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

### Steps to reduce (simplify) an ordinary fraction to lower terms

- Factorize the fraction's numerator and denominator into prime factors. If you don't know how, you can factorize numbers into prime factors at this page on www.numere-prime.ro: numbers prime factorization.
- Calculate the greatest common factor, GCF (also called the greatest common denominator, GCD) of the fraction's numerator and denominator. If you don't know how, you can calculate the greatest common factor GCF (or denominator GCD) of two numbers 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 on fraction reducing to lower terms... fraction to reduce is 12/16

- Fraction's numerator is 12 and it's factorized into prime factors as:

2^{2}* 3.

Fraction's denominator is 16 and it's factorized into prime factors as:

2^{4}.

If you don't know or you can't factorize numbers into prime factors, you can do it online at the address at www.numere-prime.ro: numbers prime factorization. - The greatest common factor, GCF (12, 16), also called GCD, is calculated by multiplying all the common factors of numerator and denominator, at their lowest powers, such as:

GCF (12, 16) = (2^{2}* 3, 2^{4}) = 2^{2}.

If you don't know how, you can calculate the greatest common factor GCF (or denominator GCD) of two numbers at this address on www.numere-prime.ro: calculate the greatest common factor GCF (or denominator GCD). - Both fraction's numerator and denominator are divided by the greatest common factor GCF (or denominator GCD):

12/16 = (12 : 4) / (16 : 4) = 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.