To reduce fractions means to simplify them by dividing the numerator (top number) and the denominator (bottom number) by their greatest common factor (GCF) until no further division is possible except by 1. Here are the general steps to reduce a fraction:
- Find the factors of both the numerator and the denominator.
- Identify the greatest common factor (GCF) of these two numbers.
- Divide both the numerator and denominator by the GCF.
- The resulting fraction is the reduced or simplest form.
For example, to reduce the fraction 8/24:
- Factors of 8 are 1, 2, 4, 8.
- Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
- The GCF is 8.
- Divide numerator and denominator by 8: (8 ÷ 8) / (24 ÷ 8) = 1/3.
- So, 8/24 reduces to 1/3.
Other methods include prime factorization and equivalent fractions, but the GCF method is most common and easiest to use. Key tips:
- If either numerator or denominator is a prime number, the fraction may not be reducible.
- If the numerator is 1, the fraction is already in simplest form.
- Improper fractions can be converted to mixed numbers but are simplified the same way.
This method works for fractions with variables too by finding common factors in algebraic terms. This explanation is based on standard mathematical procedures for reducing fractions.
