How to reduce (simplify) the common fraction 12/7 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:


12 = 22 × 3


7 is a prime number, it cannot be factored into other prime factors

Calculate the prime factors of numbers, online calculator


Calculate the greatest common factor, GCF:

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


But, the numerator and the denominator have no common factors.


gcf (22 × 3; 7) = 1

Calculate the greatest common factor, GCF, online calculator


The numerator and the denominator of the fraction are coprime numbers (no common prime factors, GCF = 1), the fraction cannot be reduced (simplified): irreducible fraction.

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.


12 ÷ 7 = 1 and remainder = 5 =>


12 = 1 × 7 + 5 =>


12/7 =


(1 × 7 + 5) / 7 =


1 + 5/7 =


5/7

As a decimal number:

5/7 =


1 + 5/7 =


1 + 5 ÷ 7 =


1.714285714286 ≈


1.71

As a percentage:

1.714285714286 =


1.714285714286 × 100/100 =


171.428571428571/100 =


171.428571428571% ≈


171.43%

Convert fractions to percentages, online calculator


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

As a positive improper fraction (numerator > denominator):
12/7 = 12/7

As a mixed number
(a whole number and a proper fraction, of the same sign):
12/7 = 5/7

As a decimal number:
12/71.71

As a percentage:
12/7171.43%

How to reduce (simplify) the common fraction: 16/10?


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

12/7 already reduced (simplified)
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 10:06 UTC (GMT)
40/177 already reduced (simplified) Jul 04 10:06 UTC (GMT)
100/1,070 = (100 ÷ 10)/(1,070 ÷ 10) = 10/107 Jul 04 10:06 UTC (GMT)
22/91 already reduced (simplified) Jul 04 10:06 UTC (GMT)
3,273/16 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
3,273 ÷ 16 = 204 and remainder = 9 =>
3,273/16 = (204 × 16 + 9)/16 = 204 + 9/16 = 204 9/16
Jul 04 10:05 UTC (GMT)
3,472/8 = (3,472 ÷ 8)/(8 ÷ 8) = 434/1 = 434 Jul 04 10:05 UTC (GMT)
206/26 = (206 ÷ 2)/(26 ÷ 2) = 103/13
Improper fraction, rewrite it as a mixed number:
103 ÷ 13 = 7 and remainder = 12 =>
103/13 = (7 × 13 + 12)/13 = 7 + 12/13 = 7 12/13
Jul 04 10:05 UTC (GMT)
4,027/527 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
4,027 ÷ 527 = 7 and remainder = 338 =>
4,027/527 = (7 × 527 + 338)/527 = 7 + 338/527 = 7 338/527
Jul 04 10:05 UTC (GMT)
80/400 = (80 ÷ 80)/(400 ÷ 80) = 1/5 Jul 04 10:05 UTC (GMT)
3/13 already reduced (simplified) Jul 04 10:05 UTC (GMT)
3,460/42 = (3,460 ÷ 2)/(42 ÷ 2) = 1,730/21
Improper fraction, rewrite it as a mixed number:
1,730 ÷ 21 = 82 and remainder = 8 =>
1,730/21 = (82 × 21 + 8)/21 = 82 + 8/21 = 82 8/21
Jul 04 10:05 UTC (GMT)
3,642/168 = (3,642 ÷ 6)/(168 ÷ 6) = 607/28
Improper fraction, rewrite it as a mixed number:
607 ÷ 28 = 21 and remainder = 19 =>
607/28 = (21 × 28 + 19)/28 = 21 + 19/28 = 21 19/28
Jul 04 10:05 UTC (GMT)
5/ - 8 already reduced (simplified) Jul 04 10:05 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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