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CASE 13. To reduce a given fraction to another equivalent one, having a given denominator.

RULE.

As the denominator of the given fraction
Is to the denominator of the intended fraction,
So is the numerator of the given fraction
To the numerator required.

EXAMPLES.

Ans. at

Ans. 4

Ans.

1. Reduce to an equivalent fraction, having its denominator 24.

As 8:24 ::7:21, num. 2. Reduce to a fraction of the same value, the denominator of which shall be 45.

3. Reduce 1, to an equivalent fraction, having its denomi. nator 68.

4. Reduce & to a fraction of the same value, the denomi. nator of which shall be 46.

Ans. 34)

46 5. Reduce jí to an equivalent fraction, having its denominator 20.

20

Ans. 121

ADDITION OF VULGAR FRACTIONS.

RULE.

Reduce compound fractions to single ones; mixed numbers to improper fractions; fractions of different integers to those of the same ; and all of them to a common denomi. nator ; then, the sum of the numerators written over the common denominator, will be the sum of the fractions required. After the fractions are prepared, multiply each numerator into all the denominators but its own, and take their sum for a new numerator-multiply all the denominators for a new denominator. See Case 6, Reduction.

EXAMPLES.

1. Add 74, of , and 7, together.

First, 74=3., and of =35, and 7=1
Then the fractions are 39, 15, and 7 ; therefore

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118

SUBTRACTION OF VULGAR FRACTIONS.

39 x 56 x 1=2184
15 x 5 x 1= 75
7 x 5 x 56=1960

4219

=151% Ans.

5 x 56 x1=280 2. What is the sum of y of 43, $ of , and 94?

Ans. 82, or 12. 3. Add together d. c. c. and Im. Ans. 20c. 9m. 4. Add £ {s. and fd. together. Ans. 2s. 81 d.

5. Add of a week, # of a day, $ of an hour, and 4 of a minute, together.

Ans. 2d. 2h. 30m. 45sec. 6. Add i of a dollar, of a dime, and of an eagle, together.

Ans. $6.03.2011 7. Add f of a dollar to of a dollar. Ans. $1.12,5. 8. Add t of a lb. troy, to i of an oz.

Ans. 6oz. 11dwt. 16gr. 9. Add 4 of a ton to do of a cwt.

Ans. 12cwt. lqr. 8lb. 12oz. 12dr. 10. Add of a mile to Z of a furlong.

Ans. 6 furlongs, 28 poles. 11. Add } of a yard to of a foot.' Ans. 2ft. 2in. 12. Add of a yard, $ of a foot, and f of a mile, together.

Ans. 1540 yards, 2 feet, 9 inches. 13. If a merchant owns f of a ship, valued at $4000, and buys another person's share, which is what part belongs to him, and what is it worth?

Ans. It belongs to him, and is worth $2750.

SUBTRACTION OF VULGAR FRACTIONS.

RULE.*

Prepare the fractions, when necessary, as in Addition,

* In subtracting mixed numbers when the fractions have a common denominator, and the numerator in the subtrahend (or lowest number) is less than that in the minuend, (or upper number) the difference of the whole numbers will be a whole number, and the difference of the numerators a numerator, to be placed over the given denominator. But when the numerator in the subtrahend is greater than that in the minuend, subtract the numerator in the subtrahend from the common denominator, adding the numerator in the minuend, set it down and carry one to the whole number, or integer of the subtrahend.

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and take the difference of the numerators, under which write the common denominator, wbich will give the difference of the fraction required. Multiply each numerator by the other denominator, and subtract the less (product) from the greater, for the numerator sought; multiply one denominator by the other for a common denominator.

EXAMPLES.

Ans. 196.

1. From & take & of.

4 of ==*. Then the fractions are $ and more
3x 28=84
5 X 4 = 20

I= and D='; therefore
64

11-10=4, remainder. 4x 28=112 2. From I take x.

Hence a fraction is subtracted from a whole number, by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number. 3. From 12%

124

12 Take 72

73
Rem. 5}

42
4. From ii subtract ige
5. From subtract .

Ans.
6. From 7 subtract 5).

Ans. 21. 7. From 8. subtract 53. 8. From 51 take f. 9. From 12 také . 10. From f of 1 subtract of . 11. Take 3fc. from } of 2 d.

Ans. 434c. 12. From 1£ take los.

Ans. 4s. 11d. 13. From 5 weeks take 194 days. Ans. 15d. 4h. 48m.

11}

Ans. is:

12

Ans. 25. Ans. 46. Ans. 114. Ans. it.

MULTIPLICATION OF VULGAR FRACTIONS.

RULE.

Reduce compound fractions to simple ones, and mixed numbers to improper fractions; if an integer be given, re. duce it to an improper fraction, by putting a unit for its

120

DIVISION OF VULGAR FRACTIONS. denominator; then multiply the numerators together for a new numerator, and the denominators together for a new denominator.

NOTE.-Where several fractions are to be multiplied, if the numerator of one fraction be equal to the denominator of another, their equal numerators and denominators may be omitted.

EXAMPLES.

1. Multiply & by 5%.

53=4

**Y=1=45, Ans. 2. Multiply 64 by 8.

Ans. 543. 3. Multiply ož by 1 of 4. 4. Multiply of 5 by of 4. 5. Multiply 54 by š.

6. Required the continued product of 78, 27, 3), and 8 of 11.

Ans. 39.

Ans. 36 Ans. 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.

1

1. Divide 4 by of 4.

prepared is % Then X2=35=4

=*:!(27 result.

*), Note.-The above may be abridged by cancelling the like numbers in the numerators and denominators.

Thus, 41,5 41

Х
20

=230

20 2. Divide by s. 3. Divide 54 by 74. 4. Divide 1 of 4 of } by $ of 4. 5. Divide 99 by 108.

Ans. 11 6. Divide ☆ by 4. 7. Divide 4 by . PROMISCUOUS QUESTIONS IN VULGAR

FRACTIONS. 1. Reduce 389 to its lowest terms.

Ans. $.

Ans. 14. Ans. 41 Ans. .

Ans. n. Ans. 44.

8

Ans.

2. Reduce 6 to a fraction whose denominator shall be 8.

Ans. 4_3 3. Reduce 2s. 6d. to the fraction of a pound.

Ans. š. 4. Reduce 365 to its equivalent improper fraction.

Ans. 392. 5. Reduce 1 to its equivalent whole number. "Ans. pe. 6. Reduce of } of & to a single fraction.

Ans. 1. 7. Reduce 1, 1, and 4to equivalent fractions, having a common denominator ?

Ans. So, and 31 8. What is the value of $ of an acre ? Åns. 3r. 174p 9. What is the sum of 3

and

195

. ? 10. What is the sum of 7% and 5* ?

Ans. 137 11. Add of a dollar to of a dollar. Ans. $1.62,5. 12. Add į of a pound troy, to pa of an oz.

Ans. 6oz. 11dwt. 16gr. 13. From of a'dollar take of a cent. Ans. $ .74,25. 14. From 3 of a cwt. take 1 of a pound.

Ans. Iqr. 27lb. 6oz. 10dr. f. 15. If a merchant own of a ship, valued at $900, and sells of his share, what part has he left, and what is it worth?

Ans. left, worth $187.50. 16. Multiply of 8 by } of 5.

Ans. 21. 17. Divide $2591% equally among 15 persons, and tell the share of each.

Ans. $17.2915. 18. What part of 3 pence is šof 2 pence? 19. A has 4 of a ship, of which he sells $ for £100what is the value of the whole ship at that rate ?

Ans. £533 6s. 8d.

Ans.

!

SINGLE RULE OF THREE IN VULGAR

FRACTIONS.

RULE.

Reduce the given numbers if necessary; mixed numbers to improper fractions ; like terms to the same denomina. tions, and each to their lowest terms.

Then state the question as in whole numbers; invert the first term, and multiply all the numerators together for a

new numerator, and all the denominators for a new denominator, and divide the upper term by the lower for the

answer.

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