What we had learned before?

A fraction is made up of two parts: the numerator and the denominator. Proper fractions, improper fractions, and mixed fractions are the three main forms of fractions that may be found.

Introduction to fraction multiplication

In the number system, multiplying fractions is just as straightforward as multiplying numbers. A fraction is a mathematical representation of the splitting of a whole number into smaller parts. In the case of fractions multiplied by whole numbers, the result might be either a fraction or a whole number. In contrast, when a variable is multiplied by a constant, the result is a variable quantity. 

Definition of Fractional multiplication or multiplying fractions

Fractional multiplication is a mathematical term that refers to the process of multiplying fractions.

Multiplication of fractions is the same as the multiplication of two given real numbers in the mathematical sense. When multiplying fractions, you may use the straightforward technique. The following is how you may write the fraction multiplication formula:

Product of fraction equals the product of numerator divtopicIded by the product of denominator (or vice versa).

Example of fractional multiplication in variables.

(x/y) x (a/b)

Note: When you are carrying out a fractional multiplication or multiplying fractions, first you have to multiple the numerators, followed by multiplying the denominator.

Fraction Multiplication Types

There are many sorts of fraction multiplication that you should be aware of. Let's take a closer look at some instances of multiplying fractions.

1. Multiplying two fractions or a fraction with another fraction

2. Fraction multiplication with whole numbers

3. Fraction multiplication with variables

I. Multiplying two fractions or multiplying a fraction with another fraction

We'll understand methods to multiply fractions with fractions in this part. The following are the fundamental stages of multiplying fractions:

1. Initially, multiply the numerators, which are the top numbers.

2. The bottom numbers, which are the denominators, are then multiplied.

3. Finally, if necessary, simplify the fraction.

Let us take an example:

(8/3) x (9/4) 

= 8  x  9

-------------- 

    3 x  4

=  72/12

Simplifying further, we get:

72/12 = 6.

II. Fractions and Whole Numbers Multiplication

When a whole number is multiplied by a fraction, the result is the real number multiplied by the fraction added.  A real number can also be multiplied by a fraction. ConstopicIder the following example of fractions multiplied by whole numbers.

What does multiplying a fraction with a whole number mean?

To understand this, we need to constopicIder a numerical example. 

4 x ½ means add ½ four times. Are the answer same? Let’s find out.

½+½+½+½= 1+1+1+1          4

                     ------------  =      --- = 2

                          2                  2

Now, 1

          --  x 4 = 2.

          2

The answer is the same.

Fraction Multiplication with Variables

The outcome of multiplying a fraction with variables is displayed below. Check out the following scenario:

4a     8a        32(a^2)        4(a^2) 

---  x  --   =    ---           = 

2        4         8

Here symbol “^” symbolizes raise to or power of.