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Complex Fractions

Mathematics is a subject that is being used for each and every person everyday either directly or indirectly. It is generally based upon different kinds of numbers, such as whole numbers, natural numbers, integers, rational and irrational numbers, prime numbers, even and odd numbers, composite numbers and many more. We come across with fractions very often. A fraction is a number in the form of $\frac{y}{z}$, where y and z are integers, y and  z have no common factor and z is not equal to zero.
For example - $\frac{3}{7}$, $\frac{11}{2}$$3$$\frac{7}{3}$

The complex fraction is a kind of fraction that we often come across in mathematics. A fraction having fractions in either numerator or denominator on in both is termed as complex fraction.

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Complex Fractions Defintion

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complex fraction is defined as a fraction where the numerator, denominator, or both contain a fraction. 
There may be one fraction or many fractions in numerator or denominator or in both.

Complex Fractions

How to Solve Complex Fractions?

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For studying the complex fraction, we have to learn the basic steps of how to solve complex fractions. They are,
Step 1: If suppose the complex fractions are obtained in the numerator of the normal fractions, then convert the denominator into fraction dividing by 1. Invert the denominator and multiply by the numerator of the complex fraction.
Step 2: If suppose the complex fractions are obtained in the denominator of the normal fractions, then invert the denominator of the complex fraction and multiply by the numerator.
Step 3: Then we have to perform our normal operations.


Simplifying Complex Fractions

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To simplify the complex fractions we need to simplify the numerator first completely and then simplify the denominator.

The final step for simplifying a complex fraction is to reduce the fraction by dividing the numerator by denominator.

A complex fraction can be simplified in following three ways. They are as follows:

  1. In the numerator terms of the normal fractions.
  2. In the denominator terms of the normal fractions. 
  3. Either in the numerator terms or in denominator terms or both of the normal fractions.

Below are some examples of simplifying complex fractions -

Solved Examples

Question 1: Solve the given complex fractions, $\frac{9}{\frac{3}{4}}$
Solution:

Step 1: The given complex fraction to solve is,

$\frac{9}{\frac{3}{4}}$

Step 2: In this, we have to bring the denominator part as the format of multiplication, we get,

$\frac{9}{\frac{3}{4}}$

$9 \times \frac{4}{3}$

$\frac{9}{1} \times \frac{4}{3}$

Step 3: The simplifications are made to the previous obtained complex fractions, we get,

$\frac{9}{1} \times \frac{4}{3}$

Correct answer is 12
Question 2: Solve the given complex fractions, $\frac{\frac{5}{10}}{4}$ .
Solution:

Step 1: The given complex fraction to solve is,

$\frac{\frac{5}{10}}{4}$

Step 2: In this, we have to bring the numerator part as the format of multiplication, we get,

$\frac{\frac{5}{10}}{4}$

$\frac{5}{10} \times \frac{1}{4}$

$\frac{5}{10} \times \frac{1}{4}$

Step 3: The simplifications are made to the previous obtained complex fractions, we get,

$\frac{5}{10} \times \frac{1}{4}$



Correct answer is $\frac{1}{8}$

Practice Problems

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Practice Problems

Question 1: Solve the given complex fractions, $\frac{6}{\frac{2}{4}}$
Question 2: Solve the given complex fractions, $\frac{\frac{4}{8}}{10}$
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