RULES.

1. The number of a letter is doubled as often as it is repeated; thus, I, represents one; II, two; X, ten; XX, twenty; XXX, thirty.

2. A less literal number placed after a greater, augments the value of the greater; if put before, it diminishes it. Thus, VI, is 6; IV, is 4; XI, is 11; IX, is 9, &c.

II. ADDITION.

ADDITION is the putting together of two or more numbers, or sums, to make them one total, or whole sum.

SIMPLE ADDITION

Is the adding of several numbers together, which are all of one sort, or kind; as, 7 pounds, 12 pounds, and 20 pounds, being added together, make a sum total, or aggregate, of 39 pounds.

RULE.

Place units under units, tens under tens, &c. draw a line underneath, and begin with the units: After adding up every figure in that column, consider how many tens are contained in their sum, and placing the excess under the units, carry so many as you have tens to the next column of tens: Proceed in the same manner through every column or row, and set down the whole amount of the last row.*

PROOF.

Begin at the top of each column, and add the figures downwards, in the same manner as they were added upwards, and, if it be right, this aggregate will be equal to the first amount. Or, cut off the upper line of figures, and find the amount of the rest; then if this amount and upper line, when added together, be equal to the sum total, the work is supposed to be right.

*This rule is founded on the known axiom, that" the whole is equal to the sum of all its parts." The method of placing the numbers, and carrying for tens, is evident from the nature of notation; for any other disposition of the numbers would alter their value; and carrying 1 for every 10, from an inferior to a superior denomination, is evidently right; because 1 unit in the latter case is equal to the value of 10 units in the former.

16. How are other numbers represented ?-17. What is Addition?18. What is Simple Addition ?- -19. Repeat the rule. -20. Why do you carry for ten, in adding simple numbers ?- -21. What is your method of proof?

ADDITION TABLE.

[It is not necessary that this Table be committed to memory, so as to repeat it wholly out of the book. This would be indeed a tedious task. When the pupil can read the two first columns, viz. 2 and 6, 2 and 3, 2 and 7, &c., and cover the third, viz. 8, 5, 9, &c., and recite it readily, it will be sufficiently committed.]

85 and 9 are 148 and 11 are 19/11 and 6 are 17

2 and 6 are

3 and 9 are 126 and 13 are 199 and 6 are 15 12 and14are26

4 and 13 are 177 and 9 are 1610 and 9 are 19 13 and 2 are 15

EXAMPLES.

. What is the amount of 3406, 7980, 345, and 27 ?

Total amount,
Amount with the

'Tens.
Units.

Hundreds.

Tens of Thousands.
Thousands. 3

3.4 0 6

7.9 8 0

3 4 5

27

Here we begin by writing down the several numbers, units under units, tens under tens, &c. Then draw a line under them. We now commence adding at the foot of the right hand column, and say, 7 and 5 are 12, and 6 are 18. This exceeding ten, we write down the right hand figure 11.7 5 8 8 under the column of units, and carry 1 to the next column; and 8.3 52 say, 1 and 2 are 3, and 4 are 7, and 8 are 15. We write down 5 11.7 5 8 at the foot of the column, and proceed to the next; 1 and 3 are 4, and 9 are 13, and 4 are 17. We write down in the same way the right hand figure, 7, under its column; and carrying 1 to the next, say 1 and 7 are 8, and 3 are 11. This being the last column, we write down the whole amount 11, and find the sum total to be 11.758. The method of proof is sufficiently explained.

upper line cut off, Proof,

8. What is the amount of three hundred and sixty-five, eight hundred and seven, five hundred and sixty, twenty-five, thirty-seven, and one hundred one? Ans. 1895.

9. The hind quarters of a cow

13. Add seventy-five millions weigh one hundred and three nine hundred and sixty thousand pounds each; the fore quarters eight hundred, two hundred and weigh ninety-seven pounds each; twenty-five thousand, and one bunthe hide sixty-three pounds, and dred and forty together. the tallow fifty-six pounds; what is the whole weight of the cow ? Aus. 519 pounds.

Ans. 76.185.940.

10. A man has four farms; the 14. What is the sum of four first is worth two thousand seven thousand and twenty five, seventyhundred and twenty-five dollars; five thousand six hundred, eight the second is worth three thousand hundred thousand four hundred eight hundred and nineteen dollars; the third is worth one thousand six hundred and ten dollars; the fourth is worth five hundred and twelve dollars; what are they all worth?

Ans. 8.666 dollars.

11. A man possesses a tract of land, which contains forty-nine thousand eight hundred and thirty-five acres; suppose he had six tracts of equal dimensions, how many acres would the whole contain? Ans. 299.010.

and fifty, five millions three hundred and ten thousand, thirty millions seven hundred and twenty, and nine hundred fifty millions?

Ans. 936.190.795.

15. What is the sum of one million five hundred thousand, three hundred and eleven thousand, ninety thousand six hundred and ten, fifty thousand and forty-five.

Ans. 1.951.655.

REMARK.-As it is of great consequence in business to perform addition readily and exactly, the learner ought to practise it till it become quite familiar. If the learner can readily add any two digits, he will soon add a digit to a higher number with equal ease. It is only to add the unit place of that number to the digit, and if it exceed ten, it raises the amount accordingly. Thus, because 8 and 6 are 14, 48 and 6 are 54. It will be proper to mark down under the sums of each column, in a small hand, the figure that is carried to the next column. This prevents the trouble of

going over the whole operation again, in case of interruption or mistake. If you want to keep the account clean, mark down the sum and figure you carry on a separate paper, and after revising them, transcribe the sum only. After some practice, we ought to acquire the habit of adding two or more figures at one glance. This is particularly useful when two figures which amount to 10, as 6 and 4, or 7 and 3, stand together in the column. Every operation in arithmetick ought to be revised to prevent mistakes; and as one is apt to fall into the same mistake if he revise it in the same manner he performed it, it is proper either to alter the order, or else to trace back the steps by which the operation advanced, which will lead us at last to the number we began with.

III. SUBTRACTION.

SUBTRACTION teaches to take a less number from a greater, to find a third, shewing the inequality, excess or difference between the given numbers. The greater number is called the Minuend; the lesser number is called the Subtrahend. The difference between them, or what is left after subtraction is made, is called the Remainder.

SIMPLE SUBTRACTION

Teaches to find the difference between any two numbers, which are of a like kind.

RULE.

Place the larger number uppermost, and the less underneath, so that units may stand under units, tens under teus, &c. ; then drawing a line underneath, begin with the units, and subtract the lower from the upper figure, and set down the remainder; but if the lower figure be greater than the upper, add ten to the upper, and subtract the lower figure therefrom: To this differ

22. What is Subtraction?-23. What is the minuend?24. What is the subtrahend?-25. What the remainder ?——26. How do you proceed in subtracting simple numbers?

C