PROBLEM 1.

To find the greatest common measure of the terms of a fraction.

RULE.

1. Range the quantities according to the dimensions of some letter, as is shewn in division.

2. Divide the greater term by the less, and the last division by the last remainder, and so on till nothing remain ; then the divisor last used will be the common measure required.

NOTE. All the letters or figures, which are common to each term of any divisor, must be rejected before such divisor is used in the operation.

Therefore the greatest common measure is c+x.

Therefore x+b is the greatest common measure.

3. To

1. Find the greatest common measure, as in the last problem.

2. Divide both the terms of the fraction by the com mon measure thus found, and it will be reduced to its lowest terms.

To reduce a mixed quantity to an improper fraction.

RULE.

Multiply the integer by the denominator of the fraction, and to the product add the numerator; then the denomi

nator being placed under this sum will give the improper fraction required.

To reduce an improper fraction to a whole or mixed quantity.

RULE.

Divide the numerator by the denominator for the inte gral part; and place the remainder, if any, over the de

nominator

nominator for the fractional part; the two joined together will be the mixed quantity required.

EXAMPLES.

1. To reduce to a mixed quantity.

=175=33 the answer required.