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Reciprocals and Complex Fractions




 
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In this lesson, we will learn what is the Reciprocal of a fraction, what is a Complex Fraction and how to simplify a Complex Fraction.

What is the Reciprocal of a fraction?
The reciprocal of a fraction is the fraction turned upside down. That is the numerator becomes the denominator and the denominator becomes the numerator, for example:

The reciprocal of

The reciprocal of or 8.

To get the reciprocal of a mixed number, first convert to improper fraction and then invert, for example:

The reciprocal of is
Any number multiplied by its reciprocal will always be 1, for example:


What is a Complex Fraction?

A complex fraction is a fraction within a fraction. If we have a fraction as the numerator, then the denominators are to be multiplied to get the simplified fraction.

For example:

If we have a fraction as the denominator, then the top numerator is multiplied with the reciprocal of the denominator to get the simplified fraction.

For example:




How to simplify a Complex Fraction?

Method 1 : Fraction Division
1. Convert any mixed numbers to improper fractions.
2. Reduce the fractions when possible.
3. Divide the fraction in the numerator with the fraction in the denominator by inverting the fraction in the denominator and then multiply with the numerator.
5. Reduce the fraction when possible.

Method 2 : LCD Multiplication
1. Convert any mixed numbers to improper fractions.
2. Reduce the fractions when possible.
3. Find the least common denominator (LCD) of all fractions appearing within the complex fraction.
4. Multiply all the fractions in the numerator and the denominator by the LCD. (This will change the complex fraction to a normal fraction)
5. Calculate and reduce the fraction when possible.

Simplifying Complex Fractions - Example 1 (Fraction Division Method)
This video shows how to simplify a complex fraction by getting common denominators, flipping, multiplying, and canceling.
Simplifying Complex Fractions - Example 2 (Fraction Division Method)


 
Simplifying complex fractions (LCD Multiplication Method)
Two examples of simplifying complex fractions using the LCD Multiplication ie. multiplying every term of the complex fraction by the LCD of all the fractions that appear in the complex fraction.
Simplify Complex Fractions (LCD Multiplication Method)


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