# How to reduce (simplify) fraction 312/213 to lowest terms? Write it as an improper fraction, a mixed number, a decimal number, a percentage

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

### Steps to simplify an ordinary fraction, to reduce it to its lowest terms:

• 1) Factor both the numerator and the denominator of the fraction into prime factors.
• 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 the greatest common factor, GCF (GCD).
• In conclusion: the fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
• A fraction reduced to its lowest terms cannot be further reduced and it is called an irreducible fraction.

### 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. Well, these values are much easier to work with, reducing the overall effort of working with fractions.