### Example 2: reduce fraction ^{130}/_{455} to its lower terms.

- Fraction's numerator, 130, prime factorization is: 130 = 2 × 5 × 13.

Fraction's denominator, 455, prime factorization is: 455 = 5 × 7 × 13. - The greatest common factor, GCF (130; 455), is calculated by multiplying all the common factors of both the numerator and denominator, by their lowest powers:

GCF (130; 455) = (2 × 5 × 13; 5 × 7 × 13) = 5 × 13 = 65. - Both fraction's numerator and denominator are divided by the greatest common factor GCF (or divisor GCD):

^{130}/_{455} = ^{(2 × 5 × 13)}/_{(5 × 7 × 13)} = ^{((2 × 5 × 13) ÷ (5 × 13))} / _{((5 × 7 × 13) ÷ (5 × 13))} = ^{2}/_{7}.

Fraction thus obtained is called a reduced fraction (simplified) to its lowest terms.

### Why reducing fractions to lower terms (simplifying)?

Operations with fractions often involve them being brought to the same denominator and sometimes both the numerators and denominators are large numbers. Doing calculations with such large numbers could be difficult. By simplifying (reducing) a fraction, both the numerator and denominator of the fraction are reduced to smaller values, much easier to work with.