4. If a man has 6 sheep in one pasture, and 4 in another, how many sheep has he in both?

5. If a man sell a sheep for 5 dollars, and a cow for 18 dollars, how much will he get for both?

6. If a man gather 4 quarts of blueberries, and buy 6 quarts, how many quarts will he have?

7. If a boy sell 9 quarts of blackberries, and give away 4, how many will he dispose of?

8. If a man shoot 5 gray squirrels, 4 black ones, and 8 red ones, how many will he shoot in all?

9. If Charles catch 6 fishes, John 4, and William 10, how many will they all catch?

All figures at the left of this point (,) are called whole numbers; all the figures at the right of this point (,) are called parts of whole numbers, or decimal fractions.

The point, therefore, is called the decimal point. All calculations in dollars, cents, and mills are performed simply as whole numbers and decimal fractions. Thus, 334,875 may represent three hundred and thirty-four dollars and eighty-seven and a half cents.

The denominations of U. S. money are eagles, dollars, dimes, cents, and mills.

This character ($) is the sign for federal money, of which 1 dollar is the unit.

10. If a man sell a cow for $18,75; a horse for $60,25; a yoke of oxen for $54,50; how much money will he receive?

As there are several sums of money in this example, it may be convenient to arrange the numbers according to the following

RULE OF ADDITION.

Write the numbers to be added under one another, so that units, tens, hundreds, tenths, hundredths, thousandths, &c.,

may be respectively under one another; that is, so that those of the same local value may be under each other.

Draw a line under the whole; then, beginning at the right-hand column, add them, one after another. If the sum be less than 10, write it under the column added; if it be 10, or more, set down the right-hand character or figure, and add the left-hand figure to the next column. Observe the same rule with each column, and at the last column write the whole amount.

$18,75 60,25 54,50 Ans. 133,50

OPERATION.

In adding the right-hand column, I find there are 10 cents, or 1 dime. I place the 0 directly under the column added, and add the 1 (dime) to the next left-hand column (of dimes). Having added this column (of dimes), I find the amount is 15 (dimes). As 10 dimes make 1 dollar, I place 5 (dimes) under the column last added, and add 1 (dollar) to the next left-hand column (of dollars). Having added the unit column of dollars, I find the amount is 13 dollars. I set down 3 dollars under units of dollars, and carry 1 (ten dollars) to the next left-hand column. Having added this column, I find the amount to be 13 (tens of dollars), which I set down in full. From the preceding remarks it will be seen, that the reason for carrying one for every ten, arises from the nature of the subject. Ten mills make a cent. Where 10 mills occur, the same value is expressed by adding one cent to the column of cents. So of every higher denomination. As ten in the right-hand column are equal to only one in the next left-hand column, dropping ten, and carrying one, is not in the least altering the value or the given sum.

ADDITION IS UNITING TWO OR MORE NUMBERS INTO ONE SUM.

PROOF.-Begin at the top of the right-hand column, and reckon all the figures downward; if the amount agree with the answer, the work may be supposed to be right.

SIGNS. The sign of addition is a short, horizontal line, crossed by a perpendicular, thus, +, and shows that a num

ber placed before it, is to be added to a number placed after it. Two parallel horizontal lines, thus,, are the sign of equality; thus, 8+4=12.

5. Add 424,375; 71,875; 33,525; 149,875; 798,125; 23,25.

6. Add three hundred seventy-nine and twenty-five hundredths, four hundred nine and seventy-five tenths of thousandths, seventy-four and four thousand three hundred and seventy-five tenths of thousandths together. Ans. 862,695.

7. Add two hundred seventy-nine and nine thousand three hundred and seventy-five tenths of thousandths, three hundred eighty-seven and one thousand eight hundred and seventy-five tenths of thousandths, eight hundred forty-three and three hundred and seventy-five thousandths, three hundred ninety-five and eight hundred and seventy-five thousandths together. Ans. 1906,375.

It should be remembered that figures increase in value in a ten-fold proportion from the right hand to the left, and diminish in the same proportion from the left hand to the right, without any reference to the decimal point. Hence, ,1 is ten times less than 1,; and,01 is ten times less than ,1. This will be seen more clearly if we call 1, one dollar. Then,1 is one tenth of a dollar, one dime, or ten cents; ,01 is one hundredth of a dollar, or one cent; ,001 is one thousandth of a dollar, or one mill.

These parts of a dollar, or unit of any kind or denomination, are clearly illustrated in the following diagram.

No. 1.

No. 2.

QUESTIONS ON THE ABOVE DIAGRAM.

Ques. What is this diagram made to represent? Ans. One dollar, or any whole thing, or unit. Ques. What do the large divisions of this diagram represent?

Ans. The parts into which one dollar or any unit may be divided.

Ques. Into how many equal squares is this diagram divided?

Ans. One hundred.

Ques. What do ten of the large squares represent?

Ans. One tenth of a dollar, one dime, ten cents, or one tenth of any unit.

Ques. What does one of the large squares represent? Ans. One hundredth of a dollar, one cent, or one hundredth of any unit.

Ques. What do two large squares represent?

Ans. Two hundredths of a dollar, two cents, or two hundredths of any unit.

Ques. What do three squares represent?

Ans. $,03, or 3 cents, or ,03 of any unit
Ques. What do eight squares represent?
Ans. $,08, or 8 cents, or ,08 of any unit.

Ques. Into how many spaces is square No. 1 divided?
Ans. Ten.

Ques. What does one space in this square (No. 1) represent?

Ans. $,001, or 1 mill, or ,001 of any unit.
Ques. What do three spaces represent?

Ans. $,003, or 3 mills, or ,003 of any unit.

Ques. Into how many spaces is square No. 2 divided? Ans. One hundred.

Ques. What does one space in this square (No. 2) represent?

Ans. $,0001, or one tenth of a mill, or ,0001 of any unit. Ques. Which is the larger number, one tenth or one hundredth ?

Ques. Which is the larger number, one hundredth or one thousandth?

Ques. Which is the larger number, five tenths of thousandths, or one thousandth?

Ques. How much larger is one tenth than one hundredth? Ques. How much larger is one hundredth than one thousandth?

Ques. How many tenths make a unit?

Ques. How many hundredths make a tenth ?

Ques. How many thousandths make a tenth?

Ques. Can whole numbers be represented by this diagram as well as decimal parts?

Ans. Yes; let one of the small squares in No. 2 be taken for a unit, and ten of them represent 10, and the whole of No. 2 100, and ten of the same sized squares 1000, and the whole diagram 10000.

Ques. Can whole numbers and decimal parts be represented in the same diagram?

Ans. Yes. If one of the ,01 parts are taken for 1, then 10 are 10, and the whole diagram 100, and one of the divi