Multiplication of fractions | Economipedia

The multiplication of fractions is a mathematical operation in which the product of the numerators and denominators is done separately and has no limit of fractions involved.

In other words, fraction multiplication is multiplying the numerators and denominators of the fractions separately and recording the result as a new fraction.

Fraction multiplication looks like this:

Fraction multiplication
Fraction multiplication

We say that the multiplication of fractions has no limit of fractions involved, since we can multiply as many fractions as we want at the same time.

Fraction Multiplication Procedure

We can understand the multiplication of fractions as a sequential process. That is, first we will do one step and then another.

The first step will be to multiply the numerators of the fractions and record the result in a new fraction. The second step will be to multiply the denominators of the fractions and record the result in the new fraction. Schematically:

  1. Write an empty fraction at the end of the multiplication. In this fraction we will write the result of multiplying the numerators and also the result of multiplying the denominators.
  2. Multiply the numerators each other and write the result in the numerator of the resulting fraction.
  3. Multiply the denominators each other and write the result in the denominator of the resulting fraction.

First step: write the resulting fraction

The resulting fraction must come after the equal and must be empty. In this way, we can fill it in once we know the result of multiplying the numerators and denominators separately.

Result fraction
Result fraction

Second step: multiply the numerators

In this step we have to multiply the numerators as if it were a simple multiplication and write the result in the result fraction.

Multiply the numerators
Multiply the numerators

Third step: multiply the denominators

In this step we have to multiply the denominators as if it were a simple multiplication and write the result in the result fraction.

Multiply the denominators
Multiply the denominators

We can see that with the third step we have managed to multiply two fractions without problem and correctly. In the event that there were more fractions, the procedure would be the same. If the letters were numbers it would be like this:

Fraction multiplication
Fraction multiplication

Fraction Multiplication Example

Multiply the following fractions:

Example
Example

The first two multiplications in the example seem to look different, yet give the same result.

Actually these two multiplications are the same since in the second multiplication, the fraction in which the number 7 has no denominator, actually has a denominator of 1. So, both the first and the second multiplication are the same but written in different way:

Fraction multiplication
Fraction multiplication
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