Mathematics: The product of two rational numbers rational number

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The product of two rational numbers rational

BossKnight

06.01.2022

Always. Rational numbers are closed under multiplication, because integers are: two rational numbers can be written as

$\dfrac{a}{b},\quad \dfrac{c}{d}$

Their product is

$\dfrac{a\cdot c}{b\cdot d}$

And both $a\cdot c$ and $b\cdot d$ are integers, because they are multiplications of integers.

So,

$\dfrac{a\cdot c}{b\cdot d}$

is still a division between integers, and thus a rational.

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