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9. Reduce of a pint to the fraction of a hhd. Ans.ads 10. Reduce of a pound to the fraction of a guinea.
Compounded thus, f of 20 of abs. Ans. 11. Express 5, furlongs in the fraction of a mile. .
Thus 51=”of =1* Ans. 12. Reduce 4 of an English crown, at Øs. 8d. to the frac tion of a guinea at 28s.
Ans. it of a guinea.
To find the value of a fraction in the known parts of the
integer, as of coin, weight, mčasure, &c.
Multiply the numerator by the parts in the rext inferici denomination, and divide the product by the denominator ; and if any thing remains, multiply it by the next inferior de. nomination, and divide by the denominator as before, and so on as far as necessary, and the quotient will be che answer.
Nore.—This and the following Case are the same with Problems II. and III. pages 70 and 71 ; but for the scho lar's exercise, I shall give a few more examples in each.
| What is the value of fit of a pound? Ano &. fd. 2. Find the value of 7 of a cwt. Ans. 3 yrs.3.0.1 oz.12409 8. Find the value of 7 of 33. ich Ans. 35. 03d. 4. How much is 94 of a pound avoirdupois ?
Ans. 7 02. 10 dr. 6. Ilow much is 4 of a hhd. of wine ? Ans. 45 gals 6. What is the value of tf of a dollar ? Ans. 5s. 71d ^ What is the value of or of a guinea ? Ans. 185
25.8. Required the value of ti? of a pound apothecaries.
Ans. 2 oz. 3 grs. 9. How much is of 51. Is. ? . Ans. £4 13s. 54d. 10. How much is of of of a hhd. of wine ?
Ans. 15 gals. 3 pts
denomination of the same kind.
EXAMPLES FOR EXERCISE. .
Ans. 49 2. Reduce 13 cwt, 3 qrs. 20 lb. to the fraction of a ton.
Ans. 3. Reduce 16s, to the fraction of a guinea. Ans. **4. Reduce 1 hhd. 49 gals. of wine to the fraction of a sin.
Ans. 5. What part of 4 cwt. 1 gr. 24 lb. is 3 cwt. 3 qrs. 17 lb. oz.
ADDITION OF VULGAR FRACTIONS.
RULE. 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.
2. Add , d, and together.
ANSWERS. 17 3. Add i, j, and together. 4. Add 12; 3; and 4 together.
2013 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.
SUBTRACTION OF VULGAR FRACTIONS.
RULE.* Prepare the fraction is in Addition, and the difference ot'the numerators written above the common denoniinator, will give the difference of the fraction required.
EXAMPLES. 1. From take of • of 1=1=in Then and ia ia la
i Therefore 9–7= = the Ans. 2. From take
Answers. 1 3. From it wake 4. From 14 lake 1
13 5. What is the difference of i' and 17? 6. What differs is from i? 7. From 141 take of 19 8. From ? take o
Oremains. 9. From it of a pound, take of a shilling. of zbrifi£. Then from ££. take tiñ£. Ans. 37£.
Note. - In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Casa VIII. in Reduction) and then subtract them in their proper Terms.
10. From 15£. take 37 shillings. Ans. 5s. 6d. 2 qrs. Jl. Froin of an oz. lake į of a pwt. Ans. Il pwt. 3 gr. 12. From 1 of a cwt. take of a lb.
Ans. I qr. 27 lb. 6 oz. 10, dr. 13. From 3 weeks, take of a day, and of of of an hour.
Ans. 3 w. 4 da. 12 ho. 19 min. 17 sec.
* In subtracting mixed numbers, when the lower fraction is greater than the upper one, you may, without reilucing them to improper fractions, subtract the numerator of the lower fraction from the conimon 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 remainder arer the denominator, then taking one from the whole number
MULTIPLICATION OF VULGAR FRACTIONS
RULE. Redace whole and mixed numbers to the improper frac tions, mixed fractions to simple ones, and those of differen integers to the same; then inultiply all the numerators, to gether for a new numerator, and all the denominators-w gether for a new denominator.
1. Multiply by
Answers. = 2. Multiply by 3. Multiply 51 by $. 4. Multiply of y by $ 5. Multiply ill by 6. Multiply of 8 by 1 of 5
131 7. Multiply 71 by 91
693 8. Multiply of} by (of 34
9. What is the continued product of of}, 7, 54 and of ?
DIVISION OF VULGAR FRACTIONS.
RULE. Prepare the fractions as before ; then, invert the divisat and proceed exactly as in Multiplication :-The producte will be the quotient required.
EXAMPLES. . .
4 x 5 1. Divide 4 by Thus,
3 X 7 2. Divide 47 by
Answers. 14 3. Divide of į by 4. What is the quotient of 17 by ? 5. Divide 5 by io 6. Divide 4 of of by 1 of 1 7. Divide 4 by of 4 8. Divide 71 by 127 9. Divide 52054 by 4 of 91