Subtract fractions: 172/16,154 - 21/3 = ? Subtraction of ordinary (simple, common) fractions, result explained

The executed operation (with ordinary fractions):
172/16,154 - 21/3

Reduce (simplify) fractions to their lowest terms equivalents:

Fraction: 172/16,154 = (22 × 43)/(2 × 41 × 197) = ((22 × 43) ÷ 2)/((2 × 41 × 197) ÷ 2) = 86/8,077;


Fraction: - 21/3 = - (3 × 7)/3 = - ((3 × 7) ÷ 3)/(3 ÷ 3) = - 7/1 = - 7;

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


Rewrite the equivalent simplified operation:

172/16,154 - 21/3 =


86/8,077 - 7 =


- 7 + 86/8,077

Rewrite the expression:

As a negative improper fraction (numerator >= denominator):

- 7 + 86/8,077 =


( - 7 × 8,077)/8,077 + 86/8,077 =


( - 7 × 8,077 + 86)/8,077 =


- 56,453/8,077

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.


- 56,453 ÷ 8,077 = - 6 and remainder = - 7,991 =>


- 56,453 = - 6 × 8,077 - 7,991 =>


- 56,453/8,077 =


( - 6 × 8,077 - 7,991)/8,077 =


( - 6 × 8,077)/8,077 - 7,991/8,077 =


- 6 - 7,991/8,077 =


- 6 7,991/8,077

As a decimal number:

- 6 - 7,991/8,077 =


- 6 - 7,991 ÷ 8,077 ≈


- 6.989352482357 ≈


- 6.99

As a percentage:

- 6.989352482357 =


- 6.989352482357 × 100/100 =


( - 6.989352482357 × 100)/100 =


- 698.935248235731/100


- 698.935248235731% ≈


- 698.94%

>> Convert fractions to percentages, online calculator


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

As a negative improper fraction (numerator >= denominator):
172/16,154 - 21/3 = - 56,453/8,077

As a mixed number (also called a mixed fraction):
172/16,154 - 21/3 = - 6 7,991/8,077

As a decimal number:
172/16,154 - 21/3 ≈ - 6.99

As a percentage:
172/16,154 - 21/3 ≈ - 698.94%

How to subtract the ordinary fractions:
- 181/16,165 - 33/11

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;

Subtract ordinary fractions, online calculator

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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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