6.3 Multiplying Fractions

Part (d) of the activity on the previous page does not give a surprising result, mathematically speaking. One-third of one-half is indeed one-sixth. To convince yourself, take a piece of notebook paper. Fold it in half along the long side and shade one half of the paper. Then, fold it into thirds along the short side. The paper is now split into six equal pieces, or sixths. If you look at the shaded half, you can see that one out of three parts of this portion represents one out of six parts of the entire paper as shown below.

Mathematically, this is written as equation left hand side one divided by three multiplication one divided by two equals right hand side one divided by six.

To multiply two fractions together, you must multiply the numerators together, then multiply the denominators together, and reduce the answer if necessary.

It is often easier to reduce before multiplying out. For example, let’s consider two divided by three multiplication one divided by two.

Multiplying the numerators together, then multiplying the denominators together gives equation left hand side two divided by three multiplication one divided by two equals right hand side two multiplication one divided by three multiplication two, but we can cancel out the 2s using division: equation sequence two super one multiplication one divided by three multiplication two sub one equals one multiplication one divided by three multiplication one equals one divided by three.

This calculation is equivalent to canceling at the start of the calculation: equation sequence two super one divided by three multiplication one divided by two sub one equals one multiplication one divided by three multiplication one equals one divided by three

The next page summarizes this procedure, followed by an exploration to help you learn how to use your calculator to aid in the multiplication of fractions.

6.2.5 Activity: Young People and Debt

6.3.1 Multiplying Mixed Numbers and Fractions