Ordinary math fractions reducing to lowest terms (simplifying)

Online calculator: reduce (simplify) fractions

How to reduce (simplify) to the 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

78/71 already reduced (simplified) to lowest terms
78 > 71 => improper fraction

Rewrite:
78 ÷ 71 = 1 and remainder = 7 =>
78/71 = (1 × 71 + 7)/71 = 1 + 7/71 =
= 1 7/71, mixed number (mixed fraction)
Nov 17 21:19 UTC (GMT)
900/12 = (900 ÷ 12)/(12 ÷ 12) = 75 Nov 17 21:19 UTC (GMT)
48/60 = (48 ÷ 12)/(60 ÷ 12) = 4/5 Nov 17 21:19 UTC (GMT)
4,520/6,418 = (4,520 ÷ 2)/(6,418 ÷ 2) = 2,260/3,209 Nov 17 21:19 UTC (GMT)
55/63 already reduced (simplified) to lowest terms Nov 17 21:19 UTC (GMT)
426/100 = (426 ÷ 2)/(100 ÷ 2) = 213/50;
213 > 50 => improper fraction

Rewrite:
213 ÷ 50 = 4 and remainder = 13 =>
213/50 = (4 × 50 + 13)/50 = 4 + 13/50 =
= 4 13/50, mixed number (mixed fraction)
Nov 17 21:19 UTC (GMT)
426/100 = (426 ÷ 2)/(100 ÷ 2) = 213/50;
213 > 50 => improper fraction

Rewrite:
213 ÷ 50 = 4 and remainder = 13 =>
213/50 = (4 × 50 + 13)/50 = 4 + 13/50 =
= 4 13/50, mixed number (mixed fraction)
Nov 17 21:19 UTC (GMT)
120/540 = (120 ÷ 60)/(540 ÷ 60) = 2/9 Nov 17 21:19 UTC (GMT)
142/283 already reduced (simplified) to lowest terms Nov 17 21:19 UTC (GMT)
102/26 = (102 ÷ 2)/(26 ÷ 2) = 51/13;
51 > 13 => improper fraction

Rewrite:
51 ÷ 13 = 3 and remainder = 12 =>
51/13 = (3 × 13 + 12)/13 = 3 + 12/13 =
= 3 12/13, mixed number (mixed fraction)
Nov 17 21:19 UTC (GMT)
392/5 already reduced (simplified) to lowest terms
392 > 5 => improper fraction

Rewrite:
392 ÷ 5 = 78 and remainder = 2 =>
392/5 = (78 × 5 + 2)/5 = 78 + 2/5 =
= 78 2/5, mixed number (mixed fraction)
Nov 17 21:19 UTC (GMT)
172/43 = (172 ÷ 43)/(43 ÷ 43) = 4 Nov 17 21:19 UTC (GMT)
1,234,567/1,234 already reduced (simplified) to lowest terms
1,234,567 > 1,234 => improper fraction

Rewrite:
1,234,567 ÷ 1,234 = 1,000 and remainder = 567 =>
1,234,567/1,234 = (1,000 × 1,234 + 567)/1,234 = 1,000 + 567/1,234 =
= 1,000 567/1,234, mixed number (mixed fraction)
Nov 17 21:19 UTC (GMT)
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Tutoring: simplifying ordinary math fractions (reducing to lower terms)

Steps to simplify an ordinary fraction, to reduce it to its lowest terms

  • Factor the fraction's both numerator and denominator into prime factors.
  • Calculate fraction's both numerator and denominator greatest common factor, GCF (or greatest common divisor, GCD).
  • Divide fraction's both numerator and denominator by the greatest common factor GCF (divisor GCD). Fraction thus obtained is called a reduced fraction (simplified) to its lowest terms.

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


Why reducing fractions to lower terms (simplifying)?

Operations with fractions often involve fractions being brought to the same denominator and sometimes both numerators and denominators are large numbers. Doing calculations with such large numbers could be difficult. By simplifying (reducing) a fraction, both the numerator and denominator of the fraction are reduced to smaller values, much easier to work with, reducing the effort of working with fractions.