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By what percent will a fraction change if its numerator is decreased by 75% and its denominator is decreased by 50%?

Respuesta :

gmany

Answer:

The fraction will decrease by 50%.

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\75\%=\dfrac{75}{100}=0.75\\\\50\%=\dfrac{50}{100}=0.5\\\\\dfrac{n}{d}-\text{a fraction}\to(n-\text{numerator},\ \text{denominator})\\\\\text{numerator is decreased by 75}\%\to n-0.75n=0.25n\\\\\text{denominator is decreased by 50}\%\to d-0.5d=0.5d\\\\\text{new fraction}\ \dfrac{0.25n}{0.5d}=\dfrac{0.25\cdot100}{0.5\cdot100}\cdot\dfrac{n}{d}=\dfrac{25}{50}\cdot\dfrac{n}{d}=\dfrac{1}{2}\cdot\dfrac{n}{d}=0.5\cdot\dfrac{n}{d}\\\\\dfrac{n}{d}-0.5\dfrac{n}{d}=0.5\cdot\dfrac{n}{d}\to\ \text{it's}\ 50\%\ \text{of}\ \dfrac{n}{d}[/tex]