Subtract fractions, online calculator: subtracting simple (common, ordinary) equal (like) or different (unlike) denominators math fractions, explanations

Subtract ordinary fractions, online calculator

The latest subtracted fractions

391,000 - 1 = ? Nov 19 08:06 UTC (GMT)
320/321 - 1/7 = ? Nov 19 08:06 UTC (GMT)
53/71 - 28/70 = ? Nov 19 08:06 UTC (GMT)
7/75 - 25/50 = ? Nov 19 08:06 UTC (GMT)
7/12 - 3/8 = ? Nov 19 08:06 UTC (GMT)
7/12 - 3/8 = ? Nov 19 08:06 UTC (GMT)
13/565 + 7 = ? Nov 19 08:06 UTC (GMT)
2/3 - 5/18 = ? Nov 19 08:06 UTC (GMT)
7/12 - 3/8 = ? Nov 19 08:06 UTC (GMT)
- 14/13 - 6/20 = ? Nov 19 08:05 UTC (GMT)
112/11 - 11/12 = ? Nov 19 08:05 UTC (GMT)
5/8 - 7/16 = ? Nov 19 08:05 UTC (GMT)
7/12 - 3/8 = ? Nov 19 08:05 UTC (GMT)
see more... subtracted fractions

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

  • 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?

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.

An example of subtracting fractions that have different denominators (unlike denominators), step by step explanations

  • 6/90 + 16/24 - 30/75 = ?

  • 1. Reduce the fractions to the lowest terms (simplify them):

    • 6/90 = (2 × 3) / (2 × 32 × 5) = ((2 × 3) ÷ (2 × 3)) / ((2 × 32 × 5) ÷ (2 × 3)) = 1/(3 × 5) = 1/15


      16/24 = 24 / (23 × 3) = (24 ÷ 23) / ((23 × 3) ÷ 23) = 2/3


      30/75 = (2 × 3 × 5) / (3 × 52) = ((2 × 3 × 5) ÷ (3 × 5)) / ((3 × 25) ÷ (3 × 5)) = 2/5


      The reduced fractions: 6/90 + 16/24 - 30/75 = 1/15 + 2/3 - 2/5

  • 2. Calculate the least common multiple, LCM, of all the fractions' new denominators

    • Factor all the denominators, break them down to their prime factors, then multiply all these prime factors, uniquely, by the largest exponents.
    • 15 = 3 × 5


      3 is already a prime number, it cannot be factored anymore


      5 is a prime number, it cannot be factored anymore


      LCM (15, 3, 5) = LCM (3 × 5, 3, 5) = 3 × 5 = 15

  • 3. Calculate each fraction's expanding number:

    • Divide the least common multiple, LCM, by the denominator of each fraction.
    • For the first fraction: 15 ÷ 15 = 1


      For the second fraction: 15 ÷ 3 = 5


      For the third fraction: 15 ÷ 5 = 3

  • 4. Expand each fraction:

    • Multiply both the numerator and the denominator of each fraction by their expanding number.
    • The first fraction stays unchanged: 1/15 = (1 × 1)/(1 × 15) = 1/15


      The second fraction expands to: 2/3 = (5 × 2)/(5 × 3) = 10/15


      The third fraction expands to: 2/5 = (3 × 2)/(3 × 5) = 6/15

  • 5. Subtract the fractions:

    • Simply subtract the numerators of the fractions. The denominator = LCM.
    • 6/90 + 16/24 - 30/75 = 1/15 + 2/3 - 2/5 = 1/15 + 10/15 - 6/15 = (1 + 10 - 6) / 15 = 5/15

  • 6. Reduce the end fraction to the lowest terms, if needed.

    • 5/15 = (5 ÷ 5)/(15 ÷ 5) = 1/3

More on ordinary (common) math fractions theory: