Prove that 3:8 is equivalent to 12:32

1 answer:

4 0

3:8 can also be written as 3/8

12:32 can also be written as 12/32

$\frac{12}{32} = \frac{3\times 4}{8\times 4} = \frac{3}{8}$

So thus 3:8 is equivalnt to 12:32

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HELP!!!!!

Sonja [21]

First off, let's convert the decimal to a fraction, notice, we have two decimals, so we'll use in the denominator, a 1 with two zeros then, two decimals, two zeros, thus $\bf 1.\underline{75}\implies \cfrac{175}{1\underline{00}}\implies \cfrac{7}{4}\implies \stackrel{ratio}{7:4}$

now, we know then the ratio dimensions for the new photograph,

$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\
\cfrac{7}{4}\implies \cfrac{4+3}{4}\implies \cfrac{4}{4}+\cfrac{3}{4}\implies 1+\boxed{\cfrac{3}{4}}\impliedby \textit{perimeter is }\frac{3}{4}\textit{ larger}
\\\\\\
\stackrel{areas'~ratio}{\cfrac{s^2}{s^2}}\implies \cfrac{3^2}{4^2}\implies \cfrac{9}{16}\impliedby \textit{area is }\frac{9}{16}\textit{ larger than original}$

6 0

3 years ago

Turn 5.4 into a percent

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