fractions of different denominations to fractions of the fame denomination. Then reduce all the fractions to fractions of the fame common denominator. Add all the numerators together, and place the fum over the common denominator; and this fraction will be equal to the fum of all the given fractions.

The total thas found, if it be an improper fraction, may be reduced to a whole or mixed number.

Example 1. Add †, †, and together.

Then 3 is equal to 7, and of is equal to or $5. Then the given fractions will be 7, 7, 25.

In this example, as in the former, I firft (after having reduced the mixed number 3 and the compound fraction of to fimple fractions) reduce all the fractions to a common denominator, by multiplying the numerator of each into all

the

the denominators except its own, for a numerator to each fraction, and all the denominators into each other for a common denominator, as taught in reduction of fractions; the numerators of these newly-discovered fractions are then added together, and their fum 3455 placed over the common denominator 875 is the answer or fraction equal to the fum of all the given fractions, which, divided by 5, gives 9, and reduced to a mixed number is 3198.

The proof of addition of fractions is wrought by finding the value of each of the given fractions, and adding them together, and then finding the value of the whole fraction or fum of the fractions, and if these two values be equal the work is right.

Qu. 3. What is the fum of of a pound and 4 of a hilling?-Anf. 73% of a pound.

In this example the fraction of a filling must be reduced to the fraction of a pound before the work can be wrought, as before directed.

Qu. 4. What is the fum of,, and of ?—Answer 276.

Qu. 5. What is the fum of of a week, of a day, and an hour?-Anf. 2 days 14 hours.

Subtraction of Vulgar Fractions.

Rule. Reduce the fractions in the fame manner as for addition; then the lefs numerator is to be fubtracted from the greater, and the difference placed over the common denominator will form the fraction required.

Example 1. Subtract 3 from 4.

Proof. Add the less number and the remainder together,

as in whole numbers.

Example 2. Subtract from of 3.

24

ofis or 14, therefore I can take from.

2

7

9

24 equal to 3.

Qu. 3. What is the difference between and 28?-Anf

27.10.

Qu. 4. What is the difference between 263 and 54%?Anf. 2811.

Qu. 5. What is the difference between 14 and of 19 Anf. :75.

Multiplication of Vulgar Fractions.

Rule. Reduce whole and mixed numbers, compound fractions, and fractions of different denominations, to fimple fractions of the fame denomination; then multiply all the numerators together for a new minerator, and all the denominators together for a new denominator, and fuch fraction will be the true product required.

Example 2. What is the product of 2 multiplied by &,

In this example 24 is to be reduced to its equivalent frac . tion, and of must be reduced to its fimple fraction, or, then the queftion will be, what is the product of ,, and multiplied together?

What is the product of of, by of

Qu. 3. Anf.or.

16.

Qu. 4.

Qu. 5.

What is the product of 24 by ?—Anf. *3 or

What is the product of of 7 by-Anf. 1. 2. 6. What is the product of 36 by?—Anf. 224 or 297T.

Thus it may be feen, that multiplication of vulgar fractions is performed in the fame manner as reducing a compound fraction to a fimple one *.

Divifion of Vulgar Fractions.

Ralc. Prepare all the fractions for divifion in the fame manner as for addition, fubtraction, and multiplication; and învert the two terms of the divifor, placing the denominator at the top and the numerator at the bottom; then pro. ceed exactly the fame as in multiplication, viz. multiply the

If any number be multiplied by a fraction, the product will be lefs than the multiplicand, and in proportion as the multiplier is lefs than an unit.

numerator

numerator of the dividend and that figure that is uppermost in the divifor together for a numerator to the quotient: and multiply the denominator of the dividend and the lower figure of the divifor for the denominator of the quotient. Proof. Multiply the quotient by the divifor, as in whole

numbers.

Example 1. Divide by -)}(1⁄2 or 21⁄2 Answer. 2. Divide of 7 by of 3 4. In this example, of 7 is equal to toor; therefore I fay, divide

3. Divide by 3.-Anf. 16.

4. Divide 10 by 1.—Anf. 40 or 54.

4, and of is equal

by .-Anf. & or 28.

5. Divide 7 by of.-Anf. 405 or 617*.

The Rule of Three direct in Vulgar Fractions.

Rule. Prepare the fractions as for the four foregoing rules; and then having placed the three numbers in their proper order according to their proportion, invert the first term or fraction, tranfpofing the numerator and denominator, as in the foregoing rule; then multiply all the three numerators together for a numerator, and all the denominators together for a denominator, and this fraction will be the answer required. Proof. The fame as in whole numbers.

Example 1. If of an ell English cost of a pound, what will of an ell Flemish cost?

In this example I fay, if of of a yard (which is an ell English) cost of a pound, what will 3 of of a yard (which is an ell Flemish) coft?

I then reduce the compound fraction of to a fimple one, and it is % or 4, and also the fraction of isof 号 a yard, which is of the fame denomination with the firft

If a whole number be divided by a proper fraction, the quotient will be greater than the dividend; but if any fraction be divided by a whole number, the quotient will be less than the dividend.

VOL. I.

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number,