THE SPEEDY CALCULATOR.

THE office of ARITHMETIC is to illustrate the principles and powers of numbers, and the art of computing thereby. In order to make arithmetical calculations with facility, a thorough knowledge of NOTATION, NUMERATION, ADDITION, SUBTRACTION, MULTIPLICATION, and DIVISION, is indispensable.

Notation teaches the writing of numbers in numerical characters; and numeration is the reading of them.

Numeration can be explained by the teacher, with the aid of the black-board, so much better than by means of the most copious examples and explanations given in the book, that it is deemed inexpedient to occupy more space than merely to introduce the subject to the learner.

4 4 4 4 4 4 4 4 4 4 4 4 Enumerate.

Write in figures, eight thousand seven hundred and thirtysix. Ninety-four thousand five hundred and fifty-three. Three millions nine thousand four hundred and forty-eight.

Nine hundred and ninety-nine millions, nine hundred and ninety-nine thousand, nine hundred and ninety-nine.

NOTE. In writing numbers, every place not occupied by a figure must be occupied by a cipher. Thus, to write seven hundred and nine, as there are no tens, a cipher must occupy the place of tens, as 709. Should we omit the cipher and write 79, the 7 would occupy the ten's place, and would not express seven hundreds, but 7 tens.

MENTAL OPERATIONS IN ADDITION.

1. A BOY bought a knife for 16 cents, and a pint of nuts for 6 cents; how much did he give for both?

2. A man bought a firkin of butter for 12 dollars, and three barrels of cider for 8 dollars; how much did he give for the whole ?

3. A boy had 14 cents, and his father gave him 6 more; how many had he then?

4. A man bought three cows, for the first he gave 13 dollars, for the second 7 dollars, and for the third 12 dollars; how much did he give for all?

5. A man bought a barrel of flour for 7 dollars, and three cords of wood for 15 dollars; what did he give for the whole? 6. John gave 11 nuts to one boy, 9 to another, and had 12 left; how many had he at first?

7. Joseph bought some oranges for 17 cents, a book for 13 cents, and a knife for 16 cents; how much did he give for the whole ?

8. A farmer sold 18 bushels of wheat to one man, 12 bushels to another, and 13 bushels to a third; how many bushels did he sell to all?

9. A man bought a cow for 28 dollars, some corn for 12 dollars, and a pig for 6 dollars; what did he give for the whole?

10. A drover bought 23 sheep of one farmer, 17 of another, and 16 of a third; how many did he buy of all?

ADDITION OF SIMPLE NUMBERS.

ADDITION is the operation by which several numbers are united in one. The number thus obtained is called the sum

or amount.

A man wishing to pay for a farm, found he had in one drawer of his bureau 7 one dollar bills, 8 ten dollar bills, and 3 hundred dollar bills. In another drawer, 4 one dollar bills, 6 ten dollar bills, and 7 hundred dollar bills. In a third drawer,

5 one dollar bills, 9 ten dollar bills, and 5 hundred dollar bills. In a fourth drawer, 6 one dollar bills, 4 ten dollar bills, 6 hundred dollar bills, and 1 thousand dollar bill, all of which he gave for the farm; what was the whole amount?

Thousand dollar bills

Hundred dollar bills

. Ten dollar bills

One dollar bills

The sum of the one dollar bills amounts to 22, this is equal to 2 ten dollar bills and 2 ones,-put the 2 one dollar bills under the ones, and count the other 2 with the tens,— this column amounts, with the two from the first, to 29 tens, this is equal to 2 hundred dollar bills and 9 tens,-put the nine tens under the tens, and count the 2 hundred with the hundreds, or third column, and the sum is 23 hundreds, which is equal to 2 thousands and 3 hundreds, put the 3 hundreds under the hundreds and count the 2 with the thousands, making 3 thousands, and we find the whole amounts to three thousand three hundred and ninety-two dollars.

387 764 595 1646 3392

RULE.

Write the numbers to be added, so that units stand under units, tens under tens, hundreds under hundreds, &c. Then begin at the units or right hand column and add up the figures in that column, if the sum can be expressed by one figure, write it down under the column of units, but if it amounts to 10 or more, put down the right hand figure only, and count the left hand figure, with the second column, and do the same with every other column, except the last or left hand column, the whole amount of which must be set down.

To prove addition, begin at the top of the units column

and count downwards, carrying the left-hand figure of each column to the next column, as before; if the sum thus obtained be the same as the first, the work may be supposed to be right.

A cross formed by two lines, one horizontal and the other perpendicular, thus, signifies that the numbers connected by it are to be added. It is called plus, (a Latin word signifiying more,) or and, thus, 8+6 are 14; that is, 8 plus 6 are 14; or 8 and 6 are 14.

Two horizontal lines thus, = mean equal, or as much as, thus, 8+6=14; that is, 8 and 6 are equal to 14; or 8 and 6 are as much as 14.

The following table should be thoroughly learned.