five hundred and thirty-six. 6. Two hundred and fifty-three thousand, eight hundred and forty-two.

7. Five millions, six hundred thousand and six.

8. Ninety millions, three hundred and five.

9. Eight hundred and twenty-nine millions, six thousand and two.

Write down in words at length the following sums :

5, 17, 35, 458, 6829, 72348, 384721, 2683200, 50678024.

Numbers are also expressed by letters, and are called numeral letters, or Roman numbers. Thus,

1 2 3 4 5 6 7 8 9 10 11 20 30 1, II, III, IV, V, VI, VII, VIII, IX, X, XI, XX, XXX, 40 41 50 60 70 80 90 100 200 500 1000 XL, XLI, L, LX, LXX, LXXX, XC, C, CC, D, M.

When a letter of less value stands before one of a greater, it diminishes, but when placed after, it increases, the value of the greater.

SECTION 2.

OF ADDITION.

ADDITION is of two kinds, viz. Simple and compound. Simple addition teacheth to collect two or more numbers of the same denomination into one sum: as, 6 dollars and 4 dollars, make 10 dollars.

RULE 1. Write the different numbers in the given sum in such a manner, that the units may stand under units, the tens under tens, the hundreds under hundreds, &c. till the whole is set down.

2. Begin with the column of units, and add it into one sum, carrying to the next column, one for every ten, and set down the remainder directly underneath: proceed in the same manner from tens to hundreds, &c. till all is finished.

Prove the work by reckoning downwards as well as upwards, and if the amounts be equal the work is right.

Application.

1. Add 125 +23+16+2060+8009574+6.

Ans. 8011801. 2. Add one hundred and twenty-nine, six hundred and fifty-four, eight thousand and seventy, ten thousand, and four millions. Ans. 4018853. 3. If I have received 125 dollars from A, 286 from B, 29 from C, 672 from D; how much have I received from all four? Ans. 1112.

4. Bought 60 barrels of flour from one man for 480 dol lars, 75 barrels from another for 675 dollars, 220 from another for 2200 dollars, and 126 from another for 1386 dollars; how many barrels of flour had I, and how much did they cost me? Ans. 481 barrels, and cost 4741 dolls. 5. A farmer raised in one year 297 bushels of wheat, 125 of rye, 754 of corn, 127 of barley, and 245 of oats; how many bushels did he raise in all! Ans. 1548.

6. Add one thousand two hundred and nine, four hundred and seventy-six, eight thousand and seventeen, three millions, one hundred and nineteen thousand, two hundred and twenty-one together. Ans. 3128923.

7. James was born in the year 1811; in what year will he Le 21 years old? Ans. 1832.

8. A father bequeathed to his 5 sons the following sums, viz: to George he gave 3560 doliars, to William 3240, to Samuel 2850, to Henry 2555, and to Thomas 2226; how much did he bequeath in all? Ans. 14431 dolls.

SECTION 3.

OF SUBTRACTION.

SUBTRACTION is either simple or compound. Simple subtraction is the taking a less number from a greater, and thereby finding the difference.

RULE.

Place the less number under the greater, with units under inits, tens under tens, &c.; begin with the units, and tale the under figure from the upper, and then proceed with te

tens, &c. in the same manner. But if the under figure is the greatest, then suppose ten added to the upper figure, and take the lower from that number, carrying 1 to the next place. Or, take the lower figure from 10 and add the upper one to the remainder.

PROOF.

Add the remainder to the less number, and that will equal the greater.

1. What was the age of a man in the year 1818, who was born in 1777 ? Ans. 41 years old. 2. A merchant owes 5648 dollars, and pays thereof 3460; how much is yet to pay? Ans. 2188 dolls. 3. D having on hand 1260 barrels of flour, sells to A 320, and to B 435; how many barrels are yet unsold? Ans. 505 barrels. 4. From six thousand take six hundred, and tell what remains. Ans. 5400.

5. Suppose a boy had 145 cents given him at one time, 75 at another, and 40 at another; and he gave 35 cents for a penknife, 25 for a slate, 64 for paper, and 30 for apples; how many cents has he left? Ans. 106 cents.

SECTION 4.

OF MULTIPLICATION.

MULTIPLICATION is either simple or compound. Simple multiplication is a compendious way of adding numbers of the same denomination into one sum.

The number to be multiplied, is called the multiplicand.
The number multiplied by, is called the multiplier.
The amount produced, is called the product.
The multiplier and multiplicand are often called factors.

MULTIPLICATION TABLE.

1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8|10|12|14|16| 18| 20| 221 24 3 6 9|12|15|18|21|24| 27| 30| 33| 36 4 8121620|24|28|32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6|12|18|24|30|36|42|48| 54| 60| 66| 72 7|14|21|28|35|42|49|56| 63| 70| 77 84 816 24 32 40|48|56|64 72 80 88 96 9|18|27|36|45|54|63|72 81 90 99108 10 20 30 40 50 60 70 80 90 100 110 120 11|22|33|44|55|66|77|88| 99|110|121|132

12|24|36|48|60|72|84|96|108|120|132|144

This table must be committed to memory, with great care and accuracy, till it can be used without difficulty or hesitation by the scholar.

Case 1.

When the multiplier does not exceed 12.

RULE.

Place the multiplier under the multiplicand; units under units, and tens under tens, and then multiply as the table directs, taking care to carry 1 for every 10.