EXAMPLES.

1. Reduce of of of to a simple fraction.

2. Reduce 42 of 3 of 8% of 23 to a simple fraction.

Rule-1. Reduce mixed numbers, if there be any, to improper fractions. 2. Form a fraction, whose numerator is the product of all the numerators, and denominator the product of all the denominators; at first indicating only the multiplication by the proper sign.

3. Cancel all factors common to numerator and denominator.

4. Multiply together all the remaining factors, the resulting fraction is the product required.

II. TO MULTIPLY A SIMPLE OR COMPOUND FRACTIONAL EXPRESSION BY

A SIMPLE FRACTION, OR BY ANOTHER COMPOUND EXPRESSION.

Rule. Reduce each expression to a simple fraction, and then perform the multiplication.

2. Simplify the expression (63 - 37 + § ) × (3,1% −2+28.)

1. TO DIVIDE ONE FRACTION BY ANOTHER.

Rule-1. Reduce mixed numbers, if any, to improper fractions. 2. Invert the divisor, and multiply the dividend by the inverted fraction.

II. TO DIVIDE A SIMPLE OR COMPOUND FRACTIONAL EXPRESSION BY A SIMPLE FRACTION, OR BY A COMPOUND EXPRESSION.

Rule. Reduce each expression to a simple fraction, and then perform the division.

I.-Reduction of Complex Fractions.

Rule-1. When numerator and denominator are simple or compound fractions, divide numerator by denominator.

2. When numerator and denominator are, one or both, fractional expressions composed by terms, multiply each term in both by the L. C. M. of the denominators of all the simple fractions, and reduce the result by performing the operations indicated.

The terms of the numerator and denominator must be put into the form of simple fractions, or whole numbers, before applying this rule.

3. If the expressions be composed by factors, reduce each to a simple fraction, and perform the operations indicated.