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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,How to Multiply FractionsandHow to Multiply Fractionsare two fractions and we want to multiply together, then:

How to Multiply Fractions

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

How to Multiply Fractions

Let's see some examples.

How to Multiply Fractions

Now we see that the numerator and denominator are divisible by 2. So, we will simplify the fractionHow to Multiply Fractions. On simplifying, we getHow to Multiply Fractions.

Hence, the multiplication ofHow to Multiply FractionsandHow to Multiply FractionsisHow to Multiply Fractions.

Multiplication of Mixed Fractions

A mixed fraction is a fraction that is in the form of How to Multiply Fractions. 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.
    How to Multiply Fractions

In general, we can say that:

How to Multiply Fractions

Example: Find the product of How to Multiply Fractions and How to Multiply Fractions.

Solution:

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

How to Multiply Fractions

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

How to Multiply Fractions

On dividing the fractionHow to Multiply Fractionsby 8 we get the mixed fractionHow to Multiply Fractions. We see that the fractionHow to Multiply Fractionsis also divisible by 2. So, we will more simplify it and getHow to Multiply FractionsorHow to Multiply Fractions.

How to Multiply Fractions

Multiplication of Whole Number and Fraction

Example: Multiply the fraction How to Multiply Fractions by 9.

Solution:

How to Multiply Fractions

Hence, the multiplication of How to Multiply Fractions and 9 is How to Multiply Fractions.

Example: Multiply 26 byHow to Multiply Fractions.

Solution:

How to Multiply Fractions

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 andHow to Multiply Fractionsis 28.

Multiplication of More Than Two Fractions

How to Multiply Fractions

Let's see some other examples.

How to Multiply Fractions
How to Multiply Fractions

Another way to find the multiplication is:

How to Multiply Fractions

Hence, the multiplication is How to Multiply Fractions.






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