# Calculator: Completely reduce (simplify) fractions to the lowest terms - to the simplest equivalent form, irreducible, with the smallest possible numerator and denominator, that are prime to each other

## The latest 13 fractions that have been fully reduced (simplified) to their lowest terms (to their simplest form, the smallest possible numerator and denominator)

 Reduce (simplify) the fraction: 6,806/408 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 452/1,000 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 489/9 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 157/56 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 1,636,126/48 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 3,200/180 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 10/45 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 34/73 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 27/392,000,000 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 9/5,698 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 490,561/1,226,400 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 91,751/990 = ? Jul 03 05:41 UTC (GMT) Reduce (simplify) the fraction: 510/180 = ? Jul 03 05:40 UTC (GMT) The list of all the fractions that were fully reduced (simplified) to their lowest terms (to their simplest form, the smallest possible numerator and denominator)

## Tutoring: simplifying fractions - reducing them to the lowest terms

### Steps to simplify a fraction, to reduce it to its lowest terms:

• A fraction fully simplified, a fraction reduced to its lowest terms is a fraction that can no longer be simplified, it has been reduced to its simplest equivalent fraction, the one having the smallest numerator and denominator possible - prime to each other.
• 1) Run the prime factorization of both the numerator and the denominator of the fraction.
• 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 their greatest common factor, GCF (GCD).
• The fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
• A fraction reduced to its lowest terms may no longer be reduced and it is called an irreducible fraction.

### Example: reduce the fraction 315/1,155 as much as possible, simplify it to the lowest terms.

• #### 1) Run the prime factorization of both the numerator and the denominator of the fraction.

• The numerator of the fraction is 315, its breaking down into prime factors is:
315 = 3 × 3 × 5 × 7 = 32 × 5 × 7
• The denominator of the fraction is 1,155, its breaking down into prime factors is:
1,155 = 3 × 5 × 7 × 11.
• #### 2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.

• The greatest common factor, gcf (315; 1,155), is calculated by multiplying all the common prime factors of the numerator and the denominator, taken by their lowest powers (their lowest exponents):
• GCF (315; 1,155) = (32 × 5 × 7; 3 × 5 × 7 × 11) = 3 × 5 × 7 = 105
• #### 3) Divide both the numerator and the denominator of the fraction by their greatest common factor, GCF (GCD).

• The numerator and denominator of the fraction are divided by their greatest common factor, GCF:
• 315/1,155 =
(32 × 5 × 7)/(3 × 5 × 7 × 11) =
((32 × 5 × 7) ÷ (3 × 5 × 7)) / ((3 × 5 × 7 × 11) ÷ (3 × 5 × 7)) =
3/11
• The fraction thus obtained is called a fraction reduced to the lowest terms.

### 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, much easier to work with, this way reducing the overall effort.