Subtract fractions: - 100/477 + 5 = ? Subtraction of ordinary (simple, common) fractions, result explained

The executed operation (with ordinary fractions):
- 100/477 + 5

Reduce (simplify) fractions to their lowest terms equivalents:

Fraction: - 100/477 already reduced to the lowest terms.
The numerator and the denominator have no common prime factors.
Their prime factorization:
100 = 22 × 52;
477 = 32 × 53;

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


Rewrite the expression:

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

5 - 100/477 =


(5 × 477)/477 - 100/477 =


(5 × 477 - 100)/477 =


2,285/477

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.


2,285 ÷ 477 = 4 and remainder = 377 =>


2,285 = 4 × 477 + 377 =>


2,285/477 =


(4 × 477 + 377)/477 =


(4 × 477)/477 + 377/477 =


4 + 377/477 =


4 377/477

As a decimal number:

4 + 377/477 =


4 + 377 ÷ 477 ≈


4.79035639413 ≈


4.79

As a percentage:

4.79035639413 =


4.79035639413 × 100/100 =


(4.79035639413 × 100)/100 =


479.035639412998/100 =


479.035639412998% ≈


479.04%

>> Convert fractions to percentages, online calculator


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

As a positive improper fraction (numerator >= denominator):
- 100/477 + 5 = 2,285/477

As a mixed number (also called a mixed fraction):
- 100/477 + 5 = 4 377/477

As a decimal number:
- 100/477 + 5 ≈ 4.79

As a percentage:
- 100/477 + 5 ≈ 479.04%

How to subtract the ordinary fractions:
109/483 - 10/3

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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