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Calculator with Fractions

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

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Calculator with Fractions -

Tag(s) : Symbolic Computation

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# Calculator with Fractions

## Fractions Calculator

 Mode Combine over a common denominator/quotient Decompose into a sum of irreductible fractions Simplify by removing common factors Simplify the fraction to the maximum

### What is a fraction? (Definition)

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.

### How to simplify fractions to irreducible form?

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 allows to check results of school exercises and will soon display the calculation step by step, meanwhile, use LCM and GCD tools.

### How to reduce to the same denominator?

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

### How to subtract fractions?

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

### How to multiply fractions?

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

### How to divide fractions?

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.

## Source code

dCode retains ownership of the "Calculator with Fractions" source code. Except explicit open source licence (indicated Creative Commons / free), the "Calculator with Fractions" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Calculator with Fractions" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Calculator with Fractions" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
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Cite as source (bibliography):
Calculator with Fractions on dCode.fr [online website], retrieved on 2024-06-18, https://www.dcode.fr/fractions-calculator

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