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Case 9th. To reduce a complex fraction to a simple one.

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to a simple fraction.

Case 10th. To find the value of a fraction in the known parts of the integer.

Example.
Required the value of g of a
pound sterling

RULE.
5
20 shillings = £1.

Multiply the numerator by 9) 100

the next lower denomination,

and divide by the denominator ; 11.1

if any thing remain, multiply it 12 pence = 1 sg.

by the next lower denomination, 9) 12

and divide as before, and so pro1.3

ceed to the lowest denomination; 4 fgs. = 1d. and the several quotients will be

the value required. 9) 12

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EXERCISES. 55. What is the value of 3 of a shilling ?

Answer, 10 d. 56. Required the value of į of a guinea.

Answer, 4s. 8d. 57. Reduce of a yard of Cloth to its proper quantity.

Answer, 3 qrs. 2 nls. 58. Reduce of a pound avoirdupois to its proper quantity.

Answer, 8 oz. 14 drs. 59. What is the proper quantity of of a hogshead of Beer ?

Answer, 36 gallons. 60 Reduce of a pound troy to its proper quantity.

Answer, 9 oz. 12 dwts. 61. Reduce 15 of a day to its proper quantity.

Answer, 12 hrs. 55 min. 23 sec. 1's 62. What is the value of 15 of a pound sterling ?-Answer, 10s. 8d. 63. Reduce of a mile to its proper quantity.

Answer, 4 fur. 22 poles. 4 yds. 2 feet, 1 in. 64. Reduce 15 of a ton to its proper quantity.

Answer, 3 Cwt 1 qr. 18 lb. 12 oz. 8 dr. I.

4

14 qrs.

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Case 11th. To reduce any given quantity to the fraction of a higher denomination, retaining the same value.

Example.
Reduce 3 Cwt. 2 qrs. 8 lb. to the

RULE. fraction of a ton.

Reduce the given quantity to 3 Cwt. 2 qrs. 8 lb.

the lowest term mentioned for a numerator and place for a deno

minator as many of the small as 28

make one of the greater denomi400 lb.

nation.* 2240 lb, = 1 ton.

Cases 10 and 11 prove each

other. Answer, 400

= 16 =

EXERCISES. 65. Reduce 18 shillings to the fraction of a pound. Answer, is 66. Reduce 7s. 3d. to the fraction of a pound.

Answer, og 67. Reduce 8 oz. 2 dwts. to the fraction of a pound troy. Ans. 68. Reduce 2 qrs. 2 nls. to the fraction of a yard of cloth.

Ans. Í 69. Reduce 4s. 8d. to the fraction of a guinea.

Answer, 70. Reduce 2 roods, 20 poles to the fraction of an acre.

Ans. Í 71. Reduce 12 gallons of beer to the fraction of a hhd.

Ans. 72. Reduce 2 weeks, 5 days, to the fraction of a month.

Ans. 1 % 73. Rednce 2 qrs. 14 lb. 1 oz. to the fraction of a Cwt.

Ans. 1132 71. Reduce 15s. 9fd. to the fraction of a pound. 75. Reduce 13s. 8 d. to the fraction of a guinea. Answer, Iz

CASE 12th. To reduce a fraction from one denomination to that of another, retaining the same value. Example.

RULE. Reduce } of a pennyweight to

When it is from a less name the fraction of a pound troy. $

to a greater, multiply the de

nominator by all the denomina5 X 20 X 14 5 X 20 X 4

tions from that given, to the one Answer, do

Answer, šu

1

1

400

4

sought.

* Some Arithmeticians have given another Rule for reducing the fractions ; but the above may be best understood by the learner.

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Answer, 6 fo
Exercises.

Answer, its 76. Reduce g of a penny to the fraction of a pound. 77. Reduce of a farthing to the fraction of a pound.

Ans. Ideo 78. Reduce of a pound to the fraction of a penny. Ans. 490 79. Reduce of a guinea to the fraction of a penny. Ans.490 80. Reduce 9 of a lb. avoir. to the fraction of a Cwt. 81. Reduce to of a Cwt. to the fraction of a pound.

Ans. 82. Reduce 11 of a week to the fraction of an hour.

Ans. 1116 83. Reduce [ of a nail to the fraction of a yard. Answer, 177 84. Reduce is of a mile to the fraction of a foot.

Ans. 2200 85. Reduce iz of a pint of wine to the fraction of a hhd. 86. Reduce ii of a pound to the fraction of a farthing. Ans. 5230

Ans. z 2

1

Ans. To

ADDITION OF VULGAR FRACTIONS.

Example.
Add it, it, and i together.

3+5+2=10 Answer, li

RULES. 1. When the fractions have a common denominator, add the numerators together, and place the common denominator under their sum.

Example. Add 4, t, and $ together. 3x6x9=162

New 5 X 4 X 9=180

numerators. 8 X 4x6 =192

2. When the fractions have not a common denominator, reduce them to one, by Case 7th, and add the numerators together, as before.

534 Total. 4X6X9=216 Com. denom. 6)}=$6=217 Answer.

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