 # Multiplication of a Fraction by Fraction – Definition, Examples | How do you Multiply a Fraction by a Fraction?

Have you stuck at some point while multiplying one fraction with another fraction and need help? Don’t bother as we are with you in this and compiled an article covering the fraction definition, how to multiply a fraction by another fraction, how to multiply two mixed fractions. Refer to the solved examples for multiplying fraction by fraction and try to solve related problems on your own.

## Fraction – Definition

Fractions are the numerical values or things that are divided into parts, then each part will be a fraction of a number. A fraction is denoted as $$\frac { a }{ b }$$, where a is the numerator and b is the denominator.

### Multiplication of a Fraction by Fraction

Multiplication of fraction by fraction starts with the multiplication of the given numerators followed by multiplication of the denominators. Then, the resultant fraction can be simplified further and reduced to its lowest terms if needed. Multiplication of fractions is not the same as addition or subtraction of fractions, where the denominator should be the same. Here any two fractions without the same denominator can also be multiplied.

### How to Multiply Two Fractions?

Follow the simple steps listed below to multiply a fraction by fraction. They are in the below fashion

Step 1: Simplify the fractions into their lowest terms.

Step 2: Multiply both the numerators of the given fractions to get a new numerator.

Step 3: Multiply both the denominators of the given fractions to get a new denominator.

Simplify the resulting fraction if needed.

Let a/b is one fraction and the other fraction is c/d. Multiplication of these fractions are

Multiplying fractions formula:

$$\frac { a }{ b }$$ * $$\frac { c }{ d }$$ = $$\frac { a * b }{ c * d }$$

### Multiplication of Fraction by another Fraction Examples

Example 1:

$$\frac { 1 }{ 3 }$$  is the first fraction. $$\frac { 2 }{ 3 }$$  is another fraction. What is the multiplication of both fractions?

Solution:

It is given that $$\frac { 1 }{ 3 }$$  is one fraction and $$\frac { 2 }{ 3 }$$  is another fraction.

When we multiply both these fractions, we multiply both the numerators and both the denominators.

Product of two fractions = (Product of numerators)/(Product of denominators).

That is (1*2) is the numerator. (3*3) is the denominator.

The final result is the product of numerators and denominators.

Therefore the final answer is $$\frac { 2 }{ 9 }$$  .

Example 2:

$$\frac { 12 }{ 5 }$$  is the first fraction. $$\frac { 23 }{ 9 }$$  is another fraction. What is the multiplication of both fractions?

Solution:

It is given that $$\frac { 12 }{ 5 }$$  is one fraction and $$\frac { 23 }{ 9 }$$  is another fraction.

When we multiply both these fractions, we multiply both the numerators and both the denominators.

Product of two fractions = (Product of the numerators)/(Product of the denominators).

That is (12*23) is the numerator. (5*9) is the denominator.

The final result is the product of numerators and denominators. The value is ($$\frac { 276 }{45 }$$  .

Therefore the final answer is $$\frac { 92 }{15 }$$ ,

Example 3:

$$\frac { 16 }{ 30 }$$  is the first fraction. $$\frac { 21 }{ 50 }$$  is another fraction. What is the multiplication of both fractions?

Solution:

It is given that $$\frac { 16 }{ 30 }$$  is one fraction and $$\frac { 21}{ 50 }$$  is another fraction.

When we multiply both these fractions, we multiply both the numerators and both the denominators.

Product of two fractions = (Product of numerators)/(Product of denominators).

That is (16 * 21) is the numerator. (30*50) is the denominator.

The final result is the product of numerators and denominators.

Therefore the final answer is $$\frac { 336 }{ 1500 }$$  .

### Multiplication of Mixed Fractions

A fraction that is represented by its quotient and remainder is a mixed fraction. So, it is a combination of a whole number and a proper fraction.  Multiplication of mixed fractions will be difficult to change each number into an improper fraction.

### How to Multiply Mixed Fractions?

Go through the below-listed steps to multiply two mixed fractions. They are in the below fashion

Step 1: Convert given mixed fractions into improper fractions.

Step 2:  Simplify the fractions into their lowest terms for easy calculations.

Step 3: Multiply both the numerators of the given fractions to get a new numerator.

Step 4: Multiply both the denominators of the given fractions to get a new denominator.

Simplify the resultant fraction if needed.

### Multiplication of Mixed Fraction by another Mixed Fraction Examples

Example 1:

Multiply mixed fractions 2$$\frac { 3 }{ 5 }$$ and 6 $$\frac { 7 }{ 8 }$$. What is the multiplication of both fractions?

Solution:

It is given that 2$$\frac { 3 }{ 5 }$$ is one fraction and the other fraction is  6$$\frac { 7 }{ 8 }$$

As we know mixed fractions cannot be multiplied. Simplify the given mixed fractions into improper fractions.

Now the given mixed fractions are $$\frac { 13 }{ 5 }$$  and the other fraction is $$\frac { 55 }{ 8 }$$.

When we multiply both these fractions, we multiply both the numerators and both the denominators.

Product of two fractions = (Product of numerators)/(Product of denominators).

That is (13 * 55) is the numerator. (5*8) is the denominator.

The final result is the product of numerators and denominators. The value is $$\frac { 715 }{ 40 }$$

Therefore the final answer is $$\frac { 715 }{ 40 }$$

Example 2:

Multiply mixed fractions 2$$\frac { 1}{ 8 }$$ and 6 $$\frac { 4 }{ 9 }$$. What is the multiplication of both fractions?

Solution:

It is given that 2$$\frac { 1 }{ 8 }$$ is one fraction and the other fraction is  6$$\frac { 4 }{ 9 }$$

As we know mixed fractions cannot be multiplied. Simplify the given mixed fractions into improper fractions.

Now the given mixed fractions are $$\frac { 17 }{ 8 }$$  and the other fraction is $$\frac { 58 }{ 9 }$$.

When we multiply both these fractions, we multiply both the numerators and both the denominators.

Product of two fractions = (Product of numerators)/(Product of denominators).

That is (17 * 58) is the numerator. (8*9) is the denominator.

The final result is the product of numerators and denominators. The value is $$\frac { 986 }{ 72 }$$

Therefore the final answer is $$\frac { 986 }{ 72 }$$.

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