How to reduce (simplify) the common fraction 208/520 to its simplest equivalent form, irreducible? Result written as a proper fraction, as a decimal number and as a percentage %

To reduce a fraction divide the numerator and the denominator by their greatest common factor, GCF

Factor both the numerator and the denominator, break them down to prime factors:

in the notation with exponents:


208 = 24 × 13


520 = 23 × 5 × 13

Calculate the prime factors of numbers, online calculator


Calculate the greatest common factor, GCF:

Multiply all the common prime factors, by the lowest exponents.


gcf (24 × 13; 23 × 5 × 13) = 23 × 13

Calculate the greatest common factor, GCF, online calculator


Divide both the numerator and the denominator by their greatest common factor, GCF:

208/520 =


(24 × 13)/(23 × 5 × 13) =


((24 × 13) ÷ (23 × 13)) / ((23 × 5 × 13) ÷ (23 × 13)) =


2/5

Rewrite the end result:

As a decimal number:

2/5 =


2 ÷ 5 =


0.4

As a percentage:

0.4 =


0.4 × 100/100 =


40/100 =


40%

Convert fractions to percentages, online calculator


The final answer:
:: written in three ways ::

As a positive proper fraction
(numerator < denominator):
208/520 = 2/5

As a decimal number:
208/520 = 0.4

As a percentage:
208/520 = 40%

How to reduce (simplify) the common fraction: 210/530?


Writing numbers: point '.' used as a decimal mark;

Symbols: / fraction bar; ÷ divide; × multiply; = equal;

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

208/520 = (208 ÷ 104)/(520 ÷ 104) = 2/5 Jun 05 11:56 UTC (GMT)
37/222 = (37 ÷ 37)/(222 ÷ 37) = 1/6 Jun 05 11:56 UTC (GMT)
- 11,111,111,092/15 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 11,111,111,092 ÷ 15 = - 740,740,739 and remainder = - 7 =>
- 11,111,111,092/15 = ( - 740,740,739 × 15 - 7)/15 = - 740,740,739 - 7/15 = - 740,740,739 7/15
Jun 05 11:56 UTC (GMT)
- 11,111,111,092/15 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 11,111,111,092 ÷ 15 = - 740,740,739 and remainder = - 7 =>
- 11,111,111,092/15 = ( - 740,740,739 × 15 - 7)/15 = - 740,740,739 - 7/15 = - 740,740,739 7/15
Jun 05 11:56 UTC (GMT)
177/16 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
177 ÷ 16 = 11 and remainder = 1 =>
177/16 = (11 × 16 + 1)/16 = 11 + 1/16 = 11 1/16
Jun 05 11:56 UTC (GMT)
177/100 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
177 ÷ 100 = 1 and remainder = 77 =>
177/100 = (1 × 100 + 77)/100 = 1 + 77/100 = 1 77/100
Jun 05 11:55 UTC (GMT)
80/1 already reduced (simplified) = 80 Jun 05 11:55 UTC (GMT)
35/2,498 already reduced (simplified) Jun 05 11:55 UTC (GMT)
23/10 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
23 ÷ 10 = 2 and remainder = 3 =>
23/10 = (2 × 10 + 3)/10 = 2 + 3/10 = 2 3/10
Jun 05 11:55 UTC (GMT)
27/84 = (27 ÷ 3)/(84 ÷ 3) = 9/28 Jun 05 11:55 UTC (GMT)
20/25 = (20 ÷ 5)/(25 ÷ 5) = 4/5 Jun 05 11:55 UTC (GMT)
- 43/9 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 43 ÷ 9 = - 4 and remainder = - 7 =>
- 43/9 = ( - 4 × 9 - 7)/9 = - 4 - 7/9 = - 4 7/9
Jun 05 11:55 UTC (GMT)
- 77/18 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 77 ÷ 18 = - 4 and remainder = - 5 =>
- 77/18 = ( - 4 × 18 - 5)/18 = - 4 - 5/18 = - 4 5/18
Jun 05 11:55 UTC (GMT)
see more... reduced fractions

Fractions reducing to lower terms (simplifying). Equivalent fractions

Let's learn by an example, let's simplify the fraction: 12/16

  • Numerator of the fraction. The number that is above the fraction bar, 12, is called the numerator of the fraction;
  • Denominator of the fraction. The number that is below the fraction bar, 16, is called the denominator of the fraction;
  • The value of the fraction. Fraction 12/16 shows us in how many equal parts the number above the fraction bar, 12, is being divided: into 16 equal parts. Thus, the value of the fraction is calculated as:
  • 12 ÷ 16 = 0.75
  • We notice that the two numbers, the numerator and the denominator, are dividing themselves without any remainder by 2, so we divide them by the same number, 2:
  • 12/16 = (12 ÷ 2)/(16 ÷ 2) = 6/8
  • The value of the fraction 6/8 is calculated as:
  • 6 ÷ 8 = 0.75
  • We notice that the value of the fraction 6/8 is equal to that of the fraction 12/16, namely 0.75
  • Reduced (simplified) fraction, Equivalent fraction. The new fraction, 6/8, is equivalent to the original one, 12/16, that is, it represents the same value or proportion of the whole, and it was calculated out of the original fraction by reducing it (simplifying it): both the numerator and the denominator of the fraction were divided by the number 2.
  • Common factor (divisor). The number 2 that was used to divide the two numbers that make up the fraction is called a common factor or a divisor of the numerator and the denominator of the fraction.
  • Find all the divisors of a number or all the common factors of two numbers, online.
  • The reduced fraction has now a numerator that is equal to 6 and a denominator that is equal to 8.
  • We also notice that the two new numbers, the new numerator and the new denominator, 6 and 8, are also dividing themselves without any remainder by 2 (2 is a common factor of 6 and 8), so we divide them again by 2:
  • 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
  • The value of the fraction 3/4 is calculated as:
  • 3 ÷ 4 = 0.75
  • The new fraction, 3/4, is a reduced fraction (a simplified fraction) and an equivalent of the fractions 12/16 and 6/8
  • Irreducible fraction. Fraction 3/4 is also called an irreducible fraction, in another words it could no longer be reduced or simplified, it is in its simplest form, the numbers 3 and 4, the numerator and the denominator of the fraction, are coprime numbers (prime to each other), not having any common factors other than 1.
  • Reduce fractions to lower terms (simplify), online, with explanations.

... Read the rest of this article, here: How to reduce (simplify) common fractions?

More on ordinary (common) math fractions theory: