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2. Add } and if together.

Ans. 15 3. Add 1 and together.

Ans. 13 4. Add 12 3 and 4. together. Ans. 2011 5. Add } of 95 and of 141 together. Ans. 4417

Note 1.- In adding mixed numbers that are not com. pounded with other fractions, you may first find the sum of the fractions, to which add the whole numbers of the given mixed numbers. 6. Find the sum of 5274 and 15. I find the sum of and to be id=l4

Then 14+5+7+15=294 Ans. 7. Add 1 and 174 together.

Ans. 17 8. Add 25, 84 and of ß of

Ans. 332 Note 2.—To add fractions of money, weight, &c. reduce fractions of different integers to those of the same.

Or, if you please you may find the value of each fraction by Case VIII. in Reduction, and then add them in their proper terms. 9. Add of a shilling to Z of a pound. 1st Method.

2d Method. of h=ito

£.=7s. 6d. Oqrs Then ito+katizo £

45.=0 6 33 Whole value by Case VIII. is 8s. Od. 34 qrs. Ans. Ans. 8

0.35

By Case VIII. Reduction 10. Add 3lb. Troy, to $ of a pwt.

Ans. 702.4pwt. 13}gr. .11. Add of a ton, to in of a cwt.

Ans. 12cut. Iqr. 8?b. 12 oz. 12. Add of a mile to jo of a furlong.

Ans. 6fur. 28po. 13. Add f of a yard, f of a foot, and of a mile to gether.

Ans. 1540yds. 2ft Sin. 14. Add of a week, } of a day, 5 of an hour, and of a minute together. Ans. 2da. 2ho. 30min. 45$pC.

SUBTRACTION OF VULGAR FRACTIONS.

RULE.* PREPARE the Fraction as in Addition, and the difference of the numerators written above the common denominator will give the difference of the fraction required.

EXAMPLES.

31 708

5 378 10 ITT

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1. From take of of }

Then and in the Ans.

Therefore 9—1=ke the Ans. 2. From 36 take

Answers. 3. From He take 4. From 14 take

1375 5. What is the difference of 14 and 17? 6. What differs dy from ? 7. From 144 take of 19 8. From 1 take 1H

O remains. 9. From 11 of a pound, take of a shilling. of báo £. Then from } } £. take tå £. Ans. } £.

Note.--In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper terms.

10. From £. takc 37 shilling. Ans. 5s: 6d. 23 qr's 11. From of an oz. take of a pwt.

Ans. 11puls. 3gr. 12. From } of a cwt. take 12 of a lb.

Ans. Iqr. 271b. 6oz. 10, dr. 13. 3 weeks, take } of a day, and off of of

Ans. 3w. 4da. 12ho, 19min. 174sec.

an hour.

* In subtracting mixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them to improper fractions, subtract the numerator of the lower fraction from the common denominator, and to that difference add the upper numerator, carrying one to the upit's place of the lower whole nuinber.

Also, a fraction may be subtracted from a whole pumber by taking sho numerator of the fraction from its denominator and placing the res Qizlinder over the chenominator, then taking one from the whole number.

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MULTIPLICATION OF VULGAR FRACTIONS

RULE. REDUCE whole and mixed numbers to the improp er fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.

EXAMPLES.

1. Multiply s by

Answers = 2. Multiply by

17 3. Multiply 54 by :

3 4. Multiply of 7 by $

315 5. Multiply 114 by 6. Multiply of 5 by 1 of 5

135 7. Multiply 73 by 91

693 8. Multiply of by of 3

9. What is the continued product of of g, 7, 51 and off?

Åns. gto

DIVISION OF VULGAR FRACTIONS.

RULE. PREPARE the fractions as before; then invert the divisor and proceed exactly as in Multiplication :--The product will be the quotient required.

EXAMPLES.

4 X 5 1. Divide by Thus, Sil Ans.

3 x 7 2. Divide 17 by }

Answers, 11s 3. Divide { of 4 by 4. What is the quotient of 17 by *? 5. Divide 5 by 3

명을 6. Divide of of by s off

35 7. Divide 43 by f of 4

221 8. Divide 71 by 127

134 8. Divide 5205} hy s of 91

71$

59}

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 name with the second or middle term.

EXAMPLES.

š. d. qrs.

1. If of a yard cost of a pound, what will it of añ Ell English cost ?

fyd.=of of =# or Ells English. Ell. £. Ell. As :4:: And *x+Xf=$£.=10 3 17 Ans.

2. If of a yard cost } of a pound, what will 401 yards come to ?

Ans, £59 Ss. 64d. 3. If 50 bushels of wheat cost 17.31. what is it per bushel ?

Ans. 7s. Od. 14iqrs. 4. If a pistareen is worth 14; pence, what are 100 pistareens worth?

Ans. £6. 5. A merchant sold 54 pieces of cloth each containing , 24} yds. at 9s. id. per yard ; what did the whole amount

Ans. £60 10s. Od. 3jqrs. 6. A person having of a vessel, sells f of his share for 3121, ;

what is the whole vessel worth ? Ans. £780. 7. If f of a ship be worth of her cargo, valued at 80001. what is the whole ship and cargo worth?

Ans. £10031 14s. 11, d.

to ?

INVERSE PROPORTION.

RULE. PREPARE the fractions and state the question as before, then invert the third term, and multiply all the three terms together the prodnet will be the answer

EXAMPLES.

1. How much shalloon that is it yard wide, will line 55 yards of cloth which is 14 yard wide ? Ids. yds. yds.

Yds.
As 11:54: And 7xX3=1644 Ans.

2. If a man perform a journey in 3} days, when the day is 12j hours long; in how many days will he do it when the day is but 9 hours ? Ans. 4,44 days. 3. If 13 men in 11f days, mow 12, acres, in how many days will 8 men do the same ? Ans. 187 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. 1451 iniles; how far may 61 cwt. be carried for the sanie money ?

Ans. 22 miles. 6. How many yards of baize which is 14 yards wideya will line 187 yards of camblet yd. wide

Ans. 11 yds. lqr. lfna.

RULE OF THREE DIRECT IN DECIMALS.

RULE. REDUCE your fractions to decimals, and state your question as in whole numbers ; multiply the second and third together; divide by the first, and the quotient will be the answer, &c.

EXAMPLES.

1. If f of a yd. cost 7 of a pound; what will 154 yds. come to ?

1875] =,583+an 3,75. Yds. £. Yds. £.

£. 3. d. qrs. As .875 : ,583 : : 15,75 : 10,494510 9 10 2,24 Ans.2. If 1 pint of wine cost 1,2s. what cost 12,5 hhds ?

Ans. £378. 3. If 41 yds, cost 33. 4fd. what will 304 yds. cost

Ans. £1 4s. 3d. 3qrs.t

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