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

## Latest reduced (simplified) fractions

 318,780/495 = (318,780 ÷ 495)/(495 ÷ 495) = 644 Jan 24 02:53 UTC (GMT) 3,636/909 = (3,636 ÷ 909)/(909 ÷ 909) = 4 Jan 24 02:53 UTC (GMT) 303/78 = (303 ÷ 3)/(78 ÷ 3) = 101/26; 101 > 26 => improper fraction Rewrite: 101 ÷ 26 = 3 and remainder = 23 => 101/26 = (3 × 26 + 23)/26 = 3 + 23/26 = = 3 23/26, mixed number (mixed fraction) Jan 24 02:53 UTC (GMT) 304/81 already reduced (simplified) to lowest terms 304 > 81 => improper fraction Rewrite: 304 ÷ 81 = 3 and remainder = 61 => 304/81 = (3 × 81 + 61)/81 = 3 + 61/81 = = 3 61/81, mixed number (mixed fraction) Jan 24 02:53 UTC (GMT) 351/195 = (351 ÷ 39)/(195 ÷ 39) = 9/5; 9 > 5 => improper fraction Rewrite: 9 ÷ 5 = 1 and remainder = 4 => 9/5 = (1 × 5 + 4)/5 = 1 + 4/5 = = 1 4/5, mixed number (mixed fraction) Jan 24 02:53 UTC (GMT) 18/8 = (18 ÷ 2)/(8 ÷ 2) = 9/4; 9 > 4 => improper fraction Rewrite: 9 ÷ 4 = 2 and remainder = 1 => 9/4 = (2 × 4 + 1)/4 = 2 + 1/4 = = 2 1/4, mixed number (mixed fraction) Jan 24 02:53 UTC (GMT) 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4 Jan 24 02:53 UTC (GMT) 500/120 = (500 ÷ 20)/(120 ÷ 20) = 25/6; 25 > 6 => improper fraction Rewrite: 25 ÷ 6 = 4 and remainder = 1 => 25/6 = (4 × 6 + 1)/6 = 4 + 1/6 = = 4 1/6, mixed number (mixed fraction) Jan 24 02:53 UTC (GMT) 947/64 already reduced (simplified) to lowest terms 947 > 64 => improper fraction Rewrite: 947 ÷ 64 = 14 and remainder = 51 => 947/64 = (14 × 64 + 51)/64 = 14 + 51/64 = = 14 51/64, mixed number (mixed fraction) Jan 24 02:53 UTC (GMT) 4/50 = (4 ÷ 2)/(50 ÷ 2) = 2/25 Jan 24 02:53 UTC (GMT) 168/332 = (168 ÷ 4)/(332 ÷ 4) = 42/83 Jan 24 02:53 UTC (GMT) 103/100 already reduced (simplified) to lowest terms 103 > 100 => improper fraction Rewrite: 103 ÷ 100 = 1 and remainder = 3 => 103/100 = (1 × 100 + 3)/100 = 1 + 3/100 = = 1 3/100, mixed number (mixed fraction) Jan 24 02:53 UTC (GMT) 3/458 already reduced (simplified) to lowest terms Jan 24 02:53 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.