47/9 + 117/9 = ? Adding Ordinary (Simple, Common) Math Fractions Calculator, Addition Explained Step by Step

The executed operation (with ordinary fractions):
47/9 + 117/9

Equal denominators fractions, work only with numerators:

47/9 + 117/9 =


(47 + 117)/9 =


164/9

Reduce (simplify) fraction to its lowest terms equivalent:

164/9 already reduced to the lowest terms.


The numerator and the denominator have no common prime factors.


Their prime factorization:


164 = 22 × 41;


9 = 32;

Reduce (simplify) fractions to their simplest form, online calculator


Rewrite the fraction

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

Mixed number = a whole number and a proper fraction, of the same sign.


Proper fraction = numerator smaller than denominator.


164 ÷ 9 = 18 and remainder = 2 =>


164 = 18 × 9 + 2 =>


164/9 =


(18 × 9 + 2)/9 =


18 + 2/9 =


18 2/9

As a decimal number:

18 + 2/9 =


18 + 2 ÷ 9 ≈


18.222222222222 ≈


18.22

As a percentage:

18.222222222222 =


18.222222222222 × 100/100 =


(18.222222222222 × 100)/100 =


1,822.222222222222/100


1,822.222222222222% ≈


1,822.22%

>> Convert fractions to percentages, online calculator


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

As a positive improper fraction (numerator >= denominator):
47/9 + 117/9 = 164/9

As a mixed number (also called a mixed fraction):
47/9 + 117/9 = 18 2/9

As a decimal number:
47/9 + 117/9 ≈ 18.22

As a percentage:
47/9 + 117/9 ≈ 1,822.22%

How to add the ordinary fractions:
- 56/16 + 127/11

Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark; numbers rounded to max. 12 decimals (whenever the case);

Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; ≈ approximation;

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How to: Adding ordinary (simple, common) math 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

  • 3/18 + 4/18 + 5/18 = (3 + 4 + 5)/18 = 12/18;

  • We simply added the numerators of the fractions: 3 + 4 + 5 = 12;
  • The denominator of the resulting fraction is: 18;
  • The resulting fraction is being reduced: 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3.

  • How to reduce (simplify) the common fraction 12/18?

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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