How to reduce (simplify) the common fraction 30/305 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:

30 = 2 × 3 × 5


305 = 5 × 61

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 (2 × 3 × 5; 5 × 61) = 5

Calculate the greatest common factor, GCF, online calculator


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

30/305 =


(2 × 3 × 5)/(5 × 61) =


((2 × 3 × 5) ÷ 5) / ((5 × 61) ÷ 5) =


(2 × 3)/61 =


6/61

Rewrite the end result:

As a decimal number:

6/61 =


6 ÷ 61 =


0.098360655738 ≈


0.1

As a percentage:

0.098360655738 =


0.098360655738 × 100/100 =


9.836065573771/100 =


9.836065573771% ≈


9.84%

Convert fractions to percentages, online calculator


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

As a positive proper fraction
(numerator < denominator):
30/305 = 6/61

As a decimal number:
30/3050.1

As a percentage:
30/3059.84%

How to reduce (simplify) the common fraction: 35/313?


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

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

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

30/305 = (30 ÷ 5)/(305 ÷ 5) = 6/61 Jul 06 23:55 UTC (GMT)
3,399/14 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
3,399 ÷ 14 = 242 and remainder = 11 =>
3,399/14 = (242 × 14 + 11)/14 = 242 + 11/14 = 242 11/14
Jul 06 23:54 UTC (GMT)
1,946/36 = (1,946 ÷ 2)/(36 ÷ 2) = 973/18
Improper fraction, rewrite it as a mixed number:
973 ÷ 18 = 54 and remainder = 1 =>
973/18 = (54 × 18 + 1)/18 = 54 + 1/18 = 54 1/18
Jul 06 23:54 UTC (GMT)
1,514/25 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
1,514 ÷ 25 = 60 and remainder = 14 =>
1,514/25 = (60 × 25 + 14)/25 = 60 + 14/25 = 60 14/25
Jul 06 23:54 UTC (GMT)
1/81 already reduced (simplified) Jul 06 23:54 UTC (GMT)
877/693 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
877 ÷ 693 = 1 and remainder = 184 =>
877/693 = (1 × 693 + 184)/693 = 1 + 184/693 = 1 184/693
Jul 06 23:54 UTC (GMT)
- 36/7 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 36 ÷ 7 = - 5 and remainder = - 1 =>
- 36/7 = ( - 5 × 7 - 1)/7 = - 5 - 1/7 = - 5 1/7
Jul 06 23:54 UTC (GMT)
4,483/1,000 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
4,483 ÷ 1,000 = 4 and remainder = 483 =>
4,483/1,000 = (4 × 1,000 + 483)/1,000 = 4 + 483/1,000 = 4 483/1,000
Jul 06 23:54 UTC (GMT)
70/120 = (70 ÷ 10)/(120 ÷ 10) = 7/12 Jul 06 23:54 UTC (GMT)
1,338/121 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
1,338 ÷ 121 = 11 and remainder = 7 =>
1,338/121 = (11 × 121 + 7)/121 = 11 + 7/121 = 11 7/121
Jul 06 23:54 UTC (GMT)
- 79/ - 14 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
79 ÷ 14 = 5 and remainder = 9 =>
79/14 = (5 × 14 + 9)/14 = 5 + 9/14 = 5 9/14
Jul 06 23:54 UTC (GMT)
70/120 = (70 ÷ 10)/(120 ÷ 10) = 7/12 Jul 06 23:54 UTC (GMT)
70/120 = (70 ÷ 10)/(120 ÷ 10) = 7/12 Jul 06 23:54 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?

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