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RULE OF THREE DIRECT IN VULGAR

FRACTIONS.

RULE. 4 Prepare the fractions as before, then state your question agreeable to the Rules already laid down in the Rule of Three in whole numbers, and invert the first term in the proportion; then inultiply all the three terms continually together, and the product will be the answer, ir: the same naine with the second or middle term.

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INVERSE PROPORTION.

RULE. ! Prepare the fractions and state the question as before.

lien invert the third term, and multiply all the threo terine -- ingether the product, will be the answer.

EXAMPLES

1. How much shalloon that is yard wide, will line of yards of cloth which is 12 yard wide ? Yds. yds. yds.

Yds. As 11:54: : And 1 X =w=1621 Ans. 2. If a man perform a journey in 3 days, when the day! is 12 hours long; in how many days will he do it when the day is but 9 hours ?

Ans. 4 days. 3. If 13 men in 11 days, mow 21 acres, in how many days will 8 men do the same?

Ans. 187i days. 4. How much in length that is 71 inches broad, will make a square foot ?

Ans. 20 inches 5. If 254s. will pay for the carriage of a cwt. 1454 miles; how far may 61 cwt. be carried for the same money?

Ans. 22 mile. 6. How many yards of baize which is 14 yards wide will line 187 yards of camblet 7 yard wide ?

Ans. Il yds. I gr. If na.

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Reduce your fractions to decimals, and state your quer tion as in whole numbers; multiply the second and third ro gether; divide by the first, and the quotient will be the ank swer, &c.

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: SIMPLE INTEREST BY DECIMALS.

A TABLE OF RATIOS.
Rate per cent. Ratio. Rate per cent. Ratio.

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Ratio is the simple interest of 11. for one year; or in federal money, of $1 for one year, at the rate per cent. agreed on.

RULE. Multiply the principal, ratio and time continually toge. ther, and the last product will be the interest required.

EXAMPLES: 1. Required the interest of 211 dols. 45 cts. for 5 years at 5 per cent, per annum?

$ cts.
211,45 principal.

,05 ratio.

10,5725 interest for one year.

5 multiply by the time. 52,8625 Ans.=$52, 86 cts. 24 m. 2. What is the interest of 645l. 10s. for 3 years, at 5 per cent. per annum ?

£645,5 x 06 X3=116,190=£116 3s. 9d. 2,4 qrs. Ans.

3. What is the interest of 1211. 8s. 6d. for 41 years, at 6 per cent. per annum ? Ans. £32 15s. 8d. 1,36 qrs.

4. What is the amount of 536 dollars, 39 cents, for 14 years, at 6 per cent. per annum ? Ans. $584,6651,

5. Required the amount of 648 dollars 50 cents for 121 years, at 5, per cent. per annum ? Ans. $1103, 26 cts.

CASE II. . The amount, time and ratio given, to find the principal. Rule.-Multiply the ratio by the time, add unity to the product for a divisor, by which.sum divide the amount, and the quotient will be the principal.

EXAMPLES. 1. What principal will amount to 1235,975 dollars, in 5 years, at 6 per cent. per annum ? $

,66 x 5+1=1,30, 1235,975(950,75 Ans. 2. What principal will amount to 8731. 19s. in 9 years, at 6 per cent. per annum ?

Ans. £567 10s. 3. What principal will amount to $626, 6 cents in 19 years, at 7 per cent. ? Ans. $340,25=$340, 25 cts,

4. What principal will amount to 956l. 10s. 4,125d. 18 84 years, at 54 per cent. ?

Ans. £645 15s.

CASE III. The amount, principal and time given, to find the ratio. Rule. Subtract the principal from the amount, divide the re. mainder by the product of the time and principal, and the quotient will bo the ratio.

EXAMPLES.

1. At what rate per cent. will 950,75 dollars amount to 1230,975 dollars in 5 years ?

From the amount = 1235,975
Take the principal = 950,75
950,75 X 5=4753,75)285,2250(,06=6 per cent.

285,2250 Ans. 2. At what rate per cent. will 5671. 10s. amount to 8731. 19s. in 9 years?

Ans. 6 per cent. 3. At what rate per cent. will 340 dols. 25 cts amount to 626 dols. 6 cts. in 12 years ?

Ans. 7 per cent. 4. At what rate per cent. will 6451. 15s. amount to 9561. 10s. 4,125d. in 8 years ?

Ans. 51 per cent.

CASE IV, The amount, principa , and rate per cent. given, to find

the time. Rule.-Subtract the principal from the amount; divide the remainder by the product of the ratio and principal; and the quotient will be the time.

EXAMPLES. - 1. In what time will 950 dols. 75 cts. amount to 1235 lollars, 97,5 cents, at 6 per cent. per annum ?

Froin the amount $1235,975
Take the principal - 950,75

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2. In what time will 5671. 10s. amount to 8731. 19s. at w per cent. per annum ?

Ans. 9 ycars. * 3. In what time will 340 dols. 25 cts. amount to 626 mols. 6 cts. at 7 per cent per annum ? Ans. 12 years. * 4. In what time will 6451. 15s. amount to 9561. 10s. 4,125d. at 51 per ct. per annum ? Ans. 8,75=87 years.

TO CALCULATE INTEREST FOR DAYS. RULE.-Multiply the principal by the given number of days, and that product by the ratio ; divide the last product by 365 (the numper of days in a year) and it will give the interest required.

EXAMPLES 1. What is the interest of 3601. 10s. for 146 days, at 6 pr. ct.?

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