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MULTIPLICATION OF VULGAR FRACTIONS.

RULE.

Reduce whole and mixed numbers to the improper fractions, mixed frations to simple ones, and those of differen integers to the same; then multiply all the numerators together for a new numerator, and all the denominators to gether for a new denominator.

EXAMPLES.

1. Multiply 1 by

Answers. = 2. Multiply by 3. Multiply 51 by 4. Multiply of 7 by

311 5. Multiply 13t by a 6. Multiply of 8 by 1 of 5 7. Multiply 7) by 9 8. Multiply off by of 34 9. What is the continued product of of 1, 7, 51 and

Ans. 46

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13

693

i Ans.

DIVISION OF VULGAR FRACTIONS.

RULE. Prepare the fractions as before ; then, invert the divisor and proceed exactly as in Multiplication: The products will be the quotient required.

EXAMPLES.

4 x 5 1. Divide by se

Thus,

3 X 7 2. Divide 47 by

Answers. 143 3. Divide of by 4. What is the quotient of 17 by ? 5. Divide 5 by mo

74 6. Divide of; of by of 7. Divide 4. by of 4 8. Divide 71 by 127 9. Divide 52051 by of 91

591

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RULE OF THREE DIRECT IN VULGAR

FRACTIONS.

RULE.

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 multiply all the three terms continually together, and the product will be the answer, in the same naine with the second or middle term.

EXAMPLES,

s. d. qrs.

1. If of a yard cost 4 of a pound, what will it's of an Ell English cost?

syd.=of of =?! or Ell English. Ell. £. Ell. As': :: 15 And xxX8=17£.10 3 1Ans. 2. If of a yard cost of a pound, what will 40 yards come to ?

Ans. £59 8s. 6.d. 3. If 50 bushels of wheat cost 1771. what is it per bushel ?

Ans. 7s. Od. 13 qrs. 4. If a pistareen be worth 147 pence, what are 100 pista reens worth ?

Ans. £6 5. A merchant sold 51 pieces of cloth, each containing 24} yards at 9s. 1d. per yard; what did the whole amount to ?

Ans. £60 10s. Od. 34 qrs. 6. A person having of a vessel, sells of his share for 3121. ; what is the whole vessel worth ? Ans. £780

7. If ? of a ship be worth of her cargo, valued at 80001. what is the whole ship and cargo worth?

Ans. £10031 14s. laid.

INVERSE PROPORTION.

RULE. Prepare the fractions and state the question as before. then invert the third term., and multiply all the three terms ingether, the product will be the answer.

EXAMPLES.

1. How much shalloon that is 3 yard wide, will line 51 yards of cloth which is 17 yard wide ? Yds. yds. yds.

Yds. As 17:5, :: And 1 XX=*=16. 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 llz days, mow 21 acres, in how many days will 8 men do the same?

Ans. 1897 days. 4. How much in length that is 7 inches broad, will make a square foot ?

Ans. 20 inches. 5. If 25 s. will pay for the carriage of a cwt. 1454 miles; how far may 61 cwt. be carried for the same money?

Ans. 220 miles. 6. How many yards of baize which is 11 yards wide, will line 187 yards of camblet yard wide?

Ans. 11 yds. I gr. 1} na.

RULE OF THREE DIRECT IN DECIMALS.

RULE.

Reduce your fractions to decimals, and state your ques. tion as in whole numbers; multiply the second and third together; divide by the first, and the quotient will be the av.

swer, &c.

EXAMPLES.

come to ?

1. If of a yard cost iz of a pound; what will 15 yards

1=,875,1=,583 -- and =,75 Yds. £. Yds. £.

£. s. d. grs. As ,875 :,583 :: 15,75: 10,491=10 9 10 2,24 Ans. 2. If1 pint of wine cost 1,2s. what cost 12,5 hhds?

Ans. £378 3. If 45 yards cost 3s. 4; d. what will 305 yards cost?

Ans. £l 4s. 3d. 3 qrs. +

4. If 1,4 cwt. of sugar cost 10 dols. 9 cts., what will 9 cwt. 3 qrs. cost at the same rate ? cict.

cut. As 1,4 :: 10,09 : : 9,75 : 70,269=$70,26 cts. 9 m. +

5. If 19 yards cost 25,75 dollars, what will 435 yards come to ?

Ans. $590, 21 cts. 71 m. 6. If 345 yards of tape cost 5 dols. 17 cents, 5 m., what will one yard cost ?

Ans. ,015=1} cts. 7. If a man lay out 121 dollars 23 cts. in merchandise, and thereby gains 39,51 dollars, how much will he gain in laying out 12 dollars at the same rate ?

Ans. $3,91=$3, 91 cts. 8. How many yards of riband can I buy for 25 dols. if 293 yards cost 4 dollars ?

Ans. 178.1 yards. 9. If 1781 yds. cost 25$ dollars, what cost 29% yards ?

Ans. $41 10. If 1,6 cwt. of sugar cost 12 dols. 12 cts., what cost 3 hhds., each 11 cwt. 3 qrs. 10,12 lb. ?

Ans. 269,072 dols.=$269, 7 cts. 2 m. +

SIMPLE INTEREST BY DECIMALS.

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

Ratio.
3
,03

,055
4
,04
6

,06
,045
6:

,065
5

7

5

,05

,07

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 together, 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?

cis.
211,45 principal.

,05 ratio.

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10,5725 interest for one year.

5 multiply by the time. 52,8625 Ans.=852, 86 cts. 21 m. 2. What is the interest of 6451. 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 4 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 123 years, at 51 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 12 years, at 7 per cent. ? Ans. $340,25=$340, 25 cts.

4. What principal will amount to 956l. 10s. 4,125d. in 83 years, at 52 per cent. ?

Ans. £645 158.

CASE III. The amount, principal and time given, to find the ratio.

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

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

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