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

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

- Factor the fraction's numerator and denominator down to their prime factors. If you don't know how, you can run your prime factorization operations on this page at www.numere-prime.ro: numbers prime factorization.
- Calculate the fraction's numerator and denominator greatest common factor, GCF (also called the greatest common denominator, GCD). If you don't know how, you can calculate the greatest common factor GCF (or denominator GCD) of two numbers on this page on www.numere-prime.ro: greatest common factor GCF (or denominator, GCD).
- Divide both fraction's numerator and denominator by their greatest common factor GCF (denominator GCD). The end fraction is called a reduced fraction, reduced to its lowest terms (or simplified).

### An example of a fraction reducing to lower terms... fraction to reduce is: ^{12}/_{16}

- Fraction's numerator is 12 and it's prime factorized as: 12 = 2
^{2}* 3.

Fraction's denominator is 16 and it's prime factorized as: 16 = 2^{4}.

If you can't factorize numbers down to prime factors, you can do it online on this page at www.numere-prime.ro: numbers prime factorization. - The greatest common factor, GCF (12; 16), also called GCD, is calculated by multiplying all the unique common factors of both the numerator and the denominator, by their lowest powers, such as:

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

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 their greatest common factor GCF (or denominator GCD):

^{12}/_{16}=^{(12 ÷ 4)}/_{(16 ÷ 4)}=^{3}/_{4}

The end fraction^{3}/_{4}is called a reduced fraction, reduced to its lowest terms (or simplified).

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

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