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2. Add and together.

3. Add

and together.

4. Add 124 s3 and 4 together.

5. Add of 95 and 7 of 14 together.

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NOTE 1. In adding mixed numbers that are not compounded with other fractions, you may first find the sum of the fractions, to which add the whole numbers of the given mixed numbers.

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6. Find the sum of 53 74 and 15.
I find the sum of and to be 31
Then 1+5+7+15=2811 Ans.
Ans. 17

7. Add and 17 together.

8. Add 25, 81 and 1 of 3 of

Ans. SS

NOTE 2.-To add fractions of money, weight, &c. reduce fractions of different integers to those of the same.

Or, if you please you may find the value of each fraction by Case VIII. in reduction, and then add them in their proper termis.

9. Add of a shilling to of a pound.

4

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SUBTRACTION OF VULGAR FRACTIONS.

RULE.*

PREPARE the fractions as in Addition, and the difference of the numerators written above the common denominator, will give the difference of the fraction required.

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11 42 31 708

13

4. From 14 take #

5. What is the difference of and 47 ?

6. What differs

from P

7. From 14 take of 19

8. From

take

O remains.

9. From of a pound, take of a shilling.

off. Then from 1. take o£. Ans. 1£. NOTE. In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper terms.

10. From take 37 shilling. Ans. 5s. 6d. 24grs. 11. From of an oz. take of a pwt.

Ans. 11pwt. 3gr. 12. From of a cwt. take of a lb.

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Ans. 1gr. 27lb. 6oz. 10 dr. 13. From 33 weeks, take of a day, and of of of an hour. Ans. Sw. 4da. 12ho. 19min. 174sec

*In subtracting mixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them to improper fractions, subtract the numerator of the lower fraction from the common denominator, and to that difference add the upper numerator, carrying one to the unit's place of the lower whole number.

Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denomina tor, and placing the remainder over the denominator, then taking one from the whole number.

MULTIPLICATION OF VULGAR FRACTIONS.

RULE.

REDUCE whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.

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8. Multiply of by

of S4

9. What is the continued product of of, 7, 5 and

of P

Ans. 4

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.

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RULE OF THREE DIRECT IN VULGAR
FRACTIONS.

RULE.

PREPARE the fractions as before, then state your question agreeable to the Rules already laid down in the Rule of Three in whole numbers, and invert the first term in the proportion; then multiply all the three terms continually together, and the product will be the answer, in the same name with the second or middle term.

EXAMPLES.

1. If of a yard cost of a pound, what will of an Ell English cost?

{yd.={ of 4 of 20 or Ell English.

Ell. £. Ell.

:

As And ×× 2. If of a yard cost

come to ?

of a

54

s. d. grs.

=.=10 3 15 Ans. pound, what will 40 yds. Ans. £59 8s. 6d. 3. If 50 bushels of wheat cost 173l. what is it per bushAns. 7s. Od. 123qrs. 4. If a pistareen be worth 143 pence, what are 100 pistareens worth?

el ?

to

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Ans. £6 5. A merchant sold 54 pieces of cloth, each containing 24 yds. at 9s. d. per yard; what did the whole amount Ans. £60 10s. Od. 33qrs. 6. A person having of a vessel, sells of his share for 3121.; what is the whole vessel worth? Ans. £780 7. If of a ship be worth of her cargo, valued at 8700l. what is the whole ship and cargo worth?

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Ans. £10031 14s. 11d.

INVERSE PROPORTION.

RULE.

PREPARE the fractions and state the question as before, then invert the third term, and multiply all the three terms together, the product will be the answer.

EXAMPLES.

1. How much shalloon that is yard wide, will line 53 yards of cloth which is 14 yard wide ?

Fds. yds. yds.

Yds.

As 14:51: And xx-1=16, Ans. 2. If a man perform a journey in 3 days, when the day is 12 hours long; in how many days will he do it when the day is but 9 hours. 44 Ans. 4 days.

Ans. 183 days.

3. If 13 men in 114days, mow 21 acres, in how many days will 8 men do the same. 4. How much in length that is 73 inches broad, will make a square foot?

5. If 25 s. will pay for the miles; how far may 6 cwt. be ney?

6. How many yards of baize will line 187 yards of camblet

Ans. 20 inches. carriage of an cwt. 1451 carried for the same mo

Ans. 22 miles. which is 14 yards wide, yd. wide ?

Ans. 11yds. 1gr. 1f na.

RULE OF THREE DIRECT IN DECIMALS.

RULE.

REDUCE your fractions to decimals, and state your question as in whole numbers; multiply the second and third together; divide by the first, and the quotient will be the answer, &c.

come to ?

Yds.

EXAMPLES.

Yds.

1. If of a yd. cost of a pound; what will 15 yds. 1,875,583+and =,75 s. d. grs. As ,875 :,583 :: 15,75: 10,494-10 9 10 2.24 Ans. 2. If 1 pint of wine cost 1,2s. what cost 12,5 hhds. ? Ans. £.378 3. If 44yds. cost 3s. 44d. what wili 30 yds. cost Ans. £.1 44 4d Pars

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