How to reduce (simplify) the common fraction 726/238 to its simplest equivalent form, irreducible? Result written as an improper fraction, as a mixed number, 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:


726 = 2 × 3 × 112


238 = 2 × 7 × 17

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 × 112; 2 × 7 × 17) = 2

Calculate the greatest common factor, GCF, online calculator


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

726/238 =


(2 × 3 × 112)/(2 × 7 × 17) =


((2 × 3 × 112) ÷ 2) / ((2 × 7 × 17) ÷ 2) =


(3 × 112)/(7 × 17) =


363/119

Positive improper fraction (numerator > denominator)
Rewrite the fraction:

As a mixed number (also called a mixed fraction):

Mixed number = a whole number and a proper fraction, of the same sign.


Proper fraction = numerator smaller than denominator.


363 ÷ 119 = 3 and remainder = 6 =>


363 = 3 × 119 + 6 =>


363/119 =


(3 × 119 + 6) / 119 =


3 + 6/119 =


6/119

As a decimal number:

6/119 =


3 + 6/119 =


3 + 6 ÷ 119 =


3.050420168067 ≈


3.05

As a percentage:

3.050420168067 =


3.050420168067 × 100/100 =


305.042016806723/100 =


305.042016806723% ≈


305.04%

Convert fractions to percentages, online calculator


The final answer:
:: written in four ways ::

As a positive improper fraction (numerator > denominator):
726/238 = 363/119

As a mixed number
(a whole number and a proper fraction, of the same sign):
726/238 = 6/119

As a decimal number:
726/2383.05

As a percentage:
726/238305.04%

How to reduce (simplify) the common fraction: 730/240?


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

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

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

726/238 = (726 ÷ 2)/(238 ÷ 2) = 363/119
Improper fraction, rewrite it as a mixed number:
363 ÷ 119 = 3 and remainder = 6 =>
363/119 = (3 × 119 + 6)/119 = 3 + 6/119 = 3 6/119
Jul 04 08:52 UTC (GMT)
4,417/6 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
4,417 ÷ 6 = 736 and remainder = 1 =>
4,417/6 = (736 × 6 + 1)/6 = 736 + 1/6 = 736 1/6
Jul 04 08:52 UTC (GMT)
1,609/1,831 already reduced (simplified) Jul 04 08:52 UTC (GMT)
239/90 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
239 ÷ 90 = 2 and remainder = 59 =>
239/90 = (2 × 90 + 59)/90 = 2 + 59/90 = 2 59/90
Jul 04 08:52 UTC (GMT)
33/30 = (33 ÷ 3)/(30 ÷ 3) = 11/10
Improper fraction, rewrite it as a mixed number:
11 ÷ 10 = 1 and remainder = 1 =>
11/10 = (1 × 10 + 1)/10 = 1 + 1/10 = 1 1/10
Jul 04 08:52 UTC (GMT)
100,951/376 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
100,951 ÷ 376 = 268 and remainder = 183 =>
100,951/376 = (268 × 376 + 183)/376 = 268 + 183/376 = 268 183/376
Jul 04 08:52 UTC (GMT)
9/620 already reduced (simplified) Jul 04 08:52 UTC (GMT)
1,296/756 = (1,296 ÷ 108)/(756 ÷ 108) = 12/7
Improper fraction, rewrite it as a mixed number:
12 ÷ 7 = 1 and remainder = 5 =>
12/7 = (1 × 7 + 5)/7 = 1 + 5/7 = 1 5/7
Jul 04 08:52 UTC (GMT)
568/1,656 = (568 ÷ 8)/(1,656 ÷ 8) = 71/207 Jul 04 08:52 UTC (GMT)
53/75 already reduced (simplified) Jul 04 08:52 UTC (GMT)
35/56 = (35 ÷ 7)/(56 ÷ 7) = 5/8 Jul 04 08:52 UTC (GMT)
142,857/999,999 = (142,857 ÷ 142,857)/(999,999 ÷ 142,857) = 1/7 Jul 04 08:52 UTC (GMT)
63/196 = (63 ÷ 7)/(196 ÷ 7) = 9/28 Jul 04 08:52 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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