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

Online calculator: reduce (simplify) fractions

How to reduce (simplify) to lowest terms ordinary math fraction:

To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

Result written as a proper or improper fraction, a mixed number or a 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.

Read the full article >> Simplifying ordinary math fractions (reducing to lower terms): steps to follow and examples


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.