ARITHMETIC.

ARITHMETIC is the science that treats of the nature and use of numbers.

Numbers are represented by figures, and are either concrete or abstract.

By the use of these, with 0, nought or cypher, all numbers whatsoever may be represented.

A unit denotes one individual of its kind; as one pound, one hour.

A. A number is said to be concrete when it represents some particular kind of unit, as eight boys, nine cows; but an abstract number is that which has reference to no particular units.

Thus 8 represents 8 units only, without referring to particular objects.

NUMERATION.

NUMERATION teaches the meaning of figures.

standing alone means so many units, thus:

5, five units; 9, nine units.

B

A figure

SEVERAL FIGURES.

When figures are placed together, they have, besides their own value, a value depending on their place.

The value of every figure is increased tenfold for every place that it stands to the left of the units' place.

B. That is, if we commence from the right, each period of three will contain units, tens, and hundreds, and each periods of six will contain units, tens, hundreds, thousands, tens of thousands, and hundreds of thousands; each period of six having its one name or value, according to place : 1st, units; 2nd, millions; 3rd, billions; 4th, trillions.

To numerate any number of figures.

RULE. Divide the figures into periods of three, beginning from the right, and then into periods of six, placing units and thousands over every alternate period of three, and units, millions, billions, trillions, &c., over every period of six, commencing from the right, thus:

Ans. Two hundred and ten thousand and one billions, three hundred

and two thousand nine hundred millions, five thousand and seventy nine (units).

N.B. The names million, billion, trillion, &c., can only be used once in the same example.

Express in words :—

EXAMPLES. I.

1. 42031.

2. 82003.

3. 10024.

4. 2340000.

5. 721000001.

6. 300010020.

7. 82130010001.

8. 7200000102345.

9. 1000000200178005.

10. 3090908000700700201.

NOTATION.

NOTATION, the converse of Numeration, teaches how to express numbers by figures.

RULE. Place the units, the thousands, the millions, &c., in their respective periods, as laid down above.

C. Thus :

Express ten billions, four hundred and five millions, ten thousand and forty six, in figures.

Express in figures :—

1. Forty thousand and twenty-six.

2. Eighty-one thousand and twenty-two.

3. Nine millions and one.

4. Seventy-nine millions, ten thousand, three hundred and one.

one.

5. One hundred millions.

6. Sixty-five billions, two thousand and one millions, and

7. One hundred and five thousand and five millions, twenty-five thousand.

8. Three trillions and three.

9. Eighty trillions, four hundred and one millions. 10. One trillion, one billion, one million and one.

ADDITION.

ADDITION is the collecting of two or more numbers into one

sum.

The sign+signifies addition thus, 7+2 means two added to seven.

To add numbers of many figures.

RULE. Set the numbers one under another, placing units under units, tens under tens, hundreds under hundreds, &c. Draw a line under the columns.

Add up the columns one after another, beginning on the right.

If the sum of any column has more than one figure, set under that column the figure of lower place, and carry the figure of higher place to the next column; at the last column set down the entire sum.

The sum of the several columns thus placed will be the entire sum.

3498.. 32 hundreds, 28 tens, 18 units.

1, 4, 5, and 8 units are 18 units, or 1 ten and 8 units; put 8 in the units' place, and carry 1 to the tens; 1, 9, 6, 7, and