13/21 - 6/21 = ? Subtracting Common (Ordinary) Fractions, Online Calculator. Subtraction Operation Explained Step by Step

Fractions' subtraction: 13/21 - 6/21 = ?

Perform the operation of calculating the fractions

All the fractions have equal denominators (the same denominator):

  • This is the simplest and happiest case when we add or subtract fractions.
  • We work only with their numerators and keep the common denominator.

13/21 - 6/21 =

(13 - 6)/21 =

7/21

Reduce (simplify) the fraction to its lowest terms equivalent:

  • To reduce a fraction to its lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.
  • A fraction that was reduced (simplified) to the lowest terms is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.

Calculate the greatest common factor, GCF,
of the numerator and denominator of the fraction:

  • The prime factorizations of the numerator and denominator:
  • 7 is a prime number
  • 21 = 3 × 7

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 (7; 21) = GCF (7; 3 × 7) = 7

The fraction can be reduced (simplified):

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


7/21 =

(7 ÷ 7)/(21 ÷ 21) =

1/3


We could have simplified the fraction without calculating the GCF. Just factor the numerator and denominator and cross out the common prime factors.


7/21 =

7/(3 × 7) =

(7 ÷ 7)/((3 × 7) ÷ 7) =

1/3 =

1/3


Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator


Rewrite the equivalent simplified operation:

7/21 =

1/3


Rewrite the fraction

As a decimal number:

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


1/3 =

1 ÷ 3 ≈

0.333333333333 ≈

0.33

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.

0.333333333333 =

0.333333333333 × 100/100 =

(0.333333333333 × 100)/100 =

33.333333333333/100 ≈

33.333333333333% ≈

33.33%


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)
13/21 - 6/21 = 1/3

As a decimal number:
13/21 - 6/21 ≈ 0.33

As a percentage:
13/21 - 6/21 ≈ 33.33%

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). The symbols used: '/' fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

Other similar operations:

How to subtract the common ordinary fractions:
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Subtract common ordinary fractions, online calculator:

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