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Fraction calculator - adding fractions step by step with explanation

With the Fractions Calculator, you can add any two mixed numbers or proper and improper fractions.
Fractions Calculator will show you the result of operations on fractions step by step and will give you explanations of the operations performed to add fractions. You will learn how to simplify fractions, how to find a common denominator, how to find the least common multiple and the greatest common divisor.

To get the result, enter the appropriate data. If the fraction is a mixed number, enter the integer (it may be negative), as well as the numerator and denominator of the fraction, respectively. If it is a proper or inproper fraction and its value is negative, put a minus sign to the numerator.

Adding fractions

Useful information

Fraction - this is an expression of the form \(\frac{a}{b} \) where \(a \) is numerator the fraction and \(b \) is denominator.
Each fraction is a quotient because its value is the result of dividing the numerator by the denominator.

Improper fraction is a fraction where the numerator is greater than or equal to the denominator.
\( \frac{a}{b} \) gdzie \( a≥b \) e.g. \( \frac{5}{3} \), \( \frac{10}{4} \), \( \frac{3}{3} \), \( \frac{12}{12} \).
Improper fraction can also take the form of a mixed number and can result from dividing the numerator by the denominator with the remainder e.g \( \frac{5}{3} = 1\frac{2}{3} \), \( \frac{10}{4} = 2\frac{1}{2} \).

Proper fraction is a fraction where the numerator is less than the denominator.
\( \frac{a}{b} \) gdzie \( a < b \) e.g \( \frac{3}{5} \), \( \frac{4}{10} \).

Shortening (reducing) a fraction consists in dividing the numerator and denominator by the same number other than zero. By shortening the fraction, we need find the greatest common divisor (GCD) of the numerator and denominator of the fraction. \( \frac{a}{b} = \frac{a : c}{b : c} for c ≠ 0 where c = NWD\) e.g. \( \frac{4}{10} = \frac{4 : 2}{10 : 2} = \frac{2}{5} for NWD=2\).
Fractions are irreducible when we cannot find the greatest common divisor greater than 1 for both the numerator and the denominator.

Expanding the fraction is the multiplication of the numerator and denominator by the same non-zero number. We use the expansion of fractions most often to bring the fractions to a common denominator
\( \frac{a}{b} = \frac{a · c}{b · c} dla c ≠ 0\) e.g \( \frac{3}{5} = \frac{3 · 2}{5 · 2} = \frac{6}{10}\).

Adding fraction

If the fractions have the same denominators, we add the numerators and leave the denominators unchanged.
\( \frac{a}{b} + \frac{c}{b} = \frac{a + c}{b} \) e.g \( \frac{3}{5} + \frac{1}{5} = \frac{4}{5} \)
If fractions have different denominators, we reduce them to a common denominator, and then, remembering about the signs of the fractions, add the numerators, leaving the denominators unchanged. Reducing to the common denominator, we find the least common multiple (LCM) for the denominators.

Fractions - Wikipedia (EN)

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