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Linux podcast recording software. There are two cases regarding the denominators when we subtract ordinary fractions:

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

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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

• ³/₁₈ + ⁴/₁₈ - ⁵/₁₈ = ^{(3 + 4 - 5)}/₁₈ = ²/₁₈;

• We simply subtracted the numerators of the fractions: 3 + 4 - 5 = 2;
• The denominator of the resulting fraction is: 18;

• The resulting fraction is being reduced as: ²/₁₈ = ^{(2 ÷ 2)}/_{(18 ÷ 2)} = ¹/₉.

• How to reduce (simplify) the common fraction ²/₁₈?

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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).

  • Factor the numerator and the denominator of each fraction, break them down to prime factors (run their prime factorization).
  • Calculate GCF, the greatest common factor of the numerator and of the denominator of each fraction.
  • GCF is the product of all the unique common prime factors of the numerator and of the denominator, multiplied by the lowest exponents.
  • Divide the numerator and the denominator of each fraction by their GCF - after this operation the fraction is reduced to its lowest terms equivalent.

• 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.

• 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.

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