1/2 - 1/3 = ? Subtracting Common (Ordinary) Fractions, Online Calculator. Subtraction Operation Explained Step by Step

Fractions' subtraction: 1/2 - 1/3 = ?

Perform the operation of calculating the fractions.

To add or subtract fractions we need them to have equal denominators (the same common denominator).

  • To perform the operation of calculating the fractions we have to:
  • 1) find their common denominator
  • 2) then calculate the expanding number of each fraction
  • 3) then make their denominators the same by expanding the fractions to equivalent forms - which all have equal denominators (the same denominator)

  • * The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.
  • The LCM will be the common denominator of the fractions that we work with.

1) Find the common denominator
Calculate the LCM of the denominators:

The prime factorization of the denominators:

2 is a prime number

3 is a prime number

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

LCM (2; 3) = 2 × 3 = 6


External link » Calculate LCM, the least common multiple of numbers, online calculator


2) Calculate the expanding number of each fraction:

Divide the LCM by the denominator of each fraction.

1/2 ⟶ 6 ÷ 2 = (2 × 3) ÷ 2 = 3

- 1/3 ⟶ 6 ÷ 3 = (2 × 3) ÷ 3 = 2


3) Make fractions' denominators the same:

  • Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above. This way all the fractions will have the same denominator.
  • Then keep the common denominator and work only with the numerators of the fractions.

1/2 - 1/3 =

(3 × 1)/(3 × 2) - (2 × 1)/(2 × 3) =

3/6 - 2/6 =

(3 - 2)/6 =

1/6


Rewrite the fraction

As a decimal number:

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


1/6 =

1 ÷ 6 ≈

0.166666666667 ≈

0.17

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.

0.166666666667 =

0.166666666667 × 100/100 =

(0.166666666667 × 100)/100 =

16.666666666667/100 ≈

16.666666666667% ≈

16.67%


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)
1/2 - 1/3 = 1/6

As a decimal number:
1/2 - 1/3 ≈ 0.17

As a percentage:
1/2 - 1/3 ≈ 16.67%

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:
- 10/14 + 7/13

Subtract common ordinary fractions, online calculator:

More on ordinary (common) fractions / theory: