10. Required the sum of 5x+

11. It is required to find the sum of 5x,

a+2x

4x

CASE VII.

To subtract one fractional quantity from another.

RULE.

Reduce the fractions to a common denominator, if necessary, as in addition; then subtract the less numerator from the greater, and under the difference write the commou denominator, and it will give the difference of the fractions required.

CASE VIII.

To multiply fractional quantities together,

RULE.

Multiply the numerators together for a new numerator, and the denominators for a new denominator; and the former of these, being placed over the latter, will give the product of the fractions, as required (k).

EXAMPLES.

1. It is required to find the product of and
6

2x

9°

the product required.

9. It is required to find the continued product of

X a+x

3. It is required to find the product of- and

(k) When the numerator of one of the fractions to be multiplied, and the denominator of the other, can be divided by some quantity which is common to each of them, the quotients may be used instead of the fractions themselves.

Also, when a fraction is to be multiplied by an integer, it is the same thing whether the numerator be multiplied by it, or the denominator divided by it. Or if an integer is to be multiplied by a fraction, or a fraction by an integer, the integer may be considered as having unity for its denominator, and the two be ther multiplied together as usual.

E

2x

6. It is required to find the continued product of

3

7. It is required to find the continued product of 2x 3ab

α

3a

and

5ac
26

8. It is required to find the product of 2a+

b

ax

9. It is required to find the continued product x+1 x-1

and

2α

a+b

bx

and

α

3x,

10. It is required to find the continued product of

a+b' axt
ax+x2'
x2

To divide one fractional quantity by another.

RULE.

Multiply the denominator of the divisor by the numerator of the dividend, for the numerator; and the nume rator of the divisor by the denominator of the dividend, for the denominator. Or, which is more convenient in practice, multiply the dividend by the reciprocal of

the divisor, and the product will be the quotient re

quired. (?)

(1) When a fraction is to be divided by an integer, it is the same thing whether the numerator be divided by it, or the denominator multiplied by it

Also, when the two numerators, or the two denominators, can be divided by some common quantity, that quantity may be thrown out of each, and the quotients used instead of the frac tions first proposed.