31/2 - 21/2 = ? Subtracting ordinary (common) fractions, online calculator, subtraction operation explained step by step. The answer, written in three ways. As a positive integer number. As a positive improper fraction (the denominator = 1). As a percentage.

31/2 - 21/2 = ?

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.


31/2 - 21/2 =


(31 - 21)/2 =


10/2

Fully reduce (simplify) the fraction to its lowest terms equivalent:

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


A fully reduced (simplified) fraction 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:


10 = 2 × 5


2 is a prime number


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 (10; 2) = GCF (2 × 5; 2) = 2


The fraction can be reduced (simplified):

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


10/2 =


(2 × 5)/2 =


((2 × 5) ÷ 2)/(2 ÷ 2) =


5/1 =


5/1 =


5



Rewrite the equivalent simplified operation:

10/2 =


5


Rewrite the intermediate result

As a positive improper fraction:
(the denominator = 1)

An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.


5 = 5/1

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.


5 =


5 × 100/100 =


(5 × 100)/100 =


500/100 =


500%



The final answer:
:: written in three ways ::

As a positive integer number:
31/2 - 21/2 = 5

As a positive improper fraction:
(the denominator = 1)
31/2 - 21/2 = 5/1

As a percentage:
31/2 - 21/2 = 500%

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:
40/10 - 30/6

Subtract common ordinary fractions, online calculator:

Fractions subtractions: the latest fractions subtracted by the users

How to: Subtracting ordinary (simple, common) math fractions. Steps.

There are two cases regarding the denominators when we subtract ordinary fractions:

  • A. the fractions have like denominators;
  • B. the fractions have unlike denominators.

A. How to subtract ordinary fractions that have like denominators?

  • Simply subtract the numerators of the fractions.
  • The denominator of the resulting fraction will be the common denominator of the fractions.
  • Reduce the resulting fraction.

An example of subtracting ordinary fractions that have like denominators, with explanations

B. To subtract fractions with different denominators (unlike denominators), build up the fractions to the same denominator. How is it done?

  • 1. Reduce the fractions to the lowest terms (simplify them).

  • 2. Calculate the least common multiple, LCM, of all the fractions\' new denominators:

    • LCM is going to be the common denominator of the added fractions, also called the lowest common denominator (the least common denominator).
    • Factor all the new denominators of the reduced fractions (run the prime factorization).
    • The least common multiple, LCM, is the product of all the unique prime factors of the denominators, multiplied by the largest exponents.
    • Calculate LCM, the least common multiple of numbers, online.

  • 3. Calculate each fraction\'s expanding number:

    • The expanding number is the non-zero number that will be used to multiply both the numerator and the denominator of each fraction, in order to build all the fractions up to the same common denominator.
    • Divide the least common multiple, LCM, calculated above, by the denominator of each fraction, in order to calculate each fraction\'s expanding number.
  • 4. Expand each fraction:

    • Multiply each fraction\'s both numerator and denominator by the expanding number.
    • At this point, fractions are built up to the same denominator.
  • 5. Subtract the fractions:

    • In order to subtract all the fractions simply subtract all the fractions\' numerators.
    • The end fraction will have as a denominator the least common multiple, LCM, calculated above.
  • 6. Reduce the end fraction to the lowest terms, if needed.


Read the rest of this article, here > How to subtract ordinary (common) fractions

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