How to reduce (simplify) to lowest terms ordinary (common) math fraction 25/125? Result written as: a proper fraction, a decimal number and a percentage

What is the fraction 25/125 written as an equivalent reduced fraction, as a decimal number and as a percent value?

Detailed calculations below:

Introduction. Fractions

A fraction consists of two numbers and a fraction bar: 25/125


The number above the bar is the numerator: 25


The number below the bar is the denominator: 125


The fraction bar means that the two numbers are dividing themselves:
25/125 = 25 ÷ 125


Divide the numerator by the denominator to get fraction's value:
Value = 25 ÷ 125


Introduction. Percent

'Percent (%)' means 'out of one hundred':


p% = p 'out of one hundred',


p% = p/100 = p ÷ 100


Note:

The fraction 100/100 = 100 ÷ 100 = 100% = 1


Multiply a number by the fraction 100/100,
... and its value doesn't change.



To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

Integer numbers prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


25 = 52;
25 is not a prime, is a composite number;


125 = 53;
125 is not a prime, is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.


Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

Multiply all the common prime factors, by the lowest exponents (if any).


gcf, hcf, gcd (25; 125) = 52 = 25



Divide both the numerator and the denominator by their greatest common factor.

25/125 =


52/53 =


(52 ÷ 52) / (53 ÷ 52) =


1/5


The fraction is now reduced to the lowest terms.

1/5 is a proper fraction.

A proper fraction: numerator smaller than denominator.


Rewrite the end result, continued below...

Rewrite the end result:

As a decimal number:

1/5 =


1 ÷ 5 =


0.2


As a percentage:

0.2 =


0.2 × 100/100 =


20/100 =


20%


In other words:

1) Calculate fraction's value.


2) Multiply that number by 100.


3) Add the percent sign % to it.



Final answer
continued below...

Final answer:
:: written in three ways ::

As a proper fraction
(numerator smaller than denominator):
25/125 = 1/5

As a decimal number:
25/125 = 0.2

As a percentage:
25/125 = 20%

More operations of this kind:

Online calculator: reduce (simplify) fractions

Latest fractions reduced (simplified) to the lowest terms

1/5 already reduced (simplified) to lowest terms Nov 25 19:33 UTC (GMT)
25/125 = (25 ÷ 25)/(125 ÷ 25) = 1/5 Nov 25 19:33 UTC (GMT)
27/5,394 = (27 ÷ 3)/(5,394 ÷ 3) = 9/1,798 Nov 25 19:33 UTC (GMT)
494/11 already reduced (simplified) to lowest terms
494 > 11 => improper fraction

Rewrite:
494 ÷ 11 = 44 and remainder = 10 =>
494/11 = (44 × 11 + 10)/11 = 44 + 10/11 =
= 44 10/11, mixed number (mixed fraction)
Nov 25 19:33 UTC (GMT)
42/9 = (42 ÷ 3)/(9 ÷ 3) = 14/3;
14 > 3 => improper fraction

Rewrite:
14 ÷ 3 = 4 and remainder = 2 =>
14/3 = (4 × 3 + 2)/3 = 4 + 2/3 =
= 4 2/3, mixed number (mixed fraction)
Nov 25 19:33 UTC (GMT)
630/180 = (630 ÷ 90)/(180 ÷ 90) = 7/2;
7 > 2 => improper fraction

Rewrite:
7 ÷ 2 = 3 and remainder = 1 =>
7/2 = (3 × 2 + 1)/2 = 3 + 1/2 =
= 3 1/2, mixed number (mixed fraction)
Nov 25 19:33 UTC (GMT)
47/4 already reduced (simplified) to lowest terms
47 > 4 => improper fraction

Rewrite:
47 ÷ 4 = 11 and remainder = 3 =>
47/4 = (11 × 4 + 3)/4 = 11 + 3/4 =
= 11 3/4, mixed number (mixed fraction)
Nov 25 19:33 UTC (GMT)
88/72 = (88 ÷ 8)/(72 ÷ 8) = 11/9;
11 > 9 => improper fraction

Rewrite:
11 ÷ 9 = 1 and remainder = 2 =>
11/9 = (1 × 9 + 2)/9 = 1 + 2/9 =
= 1 2/9, mixed number (mixed fraction)
Nov 25 19:33 UTC (GMT)
38/7 already reduced (simplified) to lowest terms
38 > 7 => improper fraction

Rewrite:
38 ÷ 7 = 5 and remainder = 3 =>
38/7 = (5 × 7 + 3)/7 = 5 + 3/7 =
= 5 3/7, mixed number (mixed fraction)
Nov 25 19:33 UTC (GMT)
999/185 = (999 ÷ 37)/(185 ÷ 37) = 27/5;
27 > 5 => improper fraction

Rewrite:
27 ÷ 5 = 5 and remainder = 2 =>
27/5 = (5 × 5 + 2)/5 = 5 + 2/5 =
= 5 2/5, mixed number (mixed fraction)
Nov 25 19:33 UTC (GMT)
36,541/60 already reduced (simplified) to lowest terms
36,541 > 60 => improper fraction

Rewrite:
36,541 ÷ 60 = 609 and remainder = 1 =>
36,541/60 = (609 × 60 + 1)/60 = 609 + 1/60 =
= 609 1/60, mixed number (mixed fraction)
Nov 25 19:33 UTC (GMT)
1/1,888,458 already reduced (simplified) to lowest terms Nov 25 19:33 UTC (GMT)
184/248 = (184 ÷ 8)/(248 ÷ 8) = 23/31 Nov 25 19:33 UTC (GMT)
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Tutoring: simplifying ordinary math fractions (reducing to the lowest terms)

Steps to simplify an ordinary fraction, to reduce it to its lowest terms:

  • 1) Factor both the numerator and the denominator of the fraction into prime factors.
  • 2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.
  • 3) Divide both the numerator and the denominator of the fraction by the greatest common factor, GCF (GCD).
  • In conclusion: the fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
  • A fraction reduced to its lowest terms cannot be further reduced and it is called an irreducible fraction.

Read the full article >> Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples


Why reducing (simplifying) fractions to lower terms?

  • When running operations with fractions we are often required to bring them to the same denominator, for example when adding, subtracting or comparing.
  • Sometimes both the numerators and the denominators of those fractions are large numbers and doing calculations with such numbers could be difficult.
  • By simplifying (reducing) a fraction, both the numerator and denominator of a fraction are reduced to smaller values. Well, these values are much easier to work with, reducing the overall effort of working with fractions.

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples