How to reduce (simplify) ordinary fraction into lower terms: 30 / 48?

Reduce (simplify) ordinary fraction to lowest terms:
30 / 48 = ?


Divide fraction's both numerator and denominator by their greatest common factor, gcf (also called gcd - divisor).
a / b = (a : gcf(a; b)) / (b : gcf(a; b));

Integer numbers prime factorization:
30 = 2 * 3 * 5;
48 = 24 * 3;

gcf, gcd: Take all the common prime factors, by the lowest powers.
gcf, gcd(30; 48) = 2 * 3 = 6;

30 / 48 =
(2 * 3 * 5) / (24 * 3) =
((2 * 3 * 5) : (2 * 3)) / ((24 * 3) : (2 * 3)) =
(30 : 6) / (48 : 6) =

5 / 8

Reduce (simplify) other fraction

Tutoring: simplifying ordinary math fractions (reducing to lower terms)

Steps to simplify an ordinary fraction, to reduce it to lowest terms

  • Factor the fraction's numerator and denominator into prime factors. If you don't know how, you can do numbers prime factorization at this page on www.numere-prime.ro: numbers prime factorization.
  • Calculate fraction's numerator and denominator greatest common factor, GCF (greatest common denominator, GCD). If you don't know how, you can calculate two numbers greatest common factor GCF (denominator, GCD) at this address on www.numere-prime.ro: greatest common factor GCF (or denominator GCD).
  • Divide both the fraction's numerator and denominator by the greatest common factor GCF (denominator GCD). Fraction thus obtained is called a reduced fraction (simplified) to its lowest terms.

Example: reduce fraction 24/32 to its lower terms.

  • Fraction's numerator, 24, prime factorization is: 23 * 3.
    Fraction's denominator, 16, prime factorization is: 25.
  • The greatest common factor, GCF (24, 32), is calculated by multiplying all the common factors of numerator and denominator, at their lowest powers, such as:
    GCF (24, 32) = (23 * 3, 25) = 23.
  • Both fraction's numerator and denominator are divided by the greatest common factor GCF (or denominator GCD):
    24/32 = (24 : 8) / (32 : 8) = 3/4.
    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 fractions being brought to the same denominator and sometimes both numerators and denominators are large numbers. Doing calculations with such large numbers could be more difficult. By simplifying (reducing) a fraction, both the numerator and denominator of the fraction are reduced to smaller values, much easier to work with, reducing the computational effort of working with fractions.