To reduce a fraction to its lowest terms.

RULE.

Divide the numerator and denominator by their greatest common measure, and it is evident that the quotients will form the lowest terms of the given fraction.

i

RULE.

If the fractions to be added have a common denominator, add their numerators together, as in Arithmetic, placing the common denominator under the numerator; the fraction thus found will be the required one. If the fractions to be added have not all the same denominator, reduce them to such, and proceed as above.

1.-Add together+. Having reduced them to

Ans...d(36+2)x + ax(4b+3)+ad(5b + 4)

d

Reduce, as in Addition, and subtract instead of add;

the result will be the difference.

Multiply the numerators together for a new numerator, and the denominators together for a new denominator; but if the numerator of one, and denominator of the other, can be divided by a quantity common to both, the results can be used, as their values are not changed.

DIVISION OF FRACTIONS.

RULE.

Divide the numerator of one by the numerator of the other, and the denominator of one by the denominator of the other, the result is the quotient; but if they are not divisible by each other, invert the divisor, and proceed as in Multiplication.

Or by dividing the numerators and denominators by 14x2 2.x 7x

each other, by = for the Answer.

3

9

3

INVOLUTION.

RULE.

This being only the multiplication of any given quantity continually by itself, to any required power, the operation will be manifest by an Example.

Required the second power of a + b, and the third and fourth power of the same.

a3+3a2b+3ab2 + 63 Third power required.

a+b

a4+3a3b+3a2b2 + ab3

a3b + 3a2b2 + 3ab3 + b4

aa + 4a3ò + 6a2b2 + 4ab3 + b4 Fourth power.