# The Equivalent Of Complex Fractions

## What is a Complex Fraction?

A complex fraction is a fraction that contains another fraction in the numerator, denominator, or both. It is also known as a compound fraction. This type of fraction is sometimes difficult to work with and can be confusing. To simplify a complex fraction, it is important to understand what it is and how it is used.

## How to Simplify a Complex Fraction

Simplifying a complex fraction can be done by breaking it down into two simpler fractions. To do this, you must first multiply the numerator and denominator of the complex fraction by the denominator of the inner fraction. This will give you a simpler fraction that is equivalent to the original.

## Example of Complex Fraction

To illustrate how to simplify a complex fraction, consider the following example:

*Which expression is equivalent to the following complex fraction?*

The complex fraction is: *(1/2)/(3/4)*

## Solution

The solution is to multiply the numerator and denominator of the complex fraction by the denominator of the inner fraction. In this case, the denominator of the inner fraction is 4. So, the equation should look like this: *(1/2) x 4/4 x 3 = 2/3*.

This means that the expression *2/3* is equivalent to the complex fraction *(1/2)/(3/4)*.

## Another Example

To illustrate another example, consider the following complex fraction: *(2/3)/(5/7)*. To simplify this fraction, we must multiply the numerator and denominator of the complex fraction by the denominator of the inner fraction. In this case, the denominator of the inner fraction is 7. So, the equation should look like this: *(2/3) x 7/7 x 5 = 10/21*.

This means that the expression *10/21* is equivalent to the complex fraction *(2/3)/(5/7)*.

## Conclusion

In conclusion, simplifying a complex fraction can be done by breaking it down into two simpler fractions. To do this, you must multiply the numerator and denominator of the complex fraction by the denominator of the inner fraction. This will give you a simpler fraction that is equivalent to the original.

For instance, the complex fraction *(1/2)/(3/4)* is equivalent to the fraction *2/3*, and the complex fraction *(2/3)/(5/7)* is equivalent to the fraction *10/21*.

## More Practice

To continue practicing with complex fractions, try the following exercises.

- Which expression is equivalent to the following complex fraction?
*(3/5)/(7/9)* - Which expression is equivalent to the following complex fraction?
*(2/3)/(5/7)* - Which expression is equivalent to the following complex fraction?
*(1/2)/(3/4)*

Answers:

- The expression
*15/63*is equivalent to the complex fraction*(3/5)/(7/9)*. - The expression
*10/21*is equivalent to the complex fraction*(2/3)/(5/7)*. - The expression
*2/3*is equivalent to the complex fraction*(1/2)/(3/4)*.