Монгол Бодлогын Сан

Заавар: $a\cdot b:c=(a\cdot b):c=a\cdot(b:c)$ болохыг ашиглан бодвол илүү хялбар байх болно.

Бодолт: $417\overset{III}{\mathstrut {}\cdot{}}\left(\dfrac2{10}\overset{I}{\mathstrut {}+{}}\dfrac{13}{990}\right)\overset{IV}{\mathstrut {}:{}}\left(\dfrac4{10}\overset{II}{\mathstrut {}+{}}\dfrac{21}{990}\right)$ байна.

I. $\dfrac{2}{10}^{\color{red}{(99}}+\dfrac{13}{990}=\dfrac{198}{990}+\dfrac{13}{990}=\dfrac{198+13}{990}=\dfrac{211}{990}$

II. $\dfrac4{10}^{\color{red}{(99}}+\dfrac{21}{990}=\dfrac{396}{990}+\dfrac{21}{990}=\dfrac{396+21}{990}=\dfrac{417}{990}$

$a\cdot b:c=(a\cdot b):c=a\cdot(b:c)$ тул

III-IV. $\dfrac{211}{990}:\dfrac{417}{990}=\dfrac{211}{990}\cdot\dfrac{990}{417}=\dfrac{211}{417}$ ба $417\cdot\dfrac{211}{417}=211$ байна.