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you would reduce it to ; then multiply all the numerators one into another for a

new numerator, and ail the denominators into each other for a new denominator, and you have the fraction required.

EXAMPLES.

1. Reduce of a penny to the fraction of a pound. By comparing we find it to be of is of is.

X1 Xa=i=io Answer.

2. Reduce of a farthing to the fraction of a pound.

X 1 X 's X zo=şdir=12'5o Answer.
See the work at large.
3 X 1 X 1 4 X 4 X 12 X 20

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3. Reduce of a penny to the fraction of a guinea.

Answer, 1067 4. Reduce of an ounce to the fraction of a Cwt.

Answer, 781

5. Reduce of a pennyweight to the fraction of a

ton,

IX. To find the value of any vulgar fraction in the

known parts of the integer.

RULL. Multiply the numerator of the fraction given, by the known parts of the next inferior denomination ; which product divided by the denominator, quotes the parts of that denomination sought ; the remainder, if any, multiplied by the parts of the next inferior des nomination, and divided as before, gives the parts of the next denomination ; and thus proceed till you have brought it into the least known parts, or titl nothing remains.

EXAMPLES.
1. What is the value of 135 of a pound ?

133 numerator.
20 shillings in a pound.

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Answer, 58. 6d. 29. 2 What is the value of of a mile ?

Answer, ofur. 26p. 11ft.

ADDITION OF VULGAR FRACTIONS.

RULE. IN Addition of Vulgar Fractions, you must first reduce compound fractions to simple ones, mixed numbers to improper fractions, fractions of different integers to those of the same, and all of them to a çommon denominator ; then write the sum of the numerators over the common denominator, which will be the sum of the fractions required.

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EXAMPLES, 1. Add 7 and 5 together.

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RULE. THE fractions must be prepared as in addition ; and the difference of the numerators,placed above the common denominator, will give the difference required,

EXAMPLES.
1. What is the difference between and ?

Answer, 4. Note- In the above question, the denominators being alike, the work was done by subtracting the less numerator from the greater

2. What is the difference between is and ?

2 X 9=18 numerator, 13 X 5=65 numerator.

13 X 9=117 for a common denominator.. Hence the fractions are 11 fif; then take the less numerator from the greater. from 65

take 18

47 remains, which placed above the common denominator thus 117, is the difference required. 3. What is the difference between 7 and ?

Answer, 6. 4. From 13 take 11 ?

Answer, 17.

MULTIPLICATION OF VULGAR FRACTIONS.

RULE. IN multiplication of fractions, reduce mixed num. bers to improper fractions, whole numbers, like fractions and compound fractions, to simple ones, abbreviating if occasion requires ; then multiply the nume rators together for a new numerator, and the denomiziators for a new denominator ; which numerator and denominator is the product sought.

EXAMPLE.

Multiply is by ?

1 X =iit, Answer.

DIVISION OF VULGAR FRACTIONS.

RULE. PREPARE the fractions as in multiplication ; then anultiply the denominator of the divisor by the numerator of the dividend, for the numerator of the quou

tient; and the numerator of the divisor by the denom. inator of the dividend, for the denominator of the quotient; and your work is done ; or invert the divisor, and proceed as in multiplication.

EXAMPLE. Divide , i by ?

new numerator.
13) 4761:)

new denominator.
then 4)::(=13) 117( Answer, required.

Questions to exercise fractions.

1. If the difference of two numbers be 21 75-97, the less 17 3-7, what is the greater?

Answer, 39 137-679. 2. There is in three chests 56 3-5lbs. ; in the first 12 5-8lbs. in the second 21 7-12168. ; what is in the third chest?

Answer, 22 47-120. 3. What number multiplied by 3-7, will produce 11 9-17 ?

Answer, 26 46-610

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