How to reduce (simplify) the common ordinary fraction 6/90 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: 6/90

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.


The prime factorizations:


6 = 2 × 3
6 is a composite number.


Written with exponents:
90 = 2 × 3 × 3 × 5 = 2 × 32 × 5
90 is a composite number.


Exponential notation. 23 is the writing in exponential notation of the repeating multiplication: 2 × 2 × 2. Also: 23 is called the power. 2 is the base. 3 is the exponent. 8 is the value of the power: 23 = 8.


Prime number: a positive integer that is dividing evenly (without a remainder) only by itself and 1. A prime number has only two factors. Composite number: a positive integer that has at least one factor (divisor) other than 1 and itself.


External link » Check whether numbers are prime or not. Factor (decompose) composite numbers into prime factors, online calculator


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).

External link » Calculate the greatest common factor, gcf, of two numbers, online calculator

GCF (2 × 3; 2 × 32 × 5) = 2 × 3


Reduce (simplify) the common ordinary fraction: 6/90

Divide the numerator and the denominator by their GCF.

6/90 =


(2 × 3)/(2 × 32 × 5) =


((2 × 3) ÷ (2 × 3)) / ((2 × 32 × 5) ÷ (2 × 3)) =


1/(3 × 5) =


1/15


The fraction is now reduced to the lowest terms equivalent.

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

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


The fraction 1/15 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:


1/15 =


1 ÷ 15 =


0.066666666667 ≈


0.07

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.


0.066666666667 =


0.066666666667 × 100/100 =


6.666666666667/100 =


6.666666666667% ≈


6.67%


In other words:


(1) Calculate the fraction's value, (2) multiply that number by 100, and (3) 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):
6/90 = 1/15

As a decimal number:
6/900.07

As a percentage:
6/906.67%

More operations like this:

» Reduce (simplify) the common ordinary fraction: -5/82

» Reduce (simplify) the common ordinary fraction: 21/97


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

Reduce (simplify) common ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

Fractions reducing (simplifying) to the lowest terms, to the simplest equivalent form, irreducible. 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.
  • External link > 1) Calculate all the factors (divisors) of a number, or 2) Find all the common factors of two numbers, online calculator.

  • 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 (simplify) common ordinary fractions to the lowest terms, to the simplest equivalent form, irreducible, with the smallest possible numerator and denominator. Online calculator


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