Tag: ratio and proportions

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$.
$\therefore$ the subtriplicate ratio of $8x^{3} : y^{3}$ is $\sqrt [3]{8x^{3}} : \sqrt [3]{y^{3}} = 2x : y$

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $64 m^{6} : 27 n^{3}$ is $\sqrt [3]{64m^{6}} : \sqrt [3]{27n^{3}}$
$= 4m^{2} : 3n$

The subduplicate ratio of $a : b$ is $\sqrt {a} : \sqrt {b}$
$\therefore$ The subduplicate ratio of $121 : 100$ is $\sqrt {121} : \sqrt {100} = 11 : 10$

The subduplicate ratio of $\dfrac {1}{4} : \dfrac {1}{36}$ is $\sqrt {\dfrac {1}{4}} : \sqrt {\dfrac {1}{36}} = \dfrac {1}{2} : \dfrac {1}{6}$

The subduplicate ratio of $a : b$ is $\sqrt {a} : \sqrt {b}$
$\therefore$ The subduplicate ratio of $x^{4} : y^{4}$ is $\sqrt {x^{4}} : \sqrt {y^{4}} = x^{2} : y^{2}$.

The subduplicate ratio of $x^{4} : y^{2}$ is $\sqrt {x^{4}} : \sqrt {y^{2}} = x^{2} : y$

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $27 : 125$ is $\sqrt [3]{27} : \sqrt [3]{125} = 3 : 5$.

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $a^{3} : b^{3}$ is $\sqrt [3]{a^{3}} : \sqrt [3]{b^{3}} = a : b$.

The reciprocal ratio of $a : b$ is $b : a$
$\therefore$ reciprocal ratio of $39 : 41$ is $41 : 39$

$a : b = 1 : 1$ and $b : c = 81 : 24$
$\therefore \dfrac {a}{b} \times \dfrac {b}{c} = \dfrac {1}{1} \times \dfrac {81}{24} = \dfrac {27}{8}$
$\therefore a : c = 27 : 8$
$\therefore$ The subtriplicate ratio of $27 : 8$ is $\sqrt [3]{27} : \sqrt [3]{8} = 3 : 2$