Simplifying Complex Fractions | Steps and Examples in Mathematics

Complex Fraction

In mathematics, a complex fraction is a fraction in which the numerator or denominator or both contain fractions

In mathematics, a complex fraction is a fraction in which the numerator or denominator or both contain fractions. In other words, it is a fraction within a fraction.

To illustrate, consider the following expression:

(3/4) / (2/5)

In this example, the numerator is the fraction 3/4 and the denominator is the fraction 2/5. Both the numerator and denominator are fractions themselves, making this a complex fraction.

To simplify a complex fraction, you can follow these steps:

1. Remove any fractional bars within the numerator or denominator by multiplying both the numerator and denominator by the least common multiple (LCM) of the denominators. This step eliminates the complex fraction structure and allows you to work with a regular fraction.

2. Simplify the resulting fraction by performing any necessary operations such as addition, subtraction, multiplication, or division.

Let’s use the above example to show the simplification process:

(3/4) / (2/5)

To eliminate the complex fraction structure, we need to multiply the numerator and denominator by the LCM of the denominators, which in this case is 20:

(3/4) * (5/2) = 15/8

The complex fraction has been simplified to a regular fraction. In this case, the resulting fraction is 15/8.

Note that it is also important to simplify the resulting fraction if possible. In this example, 15/8 is already simplified, but sometimes it may be necessary to reduce the fraction further.

Complex fractions often appear in algebraic expressions or when solving equations involving rational functions. Understanding how to simplify complex fractions is crucial for working with these types of problems.

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