ARITHMETIC.

ARITHMETIC is the art of computing by numbers. It has five principal rules for its operations; viz. numeration, addition, subtraction, multiplication, and division.

NUMERATION.

Numeration teaches to write or express numbers by figures, and to read numbers thus written or expressed.

In treating of numbers, the following terms are employed: viz. unit, ten, hundred, thousand, and million; as also billion, trillion, and some others. But the latter are seldom used.

A unit is a single one.

A ten is ten units.

A hundred is ten tens.

A thousand is ten hundreds.

A million is ten hundred thousands.

Note. As it takes ten hundred thousands to make a million, when we express a number, greater than a thousand, and less than a million, we use tens of thousands, or hundreds of thousands, or both, as the case, requires. Likewise, to express a number, greater than a million, we employ tens of millions, or hundreds of minions, &c.

The following are the figures used in numeration, with their names written above them.

One two three four five six seven eight nine 4 5 6 7

1

2

3.

9

Each of these figures represents the number which its name denotes; but it is understood to be that number of units, or that number of tens, or that number of hundreds, &c. according to its relative place: which is exemplified in the following tables.

B

These tables show that in using figures to express numbers they are placed in a horizontal row-the first figure at the right hand representing one or more units, the next tens, the next hundreds, &c. Thus a 1 is one unit, or one ten, or one hundred, &c. according to the place in which it stands; and in like manner, a 2 is two units, or two tens, or two hundreds, &c. The same rule determines the value of each of the other figures. In reading numbers, the units and tens are taken together. 1 ten and 1 unit are read eleven; 1 ten and 2 units, twelve; 1 ten and 3 units, thirteen, &c. : 2 tens and 1 unit are read, twenty-one; 3 tens and 1 unit thirty-one. &c. Thus the number expressed by the row of figures in table first is read-one hundred and eleven millions, one hundred and eleven thousands, one hundred and eleven. That expressed by the figures in table second is read--two hundred and twenty-two millions, two hundred and twenty-two thousands, two hundred and twenty-two.

The succeeding tables will further illustrate the subject.

Add the following numbers, viz. 14, 18, 99, 45, 28, 27, 19, 38, 16, 39, 48, 29, 260, 148.

Add, six hundred and forty, seventy-nine, eighty, one hundred, two hundred and ten, four hundred and fifty.

Ådd, nineteen thousands, fifty thousands, one million one hundred and one, one hundred and twenty-five.

APPLICATION.

1. If John give Charles twenty nuts, and James give him fifty-six, and Joseph give him ninety-five, how many will he have? Answer 171.

2. A person went to collect money, and received of one man ninety dollars; of another, one hundred and forty dollars; of another, one hundred and one dollars; and of another, twenty-nine dollars. How much did he collect in all? Ans: 360 dollars.

3. Deposited in bank, fifty dollars in gold; three hundred dollars in silver, and five thousand dollars in notes. What is the whole amount deposited? Ans. 5350 dols.

4. The distance from Philadelphia to Bristol is 20 miles; from Bristol to Trenton, 10 miles; from Trenton to Princeton, 12 miles; from Princeton to Brunswick, 18 miles; from Brunswick to New-York, 30 miles. How many miles from Philadelphia to New-York? Ans. 90.

5. A merchant bought of one person 50 barrels of flour for 300 dollars; of another person, 75 barrels for 525 dollars; and of another person, 125 barrels for 1000

dollars. How many barrels did he buy, and how much did he pay for the whole?

Ans. 250 barrels, and paid 1825 dollars.

SIMPLE SUBTRACTION.

By Subtraction we ascertain how much greater one number is than another: or what remains when a less number is taken from a greater.

RULE.

Place the less number under the greater, with units under units, tens under tens, &c. Then, beginning at the units place, take each lower figure from the one above it, and set down what remains. But if either of

the lower figures be greater than the upper one, conceive 10 to be added to the upper,* then take the lower from it, and set down the remainder. When 10 is thus added to the upper figure, there must be 1 added to the next lower figure.

PROOF.

Add the remainder to the less number, and their amount will be equal to the greater.

Some prefer taking the lower figure from 10, adding the remain

der to the upper, and setting down their amount.

In writing numbers which have no units, or no tens, or no hundreds, &c. the order observed in the foregoing tables must be maintained by filling the vacant places with a character called a nought or cypher, (0) which, See of itself, represents no number.

Read the following numbers, or write them in words. Note.-Making a point or dot after every third figure, counting from the units place, greatly facilitates the reading of large numbers.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 30, 31, 32, 40, 43, 44, 50, 55, 56, 60, 67, 68, 70, 71, 79, 80, 82, 83, 90, 92, 100, 101, 111, 112, 113, 114, 120, 128, 130, 132, 200, 203, 210, 300, 320, 332, 400, 500, 600, 700, 800, 900, 1000, 2001, 3010, 4020, 5200, 10250, 23450, 356789, 6789402, 76450791, 20156789, 1304136784.

Write the following numbers in figures.

Ten. Twelve. Fifteen. Seventeen. Twenty-six. Thirtynine. Fifty-two. Seventy-four. Eighty-one. Ninetysix. One hundred and fifteen. Two hundred. Three hundred and twenty. Nine hundred and nine. One thousand two hundred. Seven thousand seven hun