Subtract fractions: - 13/13 - 35/12 = ? Subtraction of ordinary (simple, common) fractions, result explained

The executed operation (with ordinary fractions):
- 13/13 - 35/12

Reduce (simplify) fractions to their lowest terms equivalents:

Fraction: - 13/13 = - (13 ÷ 13)/(13 ÷ 13) = - 1/1 = - 1;


Fraction: - 35/12 already reduced to the lowest terms.
The numerator and the denominator have no common prime factors.
Their prime factorization:
35 = 5 × 7;
12 = 22 × 3;

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


Rewrite the equivalent simplified operation:

- 13/13 - 35/12 =


- 1 - 35/12

Rewrite the expression:

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

- 1 - 35/12 =


( - 1 × 12)/12 - 35/12 =


( - 1 × 12 - 35)/12 =


- 47/12

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.


- 47 ÷ 12 = - 3 and remainder = - 11 =>


- 47 = - 3 × 12 - 11 =>


- 47/12 =


( - 3 × 12 - 11)/12 =


( - 3 × 12)/12 - 11/12 =


- 3 - 11/12 =


- 3 11/12

As a decimal number:

- 3 - 11/12 =


- 3 - 11 ÷ 12 ≈


- 3.916666666667 ≈


- 3.92

As a percentage:

- 3.916666666667 =


- 3.916666666667 × 100/100 =


( - 3.916666666667 × 100)/100 =


- 391.666666666667/100


- 391.666666666667% ≈


- 391.67%

>> Convert fractions to percentages, online calculator


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

As a negative improper fraction (numerator >= denominator):
- 13/13 - 35/12 = - 47/12

As a mixed number (also called a mixed fraction):
- 13/13 - 35/12 = - 3 11/12

As a decimal number:
- 13/13 - 35/12 ≈ - 3.92

As a percentage:
- 13/13 - 35/12 ≈ - 391.67%

How to subtract the ordinary fractions:
- 16/15 + 47/21

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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