8/12 + 5/12 = ? Adding ordinary (common) fractions, online calculator, addition operation explained step by step. The answer, written in four ways. As a positive improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage.

8/12 + 5/12 = ?

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.


8/12 + 5/12 =


(8 + 5)/12 =


13/12

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.


13/12 is already reduced to the lowest terms.


The numerator and denominator have no common prime factors.


Their prime factorization:

13 is a prime number

12 = 22 × 3


GCF (13; 22 × 3) = 1



Rewrite the fraction

As a mixed number (also called a mixed fraction):

A mixed number: a whole number and a proper fraction, both having the same sign.


A proper fraction: the value of the numerator is smaller than the value of the denominator.


Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:


13 ÷ 12 = 1 and the remainder = 1 ⇒


13 = 1 × 12 + 1 ⇒


13/12 =


(1 × 12 + 1)/12 =


1 + 1/12 =


1 1/12

As a decimal number:

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


1 + 1/12 =


1 + 1 ÷ 12 ≈


1.083333333333 ≈


1.08

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.


1.083333333333 =


1.083333333333 × 100/100 =


(1.083333333333 × 100)/100 =


108.333333333333/100


108.333333333333% ≈


108.33%



The final answer:
:: written in four ways ::

As a positive improper fraction:
(the numerator >= the denominator)
8/12 + 5/12 = 13/12

As a mixed number (also called a mixed fraction):
8/12 + 5/12 = 1 1/12

As a decimal number:
8/12 + 5/12 ≈ 1.08

As a percentage:
8/12 + 5/12 ≈ 108.33%

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 add the common ordinary fractions:
- 16/23 + 9/24

Add common ordinary fractions, online calculator:

Fractions additions: the latest fractions added by the users

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

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

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

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

  • Simply add 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 adding ordinary fractions that have like denominators, with explanations

B. To add 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 (simplifying).

  • 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.
    • 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, taken by the largest exponents.
    • Calculate LCM, the least common multiple of numbers.

  • 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 each fraction's denominator, in order to calculate each fraction's expanding number.
  • 4. Expand each fraction:

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

    • In order to add all the fractions simply add 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 add ordinary (common) fractions

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