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Simplify the Complex Fraction Calculator + Online Solver With Free Steps
The Complex Fraction Calculator is a helpful tool that converts the given complex fraction into the simplified one. The calculator takes a single input which is the target complex fraction.
Simple fractions have a denominator and numerator but when either or both of them are fractions themselves then it is said to be a Complex Fraction. In other words, you have a smaller fraction as a part of a bigger fraction.
The calculator returns a refined form of the target fraction. It is readily available in the browser at all times.
What Is a Complex Fraction Calculator?
A Complex Fraction Calculator is an online calculator designed to reduce any complex mathematical fraction into its simplified form.
In real-world problems, fractions are utilized quite commonly. There are many scenarios where you can observe the use of fractions like defining portions, dividing bigger things into small ones, and finding quantities using the ratio technique.
That’s why a fraction is a fundamental concept in maths, finance, and science. It is easy to deal with problems having simple fractions but in many cases, there are fractions in a complicated form.
Such fractions are difficult to handle and cannot be used directly as they further increase the complexity of the problem. Simplifying them by hand is a time taking and grinding task.
But you can save yourself from this tiring process using the Complex Fraction Calculator. It is an advanced calculator that solves complex fractions at the speed of knots. It delivers a detailed and accurate solution to your problem.
The tool’s interface is straightforward to understand, making it exceptionally easy to use. You only need a reliable internet connection and browser to access this tool. Read the following section to learn more about the calculator’s functionality.
How To Use the Complex Fraction Calculator?
You can use the Complex Fraction Calculator by putting the various fractions into the input boxes. It can take only one fraction at a time. Enter the equation, click the button, and get your solution, it is simple as that.
One additional feature of this calculator is that it can handle any kind of fraction with trigonometric function, exponential terms, algebraic terms, or even simple numbers.
Follow the below-given steps properly to use this calculator.
Step 1
First, ensure that you have a complex fraction. Put the numerator in the upper box and the denominator in the lower box. As both are fractions so make sure to use slash(/) and brackets () to prevent confusion and errors.
Step 2
After entering the fraction, press the Submit button to get the result. The result will include input interpretation, some necessary solving steps, and the final simplified form.
How Does the Complex Fraction Calculator Work?
The Complex Fraction Calculator works by analyzing the given fraction and then applying some basic mathematical techniques to give it a simplified shape.
To get a better understanding of how the calculator works, let’s discuss the core concepts related to it.
What Is a Complex Fraction?
Complex Fractions are the fractions that have separate values in numerator and denominator. The general form of a complex fraction is written below:
\[ \frac{ \frac{ax+b}{cx+d} }{ \frac{ex+f}{gx+h} } \]
It is possible that only one part is a fraction and another part is a simple expression and also both can be in the form of a fraction too.
There are two main methods to simplify the complex fraction. Each of them is discussed in detail below.
First Method
The first method is a simpler one with two steps. The first step is to re-arrange the numerator and denominator separately. If any of them have multiple parts so combine them to make one term.
This is done so that numerator and denominator become one simple fraction individually. It makes it easy to further solve them. Let’s suppose we have a fraction given below.
\[ \frac{\frac{1}{c} – \frac{1}{d}}{\frac{5}{cd}} \]
In this fraction, we have multiple terms in the numerator, so according to the first step, we combine them and make one fraction. The new fraction after the first step is:
\[ \frac{\frac{d – c}{cd}}{\frac{5}{cd}} \]
The second step is to multiply the numerator with the reciprocal of the denominator. In doing so you can multiply and divide some terms from each of the fractions.
The final result of this product will be an expression with no fraction in the numerator and denominator. So after applying the second step to the fraction, the final fraction is as follows:
\[ \frac{d – c}{cd} \cdot \frac{cd}{5} = \frac{d-c}{5} \]
Second Method
The second method uses the technique of least common denominator(LCD). The LCD is a list of all different factors in the denominators of both numerator and denominator fractions with their powers.
First, find the LCD by observing the complex fraction. Then multiply the LCD by both the numerator and denominator of the complex fraction. After this, you can further simplify if required.
Let’s apply this method to the example discussed previously. The LCD in the complex fraction is cd. Now multiply this with numerator and denominator separately.
\[ \frac{(\frac{1}{c} – \frac{1}{d}) \cdot (cd) }{(\frac{5}{cd}) \cdot (cd) } \]
The final result after performing the multiplication is similar to that obtained in the first method. The result is as follows:
\[ \frac{d – c}{cd} \cdot \frac{cd}{5} = \frac{d-c}{5} \]
The calculator uses either of these two methods to simplify complex fractions.
Solved Examples
Let’s discuss the problems solved using the Complex Fraction Calculator one by one.
Example 1
A mathematician while solving a problem encountered the following complex fraction:
\[ \frac{ \frac{3}{5 + x} }{ 1 + \frac{5}{x} } \]
To further solve the problem, he first needs to find the simplified form of the fraction.
Solution
The detailed solution to this problem by the calculator is given as:
\[ \frac{3x}{(x + 5)^2} \]
\[ \frac{3x}{x^2 + 10x + 25} \]
\[ – \frac{3x}{(-x-5)(x+5)} \]
Example 2
Reduce the given complex fraction into the simplified form.
\[ \frac{ \frac{4x + 1}{x^2 – 36} }{ \frac{12x^2 – 1}{x + 6} } \]
Solution
This problem can be easily solved by Complex Fraction Calculator. The result is as follows:
\[ \frac{4x + 1}{(x – 6) (12x^2 -1)} \]
\[ \frac{4x + 1}{x(x(12x – 72) – 1) + 6} \]
\[ \frac{3x}{12x^3 – 72x^2 – x + 6 } \]