Subtract fractions: - 21/6 - 33/22 = ? Subtraction of ordinary (simple, common) fractions, result explained

The executed operation (with ordinary fractions):
- 21/6 - 33/22

Reduce (simplify) fractions to their lowest terms equivalents:

Fraction: - 21/6 = - (3 × 7)/(2 × 3) = - ((3 × 7) ÷ 3)/((2 × 3) ÷ 3) = - 7/2;


Fraction: - 33/22 = - (3 × 11)/(2 × 11) = - ((3 × 11) ÷ 11)/((2 × 11) ÷ 11) = - 3/2;

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


Rewrite the equivalent simplified operation:

- 21/6 - 33/22 =


- 7/2 - 3/2

Equal denominators fractions, work only with numerators:

- 7/2 - 3/2 =


( - 7 - 3)/2 =


- 10/2

Reduce (simplify) fraction to its lowest terms equivalent:

- 10/2 =


- (2 × 5)/2 =


- ((2 × 5) ÷ 2)/(2 ÷ 2) =


- 5/1 =


- 5

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


Rewrite the equivalent simplified operation:

- 10/2 =


- 5

Rewrite the expression:

As a negative improper fraction (denominator = 1):

- 5 = - 5/1

As a percentage:

- 5 =


- 5 × 100/100 =


( - 5 × 100)/100 =


- 500/100 =


- 500%

>> Convert fractions to percentages, online calculator


The final answer:
:: written in three ways ::

As a negative integer number:
- 21/6 - 33/22 = - 5

As a negative improper fraction (denominator = 1):
- 21/6 - 33/22 = - 5/1

As a percentage:
- 21/6 - 33/22 = - 500%

How to add the ordinary fractions:
29/12 + 45/25

Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark;

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

Subtract ordinary fractions, online calculator

The latest subtracted fractions

- 21/6 - 33/22 = ? Jun 01 15:13 UTC (GMT)
- 31/6,267 - 21/10 = ? Jun 01 15:13 UTC (GMT)
3/5 - 1/3 = ? Jun 01 15:13 UTC (GMT)
19/20 - 4/5 = ? Jun 01 15:13 UTC (GMT)
6 - 1/5 = ? Jun 01 15:13 UTC (GMT)
- 47/107 - 89/37 = ? Jun 01 15:12 UTC (GMT)
9/10 - 3/14 = ? Jun 01 15:12 UTC (GMT)
141/4 - 7 = ? Jun 01 15:12 UTC (GMT)
- 24/100 - 19/31 = ? Jun 01 15:12 UTC (GMT)
3/5 - 1/3 = ? Jun 01 15:12 UTC (GMT)
27/509 + 74 = ? Jun 01 15:12 UTC (GMT)
324/56,327 + 56 = ? Jun 01 15:12 UTC (GMT)
1/6 - 7/12 = ? Jun 01 15:11 UTC (GMT)
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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.

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

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