How to Multiply Fractions

Among the four fundamental operations on fractions, multiplication is the easiest. It is just simple. Multiply the numerator and then the denominator. Of course, if the given fractions can be converted to lowest terms, the easier the multiplication will be.

In this post, we are going to learn how to multiply fractions. You must master this operation, as well as other fundamental operations on fractions because you will use them in higher mathematics and solving word problems. Below are some examples.

Example 1

\displaystyle \frac{4}{5} \times \frac{1}{3}

Solution

\displaystyle \frac{4}{5} \times \frac{1}{3} = \frac{4 \times 1}{ 5 \times 3} = \frac{4}{15}.

Answer: \displaystyle \frac{4}{15}.

Example 2

\displaystyle \frac{2}{3} \times \frac{5}{6}

Solution

\displaystyle \frac{2}{3} \times \frac{5}{6} = \frac{10}{18}

We reduce the fraction to lowest term by dividing both the numerator and the denominator by 2. This results to $latex \frac{5}{9} which is the final answer.

Answer: \displaystyle \frac{5}{9}

Example 3

\displaystyle \frac{12}{15} \times \frac{2}{3}

Solution

First, we reduce \frac{12}{15} by dividing both the numerator and the denominator by 3. This results to \frac{4}{5}. We now multiply:

\displaystyle \frac{4}{5} \times \frac{2}{3} = \frac{8}{15}.

Answer: \displaystyle \frac{8}{45}.

Example 4

\displaystyle 3 \frac{1}{2} \times \frac{1}{4}

Solution

In this example, we need to convert the mixed fraction into improper fraction. To do this, we multiply the denominator of the mixed fraction to the whole number and the product to the denominator. That is

\displaystyle \frac{2 \times 3 + 1}{2} = \frac{7}{2}.

Now, let us multiply the two fractions.

\displaystyle \frac{7}{2} \times \frac{1}{4} = \frac{7}{8}

Answer: \displaystyle \frac{7}{8}

Now, test your knowledge on multiplication of fractions by answering the Practice Exercises and then read the Answer Key with solution after.

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