Question

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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%?

Answer 1

The fraction will decrease by 50%.

Explanation:

`p\%=(p)/(100)\\\\75\%=(75)/(100)=0.75\\\\50\%=(50)/(100)=0.5\\\\(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}\ (0.25n)/(0.5d)=(0.25\cdot100)/(0.5\cdot100)\cdot(n)/(d)=(25)/(50)\cdot(n)/(d)=(1)/(2)\cdot(n)/(d)=0.5\cdot(n)/(d)\\\\(n)/(d)-0.5(n)/(d)=0.5\cdot(n)/(d)\to\ \text{it's}\ 50\%\ \text{of}\ (n)/(d)`