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ADDITION OF DECIMALS. How is the sum to be written down? Ans, Tens under tens, hundreds under hundreds, and so on.

How add? Ans. As in Simple Addition.

Where place the separatr ix? Ans. Directly under the separating points above.

What are the numbers on the right of the separatrix? Ans. Decimals.

What are the numbers on the left? Ans. Whole numbers.

What are the numbers in the other decimal rules? Ans. As in this.

What is the proof? Ans. The same as in Sime ple Addition.

EXAMPLE.
What is the sum of ,2 and ,35? Ans. ,55.
What is the sum of ,5 and ,125? Ans. ,625.

SUBTRACTION OF DECIMALS. How write the decimals down? Ans. As in Addition.

How subtract? Ans. As in simple subtraction. How place the separatrix? Ans. As in Addition of Decimals.

How prove your sums? Ans. As in Simple Addia tion of Decimals.

EXAMPLES: Fr m ,6 take ,15. Ans. ,45. From ,5 take ,25. Ans. ,35. From , 1 take ,01.' Ans. ,09. From 1 take ,9. Ans. , 1,

MULTIPLICATION OF DECIMALS.

How write down the decimals, and multiply? Ans. As in Simple Multiplication.

How many decimals point off in the product? Ans. As many, as are in both multiplicand, and multiplier.

If there should not be so many decimals in the product, what do you do? Ans, Prefix cyphers enough to make as many.

What is the meaning of prefix? Ans. To put before.

What is the meaning of annex? Ans. To put after.

For example.
Multiply , 15 by 2. Ans. ,3.
Multiplv,8 by ,7. Ans. ,66.
Multiply ,25 by. 2. Ans. ,5.
Multiply ,25 by ,2. dns. ,05.
Multiply ,25 by ,1. Ans. ,025.
Multiply ,25 by ,4. Ans. ,1

DIVISION OF DECIMALS. How write down the sum, and divide? Ans. As in Simple Division.'

How many point off in the quotient? Ans. Enough to make as many decimals in the divisor, and quo. tient, as there are decimals in the dividend.

Suppose there are not figures enough in the quotient for this purpose, what do then? Ans. Make up the deficiency by prefixing cyphers to said quotient.

What do if the quotient is not contained in the dividend? Ans. Annex cyphers.

What place do these cyphers take in the dividend! Ans. Decimal places

For Example. Divide ,24 by ,6. Ans. ,4. Divide .36 by ,9. Ans. ,4. Divide ,16 by ,2. Ans. ,8. Divide, 24 by ,6. Ans.,04.

Divide ; 36 by ,9. Àns. ,04.
Divide ,16 by ,2. Ans. ,8.

REDUCTION OF DECIMALS.

CASE. I, How do you reduce a Vulgar Fraction to its equivalent Decimal?

Ans. Annex cyphers to the numerator, and divide by denominator.

What is the answer? Ans. The quotient.

Suppose there are not so many figures in the quotient, as you have annexed cyphers, what do? Ans, Prefix cyphers to the left hand of the quotient,

RXAMPLES. Reduce to its equivalent decimal,. Ans. ,5. Reduce to its equivalent decimal. Ans. ,75.

How reduce a Decimal to a Vulgar? Ans. It is a vulgar fraction when its own denominator is written under it.

For example, change ,5 into a Vulgar Fraction.

Ans. Po

Now change my into a decimal? Ans. Take away 10 and prefix the separatrix or divide 5 by 10 annexing a cypher.

How prove that the value is not altered, by the change? Ans. reduced to a proper decimal is ,5 and ,5 means five tenths of any thing; consequently if any thing is divided into ten parts, 5 of these must be

CASE. II. To find the value of any given decimal parts of weights measures &c.

How do you multiply? Ans. By as many of the next denomination, as make one of this.

How many figures point off in the product, for the decimal remainder? Ans. As many as are in the mnltiplicand.

How proceed then? Ans. As before.
Where will

you
find
your
answer?

Ans. The several denominations on the left hand, make the

answer.

For example; what multiply ,365 of a pound by first? Ans. 20 shillings, or what makes a pound,

What multiply ,427 of a shilling by first? Ans. By

12 pence.

CASE. III. To reduce quantities composed of several denominations to a decimal, that is to reduce the several denominations found by the preceding rule back again to a decimal.

How place the several donominations? Ans. One above the other.

Which at the top? Ans. The lowest.

How divide each denomination beginning at the top? Ans. By as many as make one of the next, or shillings by shillings, pence by pence, drams by drams, &c. What is the answer.

Ans. The last quotient. Reduce 4d to the decimal of a penny;

Ans. ,5, Reduce 10s. to the decimal of a pound. Ans. ,5. Reduce 15s. to the decimal of a pound. Ans. ,75.

What divide 3 farthings by, to reduce them to the decimal of a pound? Ans. By 4, 12, and 20.

Reduce 3 shillings to the decimal of a dollar. Ans. 5 dimes or 50 cts.

Is the value altered in the reduction? Ans. It is not.

How prove this? Ans. 3 shilling are equal to 50 cents.

How can you ascertain whether your sum is right, or not? Ans. I said that 10 shillings reduced to a decimal, was ,5,now multiplying ,5 by the divisor 20 and cutting off according to the rule, I have 10 shillings.

FEDERAL MONEY. Note:--Federal Money is inserted again to show the schol ar the rise and origin of it, and that it is purely decimal.

What is the coin of the United States called? Ans. Federal Money.

When established. Ans. A. D. 1786. By what authority? Ans. Congress. Repeat the denominations of Federal Money: Note.--They are found among the tables at the beginning of the book.

Which is the money unit? Ans. Dollars.

What places do dollars occupy then? Ans. The place of units.

How are dollars distinguished from dimes, cents, and mills? Aris. By a comma, or separatrix at the right of dollars.

What are all thë figures on the left of dcllars? Ans. Eagles.

What is the first figure on the right of dollars! Ans. Dimes.

What is the 2d figure? Ans. Cents,
What is the 3å figure. Ans. Mills.
How many of these coins are real? Ans. 4.

Name them? Ans. The eagle, the dollar, the dime and the cent.

Which is a gold coin? Ans. The eagle.

Which are silver coins? Ans. The dollar and the dime.

Which is a copper coin? Ans. The cent.

Which is imaginary? Ans. The mill, as there is no piece of money of that denomination.

As Federaf Money is in a tenford proportion what are eagles, and dollars both together called in accounts? Ans Dollars.

What are dimës, and cents, called? Ans. Cents.

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