How to reduce (simplify) the common fraction 72/336 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:


72 = 23 × 32


336 = 24 × 3 × 7

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 (23 × 32; 24 × 3 × 7) = 23 × 3

Calculate the greatest common factor, GCF, online calculator


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

72/336 =


(23 × 32)/(24 × 3 × 7) =


((23 × 32) ÷ (23 × 3)) / ((24 × 3 × 7) ÷ (23 × 3)) =


3/(2 × 7) =


3/14

Rewrite the end result:

As a decimal number:

3/14 =


3 ÷ 14 =


0.214285714286 ≈


0.21

As a percentage:

0.214285714286 =


0.214285714286 × 100/100 =


21.428571428571/100 =


21.428571428571% ≈


21.43%

Convert fractions to percentages, online calculator


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

As a positive proper fraction
(numerator < denominator):
72/336 = 3/14

As a decimal number:
72/3360.21

As a percentage:
72/33621.43%

How to reduce (simplify) the common fraction: 78/342?


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

72/336 = (72 ÷ 24)/(336 ÷ 24) = 3/14 Jul 02 18:32 UTC (GMT)
- 1/8,000 already reduced (simplified) Jul 02 18:32 UTC (GMT)
44/1,885 already reduced (simplified) Jul 02 18:32 UTC (GMT)
1,079/25 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
1,079 ÷ 25 = 43 and remainder = 4 =>
1,079/25 = (43 × 25 + 4)/25 = 43 + 4/25 = 43 4/25
Jul 02 18:32 UTC (GMT)
- 23/42 already reduced (simplified) Jul 02 18:32 UTC (GMT)
20/3 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
20 ÷ 3 = 6 and remainder = 2 =>
20/3 = (6 × 3 + 2)/3 = 6 + 2/3 = 6 2/3
Jul 02 18:32 UTC (GMT)
16/29 already reduced (simplified) Jul 02 18:31 UTC (GMT)
- 1/80 already reduced (simplified) Jul 02 18:31 UTC (GMT)
163/42 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
163 ÷ 42 = 3 and remainder = 37 =>
163/42 = (3 × 42 + 37)/42 = 3 + 37/42 = 3 37/42
Jul 02 18:31 UTC (GMT)
343/21 = (343 ÷ 7)/(21 ÷ 7) = 49/3
Improper fraction, rewrite it as a mixed number:
49 ÷ 3 = 16 and remainder = 1 =>
49/3 = (16 × 3 + 1)/3 = 16 + 1/3 = 16 1/3
Jul 02 18:31 UTC (GMT)
57/4,076 already reduced (simplified) Jul 02 18:31 UTC (GMT)
755/463 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
755 ÷ 463 = 1 and remainder = 292 =>
755/463 = (1 × 463 + 292)/463 = 1 + 292/463 = 1 292/463
Jul 02 18:31 UTC (GMT)
100/46 = (100 ÷ 2)/(46 ÷ 2) = 50/23
Improper fraction, rewrite it as a mixed number:
50 ÷ 23 = 2 and remainder = 4 =>
50/23 = (2 × 23 + 4)/23 = 2 + 4/23 = 2 4/23
Jul 02 18:31 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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