How to reduce (simplify) the common fraction 125/75 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:


125 = 53


75 = 3 × 52

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 (53; 3 × 52) = 52

Calculate the greatest common factor, GCF, online calculator


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

125/75 =


53/(3 × 52) =


(53 ÷ 52) / ((3 × 52) ÷ 52) =


5/3

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.


5 ÷ 3 = 1 and remainder = 2 =>


5 = 1 × 3 + 2 =>


5/3 =


(1 × 3 + 2) / 3 =


1 + 2/3 =


2/3

As a decimal number:

2/3 =


1 + 2/3 =


1 + 2 ÷ 3 =


1.666666666667 ≈


1.67

As a percentage:

1.666666666667 =


1.666666666667 × 100/100 =


166.666666666667/100 =


166.666666666667% ≈


166.67%

Convert fractions to percentages, online calculator


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

As a positive improper fraction (numerator > denominator):
125/75 = 5/3

As a mixed number
(a whole number and a proper fraction, of the same sign):
125/75 = 2/3

As a decimal number:
125/751.67

As a percentage:
125/75166.67%

How to reduce (simplify) the common fraction: 134/77?


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

125/75 = (125 ÷ 25)/(75 ÷ 25) = 5/3
Improper fraction, rewrite it as a mixed number:
5 ÷ 3 = 1 and remainder = 2 =>
5/3 = (1 × 3 + 2)/3 = 1 + 2/3 = 1 2/3
Jul 02 18:38 UTC (GMT)
4,760/2,556 = (4,760 ÷ 4)/(2,556 ÷ 4) = 1,190/639
Improper fraction, rewrite it as a mixed number:
1,190 ÷ 639 = 1 and remainder = 551 =>
1,190/639 = (1 × 639 + 551)/639 = 1 + 551/639 = 1 551/639
Jul 02 18:38 UTC (GMT)
- 5/17 already reduced (simplified) Jul 02 18:38 UTC (GMT)
2,444/38 = (2,444 ÷ 2)/(38 ÷ 2) = 1,222/19
Improper fraction, rewrite it as a mixed number:
1,222 ÷ 19 = 64 and remainder = 6 =>
1,222/19 = (64 × 19 + 6)/19 = 64 + 6/19 = 64 6/19
Jul 02 18:38 UTC (GMT)
2,206/323 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
2,206 ÷ 323 = 6 and remainder = 268 =>
2,206/323 = (6 × 323 + 268)/323 = 6 + 268/323 = 6 268/323
Jul 02 18:38 UTC (GMT)
96/72 = (96 ÷ 24)/(72 ÷ 24) = 4/3
Improper fraction, rewrite it as a mixed number:
4 ÷ 3 = 1 and remainder = 1 =>
4/3 = (1 × 3 + 1)/3 = 1 + 1/3 = 1 1/3
Jul 02 18:38 UTC (GMT)
25/2,025 = (25 ÷ 25)/(2,025 ÷ 25) = 1/81 Jul 02 18:38 UTC (GMT)
- 111/120 = - (111 ÷ 3)/(120 ÷ 3) = - 37/40 Jul 02 18:38 UTC (GMT)
3,526/15 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
3,526 ÷ 15 = 235 and remainder = 1 =>
3,526/15 = (235 × 15 + 1)/15 = 235 + 1/15 = 235 1/15
Jul 02 18:38 UTC (GMT)
38/6 = (38 ÷ 2)/(6 ÷ 2) = 19/3
Improper fraction, rewrite it as a mixed number:
19 ÷ 3 = 6 and remainder = 1 =>
19/3 = (6 × 3 + 1)/3 = 6 + 1/3 = 6 1/3
Jul 02 18:38 UTC (GMT)
- 14/936 = - (14 ÷ 2)/(936 ÷ 2) = - 7/468 Jul 02 18:37 UTC (GMT)
- 56/4 = - (56 ÷ 4)/(4 ÷ 4) = - 14/1 = - 14 Jul 02 18:37 UTC (GMT)
5,346/2,339 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
5,346 ÷ 2,339 = 2 and remainder = 668 =>
5,346/2,339 = (2 × 2,339 + 668)/2,339 = 2 + 668/2,339 = 2 668/2,339
Jul 02 18:37 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: