Out of $16:9$ ratio, if $16$ represents $100\%$ what percentage does $9$ represent?

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Just like the title says,

Out of a $16:9$ ratio, if $16$ represents $100\%$ what percentage does $9$ represent?

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You can set up a simple proportion. $$\frac{16}{100}=\frac9x$$ Cross multiply $$16x=900$$ Simplify $$x=\frac{225}{4}\;\text{or}\;x=56.25$$

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Hint: If 16 is 100% then the 9 is x %. Divide both expressions: $9/16=x/100\%$. Solve for $x$ and you are done.