a What does the Single Rule of Three Direct teach? b How may a question be known to belong to the Single Rule of Three Direct.

c How are questions in this rule stated?

d What directions are given relative to reducing the terms?

e Having stated your questions and reduced the terms, what is to be done?

f What is the direction when there is a remainder, and the quotient be not in the lowest denomination?

g When any of the terms are given in Federal Money, how is the operation conducted?

h What does the Single Rule of Three Inverse teach? i How may a question be known to belong to the Rule of Three Inverse?

j What is the method of operation?

DOUBLE RULE OF THREE.

a THE DOUBLE RULE OF THREE, Sometimes called Compound Proportion, teaches, by having five numbers given, to find a sixth, which, if the proportion be direct, must bear the same proportion to the fourth and fifth, as the third does to the first and second. But if the proportion be inverse, the sixth number must bear the same proportion to the fourth and fifth, as the first does to the second and third.

RULE.

1. State the question, by placing the three conditional terms in such order, that the number which is the cause of gain, loss, or action, may possess the first place; that which denotes space of time, or distance of place, the second, and that which is the gain, loss, or action, the third.

2. Place the other two terms, which move the question, under those of the same name.

c 3. Then, if the blank place or term sought, fall under d] the third place, the proportion is direct, therefore, multiply the three last terms together, for a dividend, and the other two for a divisor, then the quotient will be the answer.

e 4. But if the blank fall under the first or second place, f] the proportion is inverse; wherefore, multiply the first, second, and last terms together, for a dividend, and the other two for a divisor: the quotient will be the answer

EXAMPLES.

1. If 100 dollars gain 6 dollars, in 12 months, what will 400 dollars gain in 8 months?

2. If 100 dollars gain 6 dollars, in 12 months, in what time will 400 dollars gain 16 dollars?

100: 12: :: 6

400 : :: 16

6

12

-2400

192

100

Here the blank falls under the second place, consequently the proportion is inverse.

By a little attention, the scholar will be able to comprehend the nature and use of this rule.

21,00)192,00(8 months. Ans.

192

3. If 8 men make 24 rods of fence in 6 days, how many men will make 18 rods in three days.

Ans. 12 men. 4. If a family of 9 persons, spend $150 in 5 months, how much would be sufficient to maintain them 8 months, if 5 more were added to the family? Ans. $1120.

5. If a family of 12 persons consume 40 bushels of wheat in 10 months, how much would be sufficient for 15 persons for 9 months? Ans. 45bu.

6. If $4, be the hire of 8 men for 3 days, how many days must 20 men work for $40? Ans. 12 days. 7. If 10 bushels of oats, be sufficient for 18 horses 20 days, how many bushels will serve 60 horses 36 days?

Ans. 69bu.

8. If the carriage of 8cwt. 123 miles, cost $12,80, what must be paid for the carriage of 4cwt. 32 miles?

Ans. $1,60. 9. If 3 pounds of cotton make 10 yards of cloth, 6 quarters wide, how many pounds will make 100 yards of 3 quar ters wide? Ans. 15lbs. 10. Suppose the wages of 6 persons for 21 weeks be $238, what must 14 persons receive for 46 weeks?

QUESTIONS.

Ans. $1472.

a What does the Double Rule of Three teach? b How are questions in this rule to be stated? When is the proportion direct?

d What is the rule for finding the answer, portion is direct?

e When is the proportion inverse?

when the pro

f How is the answer found when the proportion is In

verse?

INTEREST.

a INTEREST is an allowance for the use of money, giver b] by the borrower to the lender. It is computed at so macny dollars on the hundred for the year. In most of the states, the rate of interest is limited by law to 6 per cent. that is, 6 dollars for a hundred dollars.

As this is one of the most important rules of Arithmetick, and one with which every person should be acquainted, I have endeavoured to render the method of computing it as simple as possible, and have, therefore, given only one plain, easy rule, which will be found to apply in all possible cases, with a trifling variation.

d There are three things to be noticed in Interest.

e 1. The Principal; or money lent.

2. The Rate; or sum per cent. agreed on.

3. The Amount; or principal and interest added together. f Interest is of two kinds, Simple and Compound.

g Simple Interest is that which is allowed for the principal only.

RULE.

h. 1. Multiply the given sum by half the number of months in the time, and point off two places at the right hand, under

dollars, for cents: the places at the left hand of the point will be dollars.

i 2. If there are days in the given sum, multiply the given sum by the number of days, and divide the product by 60, and point off as before; or divide by 6, and point off one place under dollars for mills, and two for cents.

j 3. For any other than 6 per cent. calculate as before, and add to, or subtract from the interest thus found, as the case may require. For 7 per cent. add ; for 8, add }; for 5 per cent. subtract ; for 4, subtract, &c.

EXAMPLES.

1. What is the interest of $315,25, for one year, 4 months, and 9 days?

In this example, 8 is half the number of months in 1 year and 4 months, by which I multiply the given sum, and find the interest CO be 27,62. I then multiply the same sum by the num

ber of days, (9,) and divide the product by 60, and find the interest to be 51cts. 7m. which, added to the above, gives the interest sought.

2. What is the interest of $45,75 for 2 years and G months? Ans. $6,86,2. 3. What is the interest of $175,16, for 1 year, 7 months, and 21 days? Ans. $17,25,3. 4. What is the amount of $175,25, for 2 years, 4 months and 3 days? Ans. $512,02,2.

5. What is the interest of 45 dollars for 9 months?

Ans. $2,02,5. 6. What is the amount of $48,14, for 4 years and 22 days? Ans. $59,87. 7. What is the interest of $812,30, for 2 years, 8 months and 4 days? Ans. $130,50,9. 8. What is the amount of 1325 dollars, for 1 year and 6 months?

$1444,25.

9. What is the interest of 75 cents for 2 years?

Ans. 9 cents.

10. What is the interest of $765,13 for 3 years, 4 months,

and 5 days, at 5 per cent?

$128,05,3.

11. What is the interest of $465,17, for 1 year, 4 months and 13 days, at 7 per cent? Ans. $44,59,1. 12. What is the interest of 275 dollars 45 cents, for 2 years, 6 months, and 7 days, at 8 per cent?

Ans. $55,61,8.

12 What is the interest of 1043 dollars 25 cents, for 10 months and 27 days, at 4 per cent? Ans. $37,90,5. 14. What is the amount of 475 dollars 50 cents, for 7 months and 26 days? Ans. $494,20,3. 15. A's note of 325 dollars 50 cents, was given January 1st, 1826: what was the amount due thereon, June 15th, 1827. Ans. $353,90.

16. B's note of 175 dollars, was given June 1st, 1825, on interest after 90 days: what was there due, January 1st, 1827? Ans. $189.

There are various methods of computing interest due upon bonds, notes, and other debts bearing interest, on which partial payments have, at different times, been made.Some calculate the interest up to the time of the first payment, and if the payment exceed the interest, deduct the excess from the principal, and then again to the time of the second payment, &c. Others cast the interest on the note from the date to the time of the last payment; and hen deduct from the amount the several payments, with interest from the time they were made, to the day of final settlement. Neither of these methods is quite correct.

k The method pursued in this work is, to calculate the interest on the note for one year from the date, and then on the several payments made within the year to the same time; then if the amount of the payments exceed the interest, deduct the excess from the principal, and proceed to calculate the interest on the balance for the second year, and so on to 7] the time of final settlement. If the amount of the payments in any year be less than the interest, place both by themselves, and proceed to calculate the interest for the second year, or until the payments exceed the interest, then deduct the excess from the principal, and proceed as before.

In case no payment be made during the year, then the interest may be calculated to the end of the year in which payment was made.