How to Multiply Fractions Step by Step

3 Steps – How to Multiply Fractions

How to Multiply Fractions

Multiply fractions can discuss under three main categories.

  1. Multiplication of proper fractions 
  2. Multiplication of improper fractions
  3. Multiplication of a mixed numbers

Multiplication of Proper Fractions

A proper fraction is a fraction that is less than one, with the numerator less than the denominator.

Example :

hmf 1

To multiply proper fractions you have to follow only three simple steps

Step 1 – Multiply the numerators
Step 2 – Multiply the denominators
Step 3 – Simply the fraction to it’s the simplest form (You have to follow this step, only when we have common factors for the numerator and denominator. Otherwise keep it as it is. )

Now let’s discuss a few simple examples

Example 01 :

hmf2

Now let’s solve this one by following the above three simple steps.

Step 01 and Step 02  ( if it is difficult for you to multiply you can use a multiplication table )

How to Multiply Fractions Step by Step3

Step 03 –

By following step 01 and step 02 we got our answer as

hmf4

In step 03, we have to simplify the fraction. But in the above answer, we can see that there are no common factors (a number which divides both 2 and 15).

So the final answer will be,

hmf4

Example 02 :

hmf5

Step 01 and Step 02

how to multiply fractions 6
Step 03

Now we got

hmf7

as our answer. We can see that both 15 and 24 can 

be divided by 3 (3 is the common factor)
How to Multiply Fractions Step by Step 8

The final answer will be,

hmf9

Example 03 :

hmf10

Step 01 and Step 02

How to Multiply Fractions Step by Step 11

Step 03

For this numerator and denominator, we have several common factors such as 2,3 and 6.

out of those factors you have to select the greatest common factor (and also called as the Highest Common Factor – HCF)

How to Multiply Fractions Step by Step 12

So the final answer will be

hmf13

Think that you cannot find the greatest common factor,
which is 6 in the above example. Don’t get confused. You can continue to simplify the fraction with any common factor that you remember.

Let’s think that you could only find 2 as a common factor. Just continue with 2.

How to Multiply Fractions Step by Step 14

In our new fraction which is

hmf15

again, we can see that 3 is a common factor.

hmf16

Now you will get the same answer. These are equivalent fractions.

hmf17

Multiplication of Improper Fractions

An Improper Fraction is a fraction in which the numerator is greater than the denominator

Example:

hmf18

To multiply improper fractions you have to follow only three simple steps

Step 1 – Multiply the numerators
Step 2 – Multiply the denominators
Step 3 – Convert the improper fraction into a mixed number

Now let’s discuss a few simple examples

Example 1 :

hmf19

Step 01 and Step 02

How to Multiply Fractions Step by Step 20

Step 03

We cannot keep the answer as an improper fraction, so we have to convert it into a mixed number. There are several methods to do the conversion.

Let me explain an easy method for you.

In this method, You have to use the long division. Divide the numerator by denominator.

hmf21
hmf22

So the final answer is

hmf23

Example 02 :

hmf24

Step 01 and Step 02

How to Multiply Fractions Step by Step 25

Step 03

Divide 63 by 12, Then the quotient is 5 and the remainder is 3.

The answer is

How to Multiply Fractions Step by Step26

Multiplication of a Mixed Numbers

A number which is the sum of a whole number and a proper fraction written in this manner defined as Mixed Numbers

Examples :

mixed numbers examples (2)

To multiply mixed numbers you have to follow four simple steps

Step 1 – Convert the mixed number into improper fraction
Step 2 – Multiply the numerators
Step 3 – Multiply the denominators
Step 4 – Express the answer as a mixed number

Example 01 :

Multiplication of a Mixed Numbers​ 1

Step 01  

Write each mixed number as an improper fraction.

mixed numbers examples 3

Step 02 and Step 03

Multiply numerator by numerator and denominator by denominator

mixed numbers examples 5

Step 04

Convert the improper fraction to mixed number

mixed numbers examples 6

Example 02 :

You can remove the common factors as follows.

Multiplication of a Mixed Numbers​ 2

Example 03 :

Multiplication of a Mixed Numbers​ 3

2 thoughts on “3 Steps – How to Multiply Fractions”

  1. Pingback: Learn Calculating Perimeter of Circle with Equations | Math Tutor

Leave a Comment

Your email address will not be published. Required fields are marked *