How to Multiply Fractions

In arithmetic, multiplication is the product of two or more numbers or fractions. In this section, we will learn how to multiply fractions.

How to Multiply Fractions

To find the multiplication or product of two or more fractions, we must follow the steps given below:

Step 1: Multiply the numerators of the fractions to get the numerator.

Step 2: Multiply the denominators of the fractions to get the denominator.

Step 3: Simplify the fraction, if required.

Note: To simplify the fraction always use the same number to divide numerator and denominator.

Suppose,andare two fractions and we want to multiply together, then:

In short, we can say that multiplication of fractions is:

Let's see some examples.

Now we see that the numerator and denominator are divisible by 2. So, we will simplify the fraction. On simplifying, we get.

Hence, the multiplication ofandis.

Multiplication of Mixed Fractions

A mixed fraction is a fraction that is in the form of . While dealing with mixed fractions, first convert the mixed fraction into the improper fraction and then apply the above steps. To convert the mixed fraction into an improper fraction, follow the steps:

• Multiply the whole number (a) by the denominator (c). We get (a×c) as a result.
• In the above result (a×c) add the numerator (b). After adding the numerator, we get the numerator of the improper fraction.
• The denominator of the improper fraction will be the denominator of the mixed fraction.
  

In general, we can say that:

Example: Find the product of and .

Solution:

First, we will convert the mixed fraction into the improper fraction.

We can simplify the fraction before multiplication or simply the fraction at last. In this example, we will simplify the fraction at last.

On dividing the fractionby 8 we get the mixed fraction. We see that the fractionis also divisible by 2. So, we will more simplify it and getor.

Multiplication of Whole Number and Fraction

Example: Multiply the fraction by 9.

Solution:

Hence, the multiplication of and 9 is .

Example: Multiply 26 by.

Solution:

Or first, divide 26 by 13. It gives 2 as the result and multiply it by the numerator, we get:
2×14=28

Hence, the multiplication of 26 andis 28.

Multiplication of More Than Two Fractions

Let's see some other examples.

Another way to find the multiplication is:

Hence, the multiplication is .