# Calculator: ordinary math fractions reducing to lowest terms (simplifying) explained. Final result written as a proper fraction or as an improper one and a mixed number, as an integer or a decimal, as a percentage

## Latest fractions reduced (simplified) to the lowest terms

 89/200 already reduced (simplified) to lowest terms Nov 25 19:41 UTC (GMT) 5/468 already reduced (simplified) to lowest terms Nov 25 19:41 UTC (GMT) 189/60 = (189 ÷ 3)/(60 ÷ 3) = 63/20; 63 > 20 => improper fraction Rewrite: 63 ÷ 20 = 3 and remainder = 3 => 63/20 = (3 × 20 + 3)/20 = 3 + 3/20 = = 3 3/20, mixed number (mixed fraction) Nov 25 19:41 UTC (GMT) 144/57 = (144 ÷ 3)/(57 ÷ 3) = 48/19; 48 > 19 => improper fraction Rewrite: 48 ÷ 19 = 2 and remainder = 10 => 48/19 = (2 × 19 + 10)/19 = 2 + 10/19 = = 2 10/19, mixed number (mixed fraction) Nov 25 19:41 UTC (GMT) 88/90 = (88 ÷ 2)/(90 ÷ 2) = 44/45 Nov 25 19:41 UTC (GMT) 40/75 = (40 ÷ 5)/(75 ÷ 5) = 8/15 Nov 25 19:41 UTC (GMT) 96/39 = (96 ÷ 3)/(39 ÷ 3) = 32/13; 32 > 13 => improper fraction Rewrite: 32 ÷ 13 = 2 and remainder = 6 => 32/13 = (2 × 13 + 6)/13 = 2 + 6/13 = = 2 6/13, mixed number (mixed fraction) Nov 25 19:41 UTC (GMT) 17/1,672,619,703 already reduced (simplified) to lowest terms Nov 25 19:41 UTC (GMT) 412/3 already reduced (simplified) to lowest terms 412 > 3 => improper fraction Rewrite: 412 ÷ 3 = 137 and remainder = 1 => 412/3 = (137 × 3 + 1)/3 = 137 + 1/3 = = 137 1/3, mixed number (mixed fraction) Nov 25 19:41 UTC (GMT) 62/29 already reduced (simplified) to lowest terms 62 > 29 => improper fraction Rewrite: 62 ÷ 29 = 2 and remainder = 4 => 62/29 = (2 × 29 + 4)/29 = 2 + 4/29 = = 2 4/29, mixed number (mixed fraction) Nov 25 19:41 UTC (GMT) 4/12 = (4 ÷ 4)/(12 ÷ 4) = 1/3 Nov 25 19:41 UTC (GMT) 2,720/35 = (2,720 ÷ 5)/(35 ÷ 5) = 544/7; 544 > 7 => improper fraction Rewrite: 544 ÷ 7 = 77 and remainder = 5 => 544/7 = (77 × 7 + 5)/7 = 77 + 5/7 = = 77 5/7, mixed number (mixed fraction) Nov 25 19:41 UTC (GMT) 45/153 = (45 ÷ 9)/(153 ÷ 9) = 5/17 Nov 25 19:41 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.