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Fucit 514

92. Reduce 59 to its proper terms.

Facit 18 23. Reduce. 245 to its proper terms.

Fucit 271. 2.1. Reduce 8229

to its proper terms.

5. To reduce a compound fraction to re single one. RULE. Multiply all the numerators for a new numerator, and all the denominators for a new denominator. Reduce the new fraction to its lowest term, by rule 2.

EXAMPLES. 25. Rexluce šof ofto a single fraction.

Fuit

2X8X5= 30
3X 5X8=120

reduced to the lowest terms. 26. Recluce of of li to a single fraction.

Facit 220

750 181 27. Reiluce of of to a single fraction.

Facit 3003

787- 2327 28. Reduce

of of
to a single fraction.

Facil 135–9

276 29. Reduce ofof; to a single fraction.

Facit 168.

7

375 13. 30. Reduce of of is to a single fraction.

Fucit 80 – 8 6 To reduce fractions of one denomination to the fraction of another,

but greater, retuining the same value. Rule. Reduce the given fraction to a compound one by com. paring it with all the denominations between it, and that derromination, which you would reduce it to; then reduce that compound fraction to a single one.

21
29

10

630

EXAMPLES

19

368

1200

Facit

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31. Reduce ; of a pen:y to the fraction of a pound.

Facit f of li of i=, 32. Reduce of a penny to the fraction of a pound. Facit 33. Reduce of a dwt. to the fraction of a lb. troy. Facit 34. Recluce of a lb. avoirdupoise to the fraction of an cwt. 7 To reduce fractions of one denomination to the fraction of another,

but less, retaining the same value. RULE. Multiply the numerator by the parts contained in the several denominations between it, and that you would reduce it to, for a new numerator, and place it over the given denominator, Reduce the new fraction to its lowest terms.

EXAMPLES. 35. Reduce 120 of a pound to the fraction of a penny. Facit ;. 7 x 20 x 12=1680 16so reduced to its lowest term.

36. Reduce go of a pound to the fraction of a penny. Fucit ļ.

37 Redace aid of a pound troy, to the fraction of a penny. weight.

Facit 38. Reduce yin of a cwt. to the fraction of á lb. Facit

1020

960

1200

a

K

8. To reduce Fractions of one Denomination to another of the same

Value, having the Numerator given of the required Fraction. RULE. As the numerator of the given fraction: is to its denominator :: so is the numerator of its intended fraction: to its denominator.

EXAMPLES. 39. Reduce to a fraction of the same value, whose numerator shall be 12. As 2:3 :: 12: 18.

40. Reduce to a fraction of the same value, whose numerator shall be 25.

41. Reduce to a fraction of the same value, whose numera. tor shall be 47.

47

Facit i

Facit 5.

25

Facit 65.

9. To reduce Fractions of one L'enomination to another of the same

Value, having the Denominator given of the Fraetions required. RULE. As the denominator of the given fraction : is to its numerator :: so is the denominator of the intended fraction : to its numerator.

EXAMPLES 42. Reduce to a fraction of the same value, whose denuminator shall be 18. As 3:2 :: 18:12.

Facit 1 43. Reduce to a fraction of the same value, whose denomi. nator shall be 35.

44. Reduce to a fraction of the same value, whose denoncinator shall be 65.

47

Facit

25

Facit 65%

10. To reduce a mixed Fraction to a single one. Rule. When the numerator is the integral part, multiply it by the denominator of the fractional part, adding in the numerator of the fractional part for a new numerator; then multiply the denominator of the fraction by the denominator of the fracvional part for a new denominator.

EXAMPLES.

110

363
43. Reducem-to a simple fraction.

Facit =
48
36X3+2=110 numerator.
48 X3 =144 denominator.

23
46. Reduce--to a simple fraction.

Facit = 38 When the denominator is the integral part, multiply it by the denominator of the fractional part, adding in the numerator or the fractional part for a new denominator ; then multiply the numerator of the fraction by the denominator of the fractional part for a new numerator.

EXAMPLES

47 47. Reduce to a simple fraction.

Facit 65

19 48. Reduce to a simple fraction.

Facit 572

133 44 11. To find the proper Quuntity of a Fraction in the known Parts of

un Integer. Rule. Multiply the numerator by the common parts of the integer, and divide by the denominator.

FXAMPLES. 49. Reduce of a pound sterling to its proper quantity. 3 X 20=60-4=l5s.

Facit 158. 50. Reduce of a shilling to its proper quantity.

Fucit 4d. 3 grs. 5 51. Reduce of a pound avoirdupoise to its proper quantity

Fucit y oz. 2 dr. . 52. Reduces of an cwt. to its proper quantity;

Facit 3 qrs. 3 lb. 1 0%. 12 dr. %. 53. Reduce of a pound troy to its proper quantity.

Facit 70%. 4 dwt 54. Reduce of an ell English to its proper quantity.

Facil % qrs. 3 nuils : 55. Reduce of a mile to its proper quantity.

Fucil 6 furl. 16 poles. 56. Reduce of an acre to its proper quantity.

Facit 2 roods 20 poles 57. Reduce of an hogshead of wine to its proper quantity,

Facit 54 gallons 58. Reduce of a barrel of beer to its proper quantity.

Facit 12 gallons. 59. Reduce z of a chaldron of coals to its proper quantity.

Fucit 15 bushels. 60. Reduce of a mouth to its proper time.

Fucit 2 weeks, 2 days, 19 hours, 12 minutes. 12. To reduce uny given Quantity to the Fruction of any

greater Denomination, retaining the same value. Rule. Reduce the given quantity to the lowest term mentioned for a numerator, under which set the integral part (rea duced to the same term) for a denominator, and it will give the fraction required. 61. Reduce 15s. to the fraction of a pound sterling.

a

Facit L 62. Reduce 48d. ; to the fraction of a shilling.

Facit :

EXAMPLES.

13. Reduce 9_0%. 2 dr. ; to the fraction of a pound avoirdupoise.

Facit 64. Reduce 3 grs. 3 lb. 1 0%. 12 dr. ; to the fraction of an cwt.

Facit 65. Reduce 7 0%. 4 dwts. to the fraction of a lb. troy. Fucit ht. Reduce 2 qrs. 3 nails; to the fraction of an English ell.

Facit 67. Reduce 6 fw longs 16 poles' to the fraction of a mile.

Facit. 68. Reduce 2 roods 20 poles to the fraction of an acre. Facit s. 69. Reduce 54 gallons to the fraction of a hogshead of wine.

Facit . 70. Reduce 12 gallons to the fraction of a barrel of beer.

Facit : 71. Reduce 15 bushels to the fraction of a chaluro:1 of coals.

Facit i. 72. Reduce 2 weeks, 2 days, 19 hours, 12 minutes, to the fraction of a month.

Facit .

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Facit 1 1989

146

10

15

Facit te

ADDITION OF VULGAR FRACTIONS. RULE. Reduce the given fraction to a cornmon denominator,

then add all the numerators together, under which place the common denominator.

RXAMPLES. 1. Add and together.

Facit *-*=y=1

一驾=1.. 2. Add , , and together. 3. Add, 4and together.

Facit 4 4. Add 7 and together.

Facit 8 5. Add }, and of together. 6. Add 5 , 63, and 4 { together. Fucit 17 z

II. When the fractions are of several denominations, reduce them to their proper quantities, and add as before.

7. Add of a pound to of a shilling. Facit 15s, 10d. 8. Add is of a penny to of a pound. Fačit 13s. 444. 9. Add of a pound troy to of an ounce.

Facit 9 om. S dwt. 8 gr. 10. Add of a ton to of a lb.

Facit 16 cwt. O gr. O lb. 130%. 5 dr. j. 11. Add of a chaldron to ļof a bushel.

Facit 24 bushels, s pecks. 12. Add 1 of a yard to of an inch. Facit 6 inch. bar. €.

SUBTRACTION OF VULGAR FRACTIONS. RULE. Reduce the given fractions to a common denomina,

tor, then subtract the less numerator from the greater, and place the remainder over the commor: denominator.

II. When the lower fraction is greater than the upper, subtract the numerator of the lower fraction from the denoininator, and to that difference add the upper numerator, carrying one to the unit's place of the lower whole number.

LXAMPLES.

77

....... Fecit

. Facil 433.

10

235 •

Facit 339

| From take 5. 3x7=21.5 X 4=20.21--20=1 num. 4x1=28 den....

.Facit 2. From take of .. 3. From 5 take 4. From 3 take

.Facit 32 5. From , take of 6. From 644 take of

.Facit 631. III. When the fractions are of several denominations, reduce them to their proper quantities, and subtract as before.

7. From { of a pound take of a shilling. Facit. 145. 3d. 8. From of a shilling take of a penny.

Facit 7 d. 9. From of a lb, troy take

of an ounce.

Facil 8 oz. 16 dwts. 16 grs. 10. From of a ton take of a lb,

Fucit 15 cwt. 3 qr. 27 lh. 2 0. 10 dr. z. 11. From } of a chaldron take of a birshel.

Facit 23 bushels, 1 peck. 12. From } of a yard take s of an inch. Facit '5 in. 1 6. c.

MULTIPLICATION OF VÚLGAR FRACTIONS. RO

ULE. Prepare the given numbers (if they require it) by

the rules of Reduction ; then multiply the numerators together for a new numerator, and the denominators for a new denominator.

EXAMPLES.

27

3

194

1. Multiply by Fa. 3X3=9 num. 4x5=20 den. 2. Multiply [ by i

....Facit 3. Multiply 48 by 135

Facit 67%. 4. Multiply 430,8 by 18

.Facit 79357 5. Multiply 1 by tot of

Facit 96 6. Multiply to by of

.Facit 7. Multiply of by of s

Facit 8. Multiply 1 of by

.Facit 15 9. Multiply 5, by... 10. Multiply 24 by j.

.Facit 16. li. Multiply of 9 by :

Facit 6 12. Multiply 9 $ by 1

.Facit si

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Facit 412

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