Algebra Tutorials!

 Thursday 20th of July

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# Multiplying Fractions in General

Objective Learn how to multiply fractions.

Multiplying fractions is a little more difficult conceptually than adding fractions, but the arithmetic procedure is much easier. The discussion here will begin with the multiplication of a fraction by a whole number, proceed to the multiplication of two fractions each with numerator of 1, and then finish with the multiplication of any pair of fractions.

What if we want to multiply two fractions that do not have 1 as their numerators? The following procedure can be used to multiply any two fractions.

Key Idea

To multiply two fractions, multiply the numerators together to find the numerator of the product, and multiply the denominators together to find the denominator of the product. Simplify the resulting fraction, if possible.

Example 1

## Why Does This Procedure Work?

We can draw a model. For example, to model the multiplication of and , we start with two line segments of the same length. Divide one segment into 3 equal parts and darken 2 of the parts. Divide the other segment into 5 equal parts and darken 2 of these parts.

The two segments are then used as adjacent sides of a square and the marks are used to divide the square into 15 regions of equal size. The region formed by the two darkened parts of the segments is then shaded.

The shaded portion of the entire square includes 4 of the 15 small regions of equal size. Since each small region represents the fraction , the shaded portion represents the fraction , which is the product of and .