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179

5 Reduce 1 to a simple fraction.

6 Reduce to a simple fraction.

ADDITION OF VULGAR FRACTIONS.
RULE.

facit

Reduce, the given fractions (if necessary) to simple fractions, and to a common denominator (omitting integers :) Place the sum of the numerators over the common denominator; then to the value of said fractions add the integers (if any.)

If fractions be of different integers, find their values separately, and add as in compound addition.

EXAMPLES.

1 Add and together.
1+3=8+14=23-13. facit.

9

2 Add and together.
3 Add 19,7 and of together.
4 Add off and of 12 together.
5 Add of 95, and 3 of 14 together.
6 Add, and 174 together.

7 Add 121, 33, and 42 together.

20

8 Add 6,of, of, and 7 together. 9 Add 3,, of, and 9, together. 10 Add of a penny to of a pound. 11 Add of a pound to of a shilling. 12 Add of a lb. Troy to 1 of an oz..

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21 Add of 12L. +43L. +‡ of shilling into one sum.

facit 8hr. 30min. of an hour togefacit 2da. 14hr. and of a mile togefacit 1540yd. 2ft. 9in. of a shilling, and of answer 3s 1d. 110qr. 34L. of of of a L. answer 71 17s 5d. 04qr. of a L. +3 of 5 of a facit 91 88 8d. 03 qr.

12

22. If a merchant owns of a ship, valued at 15007. and buys another person's share of her, which is

belongs to him, and what is it worth?

what part

answer, worth 1031/ 5s.

SUBTRACTION OF VULGAR FRACTIONS.

RULE.

Prepare the fractions as in addition, and subtract the lower numerator from the upper, placing the difference over the common denominator.

If the lower numerator be the greater, subtract it from the common denominator, adding in the upper numerator, and carry 1 to the units place of the integer.

If fractions be of different integers, find their values separately, and subtract as in compound subtraction.

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8 From 141 take of 19.

10 From

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9 From of a L. take of a shilling.
of a shilling, take of a penny.
of an oz. troy, take of a dwt.
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11 From

12 From of an C.wt. take of a lb.

13 From of a league, take

14 From 1 ell English, take

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facit 11dwt. 3gr.

facit 1gr. 27lb. 6oz. 103dr.
of a mile.
facit 1M. 2fur. 16pls.

of a quarter.

15 From 7 weeks, take 97 days.

facit lyd. Ina.

facit 5w. 4da. 7hr. 12min. 16 From 4 days, 74hours, take 1 day, 9 hours.

facit 2da. 224hr.

17 Borrowed 53L. paid 4 of 43L. what remains?

answer 41 3s 8d. 14gr.

of of

answer 10s. 7d. 11gr.

3

18 What is the difference between of a L. and a shilling ? 19 Take of a shilling from 4 of 51 L. and what is left? answer 11. 8s. 11d.3 20 If a merchant own of a ship, valued at 9001. and sell of his share; what part has he left, and what is it worth? answer, worth 1877 10s.

MULTIPLICATION OF VULGAR FRACTIONS.
RULE.

If a compound fraction, or mixt number, be given, reduce them to single, or improper fractions; multiply the numerators together for a new numerator, and the denominators for a new denominator.

1 Multiply by

2 Multiply by 7.

EXAMPLES.

facit.

facit 3 Multiply

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9 16

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5 Multiply 4 by 6 Multiply by 13. 7 Multiply of 7 by 3. 8 Multiply of 8 by of 5. 9 Multiply by of 11. 10 Multiply of 91 by 711. 11 Multiply 12 by 4 of 7. 12 Multiply 7 by 94.

13 What is the product of of, and § of 32?

14 What is the product of 5 X3, X4, of 2×41 P

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15 What is the continued product of 3, 34, 5, and 3 of

3

answer 47

16 If 3 be multiplied by, and this product again by of, what is the last product?

33

answer fo

DIVISION OF VULGAR FRACTIONS.

RULE.

Prepare the fractions, if necessary, as in multiplication : multiply the denominator of the divisor into the numerator of the dividend for a numerator; and the numerator of. the divisor into the denominator of the dividend for a denominator.

1 Divide 17 by 3.

85

EXAMPLES.

=

3)(8132 facit., Or thus, 17÷388-173.

2 Divide 13 by

8

3 Divide by To
4 Divide 1 by 410
5 Divide 7 by 4.
6 Divide 4 by 7.

7 Divide of 19 by of 3. 8 Divide of by 4 of 4. 9 Divide of by of. 10 Divide 4 by

of 4.

facit 117

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11

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11 Divide

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12 Divide

of 6 by 3 of 4 of 11.

13 What is the quotient of 7 divided by 94?

facit 20 819

answer

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Prepare the given terms, if necessary, by reduction, and state them as in whole numbers; multiply the second and third terms together, and divide that product by the first; Or,

Invert the dividing term, and multiply the three together for the fractional answer.

Note. When the dividing term is inverted, the note to case 5 in reduction is applicable here.

EXAMPLES.

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1 If of a yard cost of a L. what cost yards?

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: 195-1-38 4d. answer.

630

3 1

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L.-3s 4d.

2×2

2 If 1lb. of sugar costs. what cost 33lb. ?

3 If of an ell English cost

4 When 20%. of silver cost

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answer 4d. 3gr. 1983 L. what is that per ell? answer 18s 10d. 2 16s. what is the value of answer 6s 1d 3qr.1⁄2

5 If 6 yards cost 18s. what buys 9 yards?

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6 Sold 500 bushels of wheat, at 563d. per bu. what sum passes to the credit of that article ?

answer 1171 18s 4d.

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