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8. Required the value of 1:7 of a pound apothecaries.
Ans. 2 oz. 9. How much is of 51. 9s. ? Ans. £4 13s. 5 d. 10. How much is į of of of a hhd. of wine?
Ans. 15 gals. 3 qts.
To reduce any given quantity to the fraction of any greater
denomination of the same kind.
1. Reduce 12 lb. 3 oz. to the fraction of a cwt.
Ans. Vi 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton.
Ans. 3. Reduce 16s. to the fraction of a guinea. 4. Reduce 1 hhd. 49 gals. of wine to the fraction of a
17 lb. 5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3
Ans. 7 8 oz.?
ADDITION OF VULGAR FRACTIONS.
Reduce compound fractions to single ones; mixed numbers to improper fractions; and all of them to their least common denominator, (by Case VI. Rule II.) then the sum of the numerators written over the common denominator will be the sum of the fractions required.
1. Add 5, and of together.
5}=\ and of Z=14 Then y, , 14 reduced to their least common denominator
by Case VI. Rule II. will become , id, it Then 1:32+18+14='=63; or 6. Ans.
13 2011 4417
2. Add }, á, and together.
ANSWERS. 17 3. Add ], ;, and í together. 4. Add 12, 33 and 4 together. 5. Add of 95 and 1 of 141 together,
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 53, 74 and 15.
Then 136+5+7+15=283. Ans. 7. Add and 174 together. ANSWERS. 1746 8. Add 25, 81 and į of of po
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 of a pound. 1st method
2d method. 4 of £.
3£=7s.6d. Oqro Then töti=*,£.
5.0 6 37 Whole value by Case VIII. is 8s. Od. 34 qrs. Ans.
Ans. 8.0 3.
By Case VIII. Reduction. 10. Add } lb. Troy, to of a pwt.
Ans. 7 oz. 4 prot. 13} grs. 11. Add of a ton, to io of a cwt.
Ans. 12 cwt. I gr. 8 lb. 12,6 oz. 12. Add of a mile to it of a furlong. Ans. 6 fur. 29 po. 13. Add of a yard, of a foot, and of a mile together.
Ans. 1540 yds. 2 ft. 9 in. 14. Add į of a week, of a day, of an hour, and of a min: tngather.
Au. 2 da. 2 ho. 30 min. 45 sec.
SUBTRACTION OF VULGAR FRACTIONS.
Prepare the fraction us in Addition, and the difference ot the numerators written above the common denominator, will give the difference of the fraction required.
1. From | takes of
Therefore 97== the Ans. 2. From take 4 3. From it take 4. From 14 lake 13 5. What is the difference of it and 17 ? 6. What differs is from ? 7. From 141 take of 19 8. From 21 take 111
O remains, 9. From i) of a pound, take of a shilling. of bro£. Then from 1£. take to£. Ans. £.
Note. - In fractions of money, weight, &c. you may, is you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper terms.
10. From 15£. take 3,7 shillings. Ans. 5s. 6d. 23 qrs. 11. From of an oz. take of a pwt. Ans. 11 pwt. 3 gr. 12. From į of a cwt. take ia of a lb.
Ans. I qr. 27 lb. 6 oz. 10, dr. 13. From 33 weeks, take of a day, and } off of of an hour.
Ans. 3 w. 4 da. 12 ho, 19 min. 174 sec.
* 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 unit's place of the lower whole number.
Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denominator, and placing the remaind. over the denominator, then taking one from the whole number,
MULTIPLICATION OF VULGAR FRACTIONS.
RULE. Reduce whole and mixed numbers to the improper 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 to. gether for a new denominator.
EXAMPLES. 1. Multiply : by
Answers. = 2. Multiply by 4
語 3. Multiply 51 by 4. Multiply of 7 by 5. Multiply just by Ma 6. Multiply of 8 by 1 of 5
131 7. Multiply 7} by 91 8. Multiply of} by of 37
9. What is the continued product of of, 7, 5} and } of ?
31} 2 응을
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.
4 x 5 1. Divide by Thus,
3 X 7 2. Divide 7 by i
Answers, 1 3. Divide of by } 4. What is the quotient of 17 by 4?
591 5. Divide 5 by 'n
74 6. Divide off of 1 by of
31 7. Divide 4 by of 4
2 8. Divide 71 by 127 9. Divide 5205} by of 91
RULE OF THREE DIRECT IN VULGAR
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.
s. d. grs.
come to ?
1. If of a yard cost of a pound, what will is of an Ell English cost ?
Syd.=of of f=46 or Ell English. El. £. EN. As:4::Ps And 1 X X = £.=10 3 14 Ans. 2. If of a yard cost of a pound, what will 40% yards
Ans. £59 8s. 6d. 3. If 50 bushels of wheat cost 1731. what is it per bushel ?
Ans. 7s. Od. 13 qrs. 4. If a pistareen be worth 14 pence, what are 100 pista reens worth?
Ans. £6 5. A merchant sold 5} pieces of cloth, each containing 24} yards at 9s. d. per yard ; what did the whole amount to ?
Ans. £60 10s. Od. 3 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. 11 d.
RULE. Prepare the fractions and state the question as before. then invert the third term, and multiply all the three terms together, the product will be the answer.