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EXAMPLES.

5. Reduce 23 to an improper fraction.
6. Reduce 127 to an improper fraction.
7. Reduce 7913 to an improper fraction.
8. Reduce 100 to an improper fraction.

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III. To reduce an improper Fraction to a whole or mixed number. RULE. Divide the numerator by the denominator, and the quotient will be the whole or mixed number.

EXAMPLES.

9. Reduce to its equivalent or proper number. Ans. 24. 10. Reduce 12 to its proper number.

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11. Reduce 1362 to its equivalent number. 12. Reduce 2918

5

17 to its equivalent number.

Ans.

4.

5412. 17111..

IV. To reduce a compound Fraction to a single one. RULE.-Multiply all the numerators together for a new numerator, and all the denominators for a new denominator.

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V. To reduce given fractions to others of a common denominator.

RULE.-Multiply each numerator into all the denominators except its own, for a new numerator, and all the denominators together for a common denominator.

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19. Reduce 1,, and to a common denominator.

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10

Ans.

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20. Reduce, 23 and 4 to fractions of a common denom

inator.

Ans.

25
38, 78, 120.
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VI. To reduce a fraction of one denomination to the fraction of another, but greater, retaining the same value.

RULE-Reduce the given fraction to a compound one, by comparing it with all the denominations between it and that denomination you would reduce it to; lastly reduce this compound fraction to a single one.

EXAMPLES.

21. Reduce of a penny to the fraction of a pound.

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22. Reduce dwt. to the fraction of a lb. troy. Ans. 300 23. Reduce of a lb. avoirdupois to the fraction of a cwt. 급

Ans.

24. Reduce of 58. to the fraction of 21 shillings.

Ans.

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VII. To reduce a fraction of one denomination to the fraction of another, but less, retaining the same value.

RULE-Multiply the given numerator by the parts of the denominations between it and that denomination you would reduce it to, for a new numerator, which place over the given denominator.

25. Reduce
26. Reduce 1
3

EXAMPLES.

of a pound to the fraction of a penny. Ans. of a lb. troy to the fraction of a pennyweight.

Ans.

27. Reduce of a cwt. to the fraction of a lb. 3

Ans.

28. Reduce 25 of 21s. to the fraction of 5 shillings. Ans. 168

VIII. To find the value of a fraction, in the known parts of coin, weight, measure, &c.

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RULE-Multiply the numerator by the integer, and divide by the denominator: if any thing remain, multiply it by the next inferior denomination, and divide as before.

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IX. To reduce any given quantity to the fraction of any greater denomination of the same kind.

RULE-Reduce the given quantity to the lowest term mentioned, for a numerator; then reduce the integral part to the same term, for a denominator, which will be the fraction required.

EXAMPLES.

35. Reduce 12s. to the fraction of a pound. 36. Reduce £4 13s. 54d. to parts of £5 9s.

Ans. 옥

37. Reduce 3 cwt. O qrs. 8lb. 9oz. 13 dr. to the fraction of a

ton.

13

Ans. 6

38. Reduce 1 fur. 28 po. 34 yds. to the fraction of a mile.

39. Reduce 2ro. 20po. to the fraction of an acre. 40. Reduce 7ho. 12min. to the fraction of a day.

Ans.

ADDITION OF VULGAR FRACTIONS.

39

RULE. Reduce the given fractions to a common denominator, then add all the numerators together, under which place the common denominator.

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When fractions are of several denominations. RULE. Reduce them to their proper values, and add as before.

5. Add of a pound to of a shilling.
6. What is the sum of £.3+3s.+3d.
7. What is the sum of £4+3+5d.
8. Add of a pound Troy to of an ounce.

9. Add of a ton to 48 of a lb.
10. Add of a mile to 7 of a furlong.
11. Add of a week, 4 of a day, and

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Ans. 15s. 10d.

15s. 93d. 3s. 1d. 110 grs.

Ans. 9 oz. 3 dwt. 8 grs. 16 cwt. 13 oz. 5 dr. Ans. 6 fur. 28 po. of an hour together. Ans. 2 days, 14 hours. 12. A grocer sold the following parcels of sugar, viz: 16 lb. 194 lb. 134 lb. 20 lb. 2511 lb. 305 lb. and 114 lb. I demand how many lb. he sold in all ? Ans. 362 lb.

MULTIPLICATION OF VULGAR FRACTIONS.

55

SUBTRACTION OF VULGAR FRACTIONS. RULE 1.-Reduce the given fractions to a common denominator, then subtract the less numerator from the greater and place the remainder over the common denominator.

2. In mixed numbers when the lower fraction is greater than the upper, subtract the numerator of the lower from the denominator, and to that difference add the upper numerator, carrying one to the units place of the lower whole number. EXAMPLES.

1. Subtract from 111.
2. Subtract from 97
3. Subtract 143 from 963.

100

Ans.

27 112.

4. From 19 take of 3.

5. From 644 take of .

When fractions are of several denominations.

379 700 8119. 21 359 422

632.

RULE. Reduce them to their proper values and subtract

as before.

6. From of a pound take of a shilling. 7. From of a lb. Troy, take 1 of an ounce. of a ton, take of a lb.

8. From

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Ans. 15 cwt. qrs. 27 lb. 2 oz. 103 dr.

9. From of a league take 7 of a mile.

Ans. 1m. 2 fur. 16 po.

10. From of a chaldron take of a bushel.

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MULTIPLICATION OF VULGAR FRACTIONS. RULE.-Reduce compound fractions to single ones, and mixed numbers to improper fractions; then multiply the numerators together for a new numerator, and the denominators for a new denominator.

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56 RULE OF THREE INVERSE IN VULGAR FRACTIONS.

RULE.-Prepare the numbers if necessary by the rules of reduction; and divide the numerator by the numerator, and the denominator by the denominator, if they will exactly divide; but if not, then invert the terms of the divisor, and proceed as in multiplication.

1. Divide 25 by 5.

EXAMPLES.

25×3

35÷§—§—13 Ans. Or thus, 2+13=13 Ans.

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RULE OF THREE DIRECT IN VULGAR FRACTIONS.

RULE-Make the necessary preparations as before directed; then multiply continually together, the second and third terms, and the first with its parts inverted as in division, for the answer.

EXAMPLES.

1. If § of a gallon cost what will § of a tun cost?

gal. . tun. 8×5×5×4×63

If : : : 5/

5X8X9X1x1

=$140 Ans.

2. What is the purchase of $1230 bank stock, at 108 per

sent?

Ans.

$1336 8 cts.

3. If 3 yards cost £24 what will 14 yards cost?

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RULE-State and prepare as in the rule of three direct, in

vert the third term in place of the first, and proceed as in di

vision.

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