Subtracting common (ordinary) fractions, online calculator: subtract fractions with different (unlike) or equal (like) denominators, by the method of building up their denominators the same (up to a common denominator), by expanding the fractions to equivalent forms. Result and the subtraction process explained

Please check the entered string:
82 - The denominator of the fraction is not an integer.

To add, subtract, multiply or divide - at least two valid fractions are needed.

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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