Write the ratio as a ratio of a whole numbers using fractional notation 6 1/2 to 15 1/6

1 answer:

5 0

$\bf 6\frac{1}{2}:15\frac{1}{6}\qquad 
\begin{cases}
6\frac{1}{2}\implies \cfrac{6\cdot 2+1}{2}\\\\
15\frac{1}{6}\implies \cfrac{15\cdot 6+1}{6}
\end{cases}\implies \cfrac{ \frac{6\cdot 2+1}{2}}{\frac{15\cdot 6+1}{6}}\\\\
-----------------------------\\\\
\cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus
\\\\\\
\cfrac{6\cdot 2+1}{2}\cdot \cfrac{6}{15\cdot 6+1}$

simplify away

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Step-by-step explanation:

${(27 \times 250)}^{ \frac{1}{3} } = {(27 \times 125 \times 2)}^{ \frac{1}{3} } \\ = {27}^{ \frac{1}{3} } \times {125}^{ \frac{1}{3} } \times {2}^{ \frac{1}{3} } \\ = \sqrt[ 3]{27} \times \sqrt[3]{125} \times \sqrt[3]{2} \\ = \sqrt[3]{ {3}^{3} } \times \sqrt[3]{ {5}^{3} } \times \sqrt[3]{2} \\ = 3 \times 5 \times \sqrt[3]{2} \\ = 15 \sqrt[3]{2}$