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EQUATION OF PAYMENTS. What is the process of finding, when a debt is payable at different times, how it may be paid without disadvantage to either party, called? Ans. Equation of Payments.

How multiply? Ans. Each payment by its time.

What divide the sum of the products by? Ans.By the whole debt.

What is the quotient? Ans. The equated time for paying the whole.

BARTER.
What is the exchanging one sort of goods for an-

How are questions in this rule answered? Ans. By the Rule of Three.

You sell 20 knives for 4 cents a piece, to Harry, and agree to take what the knives come to in marbles at 2 cents a piece; how many inarbles do you get?

You borrow 20 uew marbles of John, worth six cents a piece, and lose them; how many of your old ones, which are worth no more than 4 cents a piece, ought you to give John?

LOSS AND GAIN. What is the rule which enables merchants to estimate their profit or loss, in selling gocds. and to raise or lower the price, so as to gain or lose so much per cent? Ans. Loss and Gain.

How are questions in this rule answered? Ans. By the Rule of Three.

To find what is lost or gained per cent. How ascertain the gain or loss? Ans. By Subtraction:

Then what make the first term in stating Ans. The cost.

What make the middle term? Ans. The gain or loss.

What the third term? Ans. 100.

To find how goods may be sold, to lose or gain sa much per cent.

RULE. What make the first term? Ans. 100 pounds, or dollars.

What make the middle term? Ans. The cost.

What make the third term? Ans. 100 dollars or 100 pounds, with the profit added, or loss subtracted

What will the answer be? Ans. The price of sale.

FELLOWSHIP. What is the rule to settle the account of people who have been trading in company, called? Ans. Fel lowship.

When the several shares are continued in trade; an equal length of time, what is it called? Ans. Sina gle Fellowship.

When the shares of stock are continued in trade an unequal length of time, what is it called? Ans: Double Fellowship.

RULE. What make the first term? Ans. The whole stock:

What the middle term? Ans. The whole gain or loss.

What the third term? Ans. Each man's stock. !

What will the answer be? Ans. Each man's gain or loss

By what rule is a bankrupt's estate divided among his creditors? Ans. Single Fellowship. DOUBLE FELLOWSHIP,

RULE. What is the first thing to be done? Ans. Multiply each man's stock by the time it was in trade.

What make the first term in stating? Ans. The sum of the several products.

What make the middle term? Ans. The whole gain or loss.

What make the third term? Ans. Each man's particular product.

What will the answer be? Ans. Each man's particular gain or loss.

DOUBLE RULE OF THRFE. What rule teacheth to resolve such questions as require two or more statings in simple proportion, whether direct or inverse, called? Ans. Double Rule of Three.

How many terms are there always given? Ans. 5.

For what purpose are they given? Ans. To find a sixth.

What are the three first terms? Ans. Supposition. What are the two last? Ans. Demand.

In stating the question ; what of the supposition make the first term? Ans. The principal cause of gain, loss, &c.

What of the supposition make the second term? Ans. The time, distance of place, &c.

What in the third place? Ans. The remaining term of the supposition.

Where are the terms of the demand to be placed? Ans. Under those of the same kind in the supposition.

If the blank place or term sought, fall under the third term, what is the proportion? Ans. Direct.

Which terms multiply together for a divisor? Ans. 1st and 2di

Which for a dividend! Ans. The other three.

But if the blank place or term sought, fall under the first or second term, what is the proportion? Ans, Inverse.

Which terms multiply together for a divisor? Ans. 3d and 4th.

Which for a dividend? Ans. The other three.

What will the quotient be! Ans. The answer.

For Exanple.--If a man can build 36 rods of wall in 2 days, how many rods can 26 men build in 10 days--how state this sum, and why?

VULGAR FRACTIONS:

MORE PARTICULARLY. How many parts are vulgar fractions divided into? Ans. 4.

What are they? Ans. Proper, improper,compound, and mixed.

What is a proper fraction? Ans. When the numerator is less than the denominator.--Give an example? Ans. or.

What is an improper fraction? Ans. When the numerator is inore than the denominator.-Give an example ? Ans. 2 or.

What is a compound fraction? Ans. The fraction of a fraction..

What is it coupled by? Ans. Of.
Give an example? Ans. I ofof off of a.

What is a mixed number? Ans. It is composed of a whole number and a fraction.

Give an example? Ans. 153.

How can any whole number be converted into a fraction? Ans. By putting I under it.

Give an example? Ans. 6 makes, converted into a fraction, 6.

What is the value of a fraction? Ans. The quotient of the numerator divided by the devomina

What is the value of & then? Ans. 6 for 1 gocs in 6, 6 times.

When a building is divided into 20 parts and you own 8; how would you express your part in fractions. Ans.

tor.

What part must another man have to own the rest of the building? Ans. 13.

How prove this? Ans. 8 and 12 are 20, just the number of par's the building was divided into.

You have said the value of a fraction was the quotient of the numerator divided by the denominator, then tell me the value of Ans. 2.

How prove this? Ans. If 12 apples is divided into 4 parts each, or quarters, 8 must mean a quarters,

and 3 quarters make 2 whole apples. i. What is the value of 20? Ans. 5.

What is the value of g? Ans. 1.

What is the common measure of two or more numibers? Ans. That number that will divide them without a remainder.

What is the common measure of 12, 24, and 30? Ans. 3.

Why? Ans. Because it will dividc each of them without a remainder.

What is the greatest number that will do this called? Ans. The greatest common measure.

What is a number that can be measured by two or more numbers called? Ans. Their common multiple.

If it be the least number that can be so measured what is it called? Ans. Their least common mul. tiple.

What is the common multiple of 2, 3, and 4? Ans. 24.

Why? Ans. Because 24 can be divided by 2, 3 and 4, without a remainder.

What is the last common multiple of these num= bers? Ans. 12.

Note. The rule for reducing a fraction to its lowest term has been given previously.

How do you reduce a mixed number to an improp

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