How to Get Rid of Complex Fractions?

To eliminate complex fractions, you can use a few simple methods:

Method 1: Multiplying by the Least Common Multiple (LCM)

1. Identify the LCM: Determine the least common multiple of all the denominators within the complex fraction.
2. Multiply: Multiply both the numerator and denominator of the complex fraction by this LCM.
3. Simplify: Simplify the resulting fraction by canceling out any common factors.

Example:

• Complex Fraction: (1/2 + 1/3) / (1/4 + 1/5)
• LCM of 2, 3, 4, and 5 is 60.
• Multiply numerator and denominator by 60: [(60/2) + (60/3)] / [(60/4) + (60/5)]
• Simplify: (30 + 20) / (15 + 12) = 50/27

Method 2: Dividing by the Reciprocal

1. Simplify Numerator and Denominator: If possible, simplify the fractions within the numerator and denominator of the complex fraction.
2. Flip and Multiply: Multiply the numerator by the reciprocal of the denominator.
3. Simplify: Simplify the resulting fraction by canceling out any common factors.

Example:

• Complex Fraction: (2/3) / (1/4)
• Flip the denominator and multiply: (2/3) * (4/1)
• Simplify: 8/3

By applying these methods, you can easily get rid of complex fractions and express them in a simpler form.