Calculator: Completely reduce (simplify) fractions to the lowest terms - to the simplest equivalent form, irreducible, with the smallest possible numerator and denominator, that are prime to each other

Online Calculator: Completely reduce (simplify) fraction to the lowest terms

To fully reduce (simplify) fractions to the lowest terms:

Divide the numerator and denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd).

Result written as a proper or an improper fraction, as a mixed number, as a decimal or an integer and as a percentage.

The latest 13 fractions that have been fully reduced (simplified) to their lowest terms (to their simplest form, the smallest possible numerator and denominator)

Tutoring: simplifying fractions - reducing them to the lowest terms

Steps to simplify a fraction, to reduce it to its lowest terms:

A fraction fully simplified, a fraction reduced to its lowest terms is a fraction that can no longer be simplified, it has been reduced to its simplest equivalent fraction, the one having the smallest numerator and denominator possible - prime to each other.

1) Run the prime factorization of both the numerator and the denominator of the fraction.

2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.

3) Divide both the numerator and the denominator of the fraction by their greatest common factor, GCF (GCD).

The fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.

A fraction reduced to its lowest terms may no longer be reduced and it is called an irreducible fraction.

Example: reduce the fraction ^{315}/_{1,155} as much as possible, simplify it to the lowest terms.

1) Run the prime factorization of both the numerator and the denominator of the fraction.

The numerator of the fraction is 315, its breaking down into prime factors is: 315 = 3 × 3 × 5 × 7 = 3^{2} × 5 × 7

The denominator of the fraction is 1,155, its breaking down into prime factors is: 1,155 = 3 × 5 × 7 × 11.

2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.

The greatest common factor, gcf (315; 1,155), is calculated by multiplying all the common prime factors of the numerator and the denominator, taken by their lowest powers (their lowest exponents):

The fraction thus obtained is called a fraction reduced to the lowest terms.

Why reducing (simplifying) fractions to lower terms?

When running operations with fractions we are often required to bring them to the same denominator, for example when adding, subtracting or comparing.

Sometimes both the numerators and the denominators of those fractions are large numbers and doing calculations with such numbers could be difficult.

By simplifying (reducing) a fraction, both the numerator and denominator of a fraction are reduced to smaller values, much easier to work with, this way reducing the overall effort.