How to reduce (simplify) the common ordinary fraction 60/4,415 to the lowest terms, to the simplest equivalent form, irreducible, with the smallest possible numerator and denominator? The result written: As a proper fraction. As a decimal number. As a percentage %

Reduce (simplify) the common ordinary fraction: 60/4,415

Detailed calculations and explanations, below

Common ordinary fractions. Introduction:

A common ordinary fraction is made up of two integer numbers and a fraction bar: 60/4,415


The integer number above the bar is called the numerator: 60


The integer number below the bar is called the denominator: 4,415


The fraction bar means that the numerator is dividing by the denominator.


To get the fraction's value divide the numerator by the denominator:
The value = 60 ÷ 4,415



To completely reduce a fraction to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF

To calculate the greatest common factor, GCF:

1. Factor the numerator and the denominator (into prime factors), build their prime factorizations.


2. Multiply all their common prime factors, taken by the lowest exponents.


1. Factor the numerator and the denominator:

To factor a number (into prime factors) - or, in other words, to break it down to prime factors - or, in other words, to build its prime factorization: find the prime numbers that multiply together to get that number.

Example 1: 6 = 2 × 3.
Example 2: 24 = 2 × 2 × 2 × 3 = 23 × 3.


Exponential notation. In the second example, 23 is the writing in exponential notation of the repeating multiplication: 2 × 2 × 2. 23 is called the power, 2 is the base, 3 is the exponent and 8 is the value of the power: 23 = 8.


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


The prime factorizations:


Written with exponents:
60 = 2 × 2 × 3 × 5 = 22 × 3 × 5
60 is a composite number.


4,415 = 5 × 883
4,415 is a composite number.



2. Multiply all the common prime factors:

Multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).


GCF (22 × 3 × 5; 5 × 883) = 5



Reduce (simplify) the common ordinary fraction: 60/4,415

Divide the numerator and the denominator by their GCF:

60/4,415 =


(22 × 3 × 5)/(5 × 883) =


((22 × 3 × 5) ÷ 5) / ((5 × 883) ÷ 5) =


(22 × 3)/883 =


12/883


The fraction is now reduced to the lowest terms equivalent.


The fraction is called irreducible and it has the smallest possible numerator and denominator.


* When it's 1, the denominator of the fraction can be omitted.


Why do we try to simplify fractions?

By reducing the values of the numerator and of the denominator of a fraction the calculations with that fraction are easier to do.


The fraction 12/883 is a positive proper fraction (the numerator < the denominator).


Rewrite the fraction

As a decimal number:

Simply divide the numerator by the denominator, without a remainder, as shown below:


12/883 =


12 ÷ 883 =


0.013590033975 ≈


0.01

As a percentage:

A percentage value p% is equal to the fraction: p/100, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.


To do that, multiply the number by the fraction 100/100.


The value of the fraction 100/100 = 1, so by multiplying the number by this fraction the result is not changing, only the form.


0.013590033975 =


0.013590033975 × 100/100 =


1.359003397509/100 =


1.359003397509% ≈


1.36%


In other words:


(+) Calculate the fraction's value, (+) multiply that number by 100, and (+) add the percent sign % to it.


External link > Convert and write integer and decimal numbers, fractions and ratios as percentages, online calculator


The final answer:
written in three ways

As a positive proper fraction:
(the numerator < the denominator):
60/4,415 = 12/883

As a decimal number:
60/4,4150.01

As a percentage:
60/4,4151.36%

How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

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Read the rest of the article > How to reduce (simplify) common ordinary fractions to the lowest terms, to the simplest equivalent form, irreducible

More on ordinary (common) fractions / theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Changing the form of fractions, by expanding or reducing (simplifying)


(3) How to reduce fractions (simplifying). The greatest common factor, GCF


(4) How to compare two fractions with unlike (different) numerators and denominators


(5) How to sort out fractions in ascending order


(6) Adding common (ordinary) fractions


(7) Subtracting common (ordinary) fractions


(8) Multiplying common (ordinary) fractions


(9) Fractions as rational numbers