# Modulo over rational numbers

The calculator performs modulo division over rational dividend and rational divisor.

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Created: 2021-01-28 11:54:14, Last updated: 2021-02-24 12:19:41

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The calculator performs integer division with remainder. Both the dividend and the divisor can be rational numbers. It displays the integer quotient and the rational remainder (modulo). The calculator outputs an integer quotient and a rational remainder (modulo).

#### Modulo over rational numbers

Remainder

Quotient

Given two rational numbers $a=\frac{n_1}{d_1}, b=\frac{n_2}{d_2}$ find the quotient and the remainder of division a/b:
The quotient can be obtained as:
$q = \left\lfloor\frac{{n_1}{d_2}}{{d_1}{n_2}}\right\rfloor$
The remainder can be obtained as:
$r = \frac{n_1}{d_1} - q \frac{d_2}{n_2}$

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PLANETCALC, Modulo over rational numbers