Tool/Calculator with fractions and simplification. Calculating with fractions involves specific computation steps for numerator and denominator, before simplifying.

Calculator with Fractions - dCode

Tag(s) : Symbolic Computation

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A fraction (or fractional notation) is a mathematical value composed of a numerator and a denominator generally represented one above the other and separated by a fraction line.

In practice, a fraction is a division, the numerator is the dividend and the denominator is the divisor, the result is sometimes called a quotient.

dCode first performs calculations (addition, subtraction, multiplication or any other calculation of the initial mathematical expression) and makes them irreducible fractions by reducing them to the same denominator. Simplification is given in result, as a fraction in irreducible form.

__Example:__ $$ \frac12 + \frac14 = \frac34 $$

dCode can calculate the LCM least common multiple of the denominators in order to realize additions and subtractions.

__Example:__ If the denominators of the fractions to be added are `8` and `3` then `LCM(8,3)=24` and the fraction should have as denominator 24: `15/8-2/3 = 29/24`

A multiplication of the numerator implies a multiplication of the denominator to preserve the equality of the fraction.

Addition of a fractions requires reducing the fractions to the same denominator (attempting to simplify the fractions beforehand if possible), then adding the numerators (attempting to simplify the resulting fraction if possible).

__Example:__ $$ \frac{1}{2} + \frac{1}{3} = \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} = \frac{3}{6} + \frac{2}{6} = \frac{3+2}{6} = \frac{5}{6} $$

Fractions subtraction is the same as addition, except numerators are subtracted instead of adding them.

__Example:__ $$ \frac{1}{2} - \frac{1}{3} = \frac{1 \times 3}{2 \times 3} - \frac{1 \times 2}{3 \times 2} = \frac{3}{6} - \frac{2}{6} = \frac{3-2}{6} = \frac{1}{6} $$

The multiplication of fractions consists in multiplying the numerator between them then the denominators between them (try to simplify the fractions before and / or after if possible).

__Example:__ $$ \frac{1}{2} \times \frac{2}{3} = \frac{1 \times 2}{2 \times 3} = \frac{2}{6} = \frac{1}{3} $$

The division of fractions can be written as the multiplication of the first fraction by the inverse of the second fraction (inversion of the numerator and the denominator). Then apply the multiplication technique.

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Cite as source (bibliography):

*Calculator with Fractions* on dCode.fr [online website], retrieved on 2024-10-05,

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