# Calculator: ordinary math fractions reducing to lowest terms (simplifying) explained. Result as a proper, improper fraction (mixed number), decimal

## Latest reduced (simplified) fractions

 38/41 already reduced (simplified) to lowest terms Jan 22 13:49 UTC (GMT) 8/5 already reduced (simplified) to lowest terms 8 > 5 => improper fraction Rewrite: 8 ÷ 5 = 1 and remainder = 3 => 8/5 = (1 × 5 + 3)/5 = 1 + 3/5 = = 1 3/5, mixed number (mixed fraction) Jan 22 13:49 UTC (GMT) 130/143 = (130 ÷ 13)/(143 ÷ 13) = 10/11 Jan 22 13:49 UTC (GMT) 369/500 already reduced (simplified) to lowest terms Jan 22 13:49 UTC (GMT) 998/23 already reduced (simplified) to lowest terms 998 > 23 => improper fraction Rewrite: 998 ÷ 23 = 43 and remainder = 9 => 998/23 = (43 × 23 + 9)/23 = 43 + 9/23 = = 43 9/23, mixed number (mixed fraction) Jan 22 13:49 UTC (GMT) 9/11 already reduced (simplified) to lowest terms Jan 22 13:49 UTC (GMT) 480/179 already reduced (simplified) to lowest terms 480 > 179 => improper fraction Rewrite: 480 ÷ 179 = 2 and remainder = 122 => 480/179 = (2 × 179 + 122)/179 = 2 + 122/179 = = 2 122/179, mixed number (mixed fraction) Jan 22 13:49 UTC (GMT) 2/17 already reduced (simplified) to lowest terms Jan 22 13:49 UTC (GMT) 39/155 already reduced (simplified) to lowest terms Jan 22 13:49 UTC (GMT) 3/21 = (3 ÷ 3)/(21 ÷ 3) = 1/7 Jan 22 13:49 UTC (GMT) 30/36 = (30 ÷ 6)/(36 ÷ 6) = 5/6 Jan 22 13:49 UTC (GMT) 132/681 = (132 ÷ 3)/(681 ÷ 3) = 44/227 Jan 22 13:49 UTC (GMT) 26/46 = (26 ÷ 2)/(46 ÷ 2) = 13/23 Jan 22 13:48 UTC (GMT) reduced fractions, see more...

## 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.