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

Online calculator: reduce (simplify) fractions

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

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

Result written as a proper or an improper fraction, a mixed number, a decimal or an integer, a percentage

Latest reduced (simplified) fractions

63/35 = (63 ÷ 7)/(35 ÷ 7) = 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)
Sep 24 15:17 UTC (GMT)
150/100 = (150 ÷ 50)/(100 ÷ 50) = 3/2;
3 > 2 => improper fraction

Rewrite:
3 ÷ 2 = 1 and remainder = 1 =>
3/2 = (1 × 2 + 1)/2 = 1 + 1/2 =
= 1 1/2, mixed number (mixed fraction)
Sep 24 15:17 UTC (GMT)
121/144 already reduced (simplified) to lowest terms Sep 24 15:17 UTC (GMT)
191/18 already reduced (simplified) to lowest terms
191 > 18 => improper fraction

Rewrite:
191 ÷ 18 = 10 and remainder = 11 =>
191/18 = (10 × 18 + 11)/18 = 10 + 11/18 =
= 10 11/18, mixed number (mixed fraction)
Sep 24 15:17 UTC (GMT)
26/26 = (26 ÷ 26)/(26 ÷ 26) = 1 Sep 24 15:17 UTC (GMT)
60/683 already reduced (simplified) to lowest terms Sep 24 15:17 UTC (GMT)
90/80 = (90 ÷ 10)/(80 ÷ 10) = 9/8;
9 > 8 => improper fraction

Rewrite:
9 ÷ 8 = 1 and remainder = 1 =>
9/8 = (1 × 8 + 1)/8 = 1 + 1/8 =
= 1 1/8, mixed number (mixed fraction)
Sep 24 15:17 UTC (GMT)
825/999 = (825 ÷ 3)/(999 ÷ 3) = 275/333 Sep 24 15:17 UTC (GMT)
115/360 = (115 ÷ 5)/(360 ÷ 5) = 23/72 Sep 24 15:17 UTC (GMT)
112/144 = (112 ÷ 16)/(144 ÷ 16) = 7/9 Sep 24 15:17 UTC (GMT)
2,333/10,000 already reduced (simplified) to lowest terms Sep 24 15:17 UTC (GMT)
127/250 already reduced (simplified) to lowest terms Sep 24 15:17 UTC (GMT)
3,800/19,000 = (3,800 ÷ 3,800)/(19,000 ÷ 3,800) = 1/5 Sep 24 15:17 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 (common) 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.

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples