Question

By what percent will a fraction change if its numerator is decreased by 50% and its denominator is decreased by 25%?

Answer 1

Answer:

The fractional change is $\frac{1}{3}$ % .

Step-by-step explanation:

Given as :

The original fraction = $\dfrac{x}{y}$

Where numerator = x

Denominator = y

According to question

The numerator decreased by 50%

Let The new numerator = x' = x - 50% of x

I,e x' = x ( 1 - $\frac{50}{100}$)

Or, x' = x ($\frac{100-50}{100}$)

Or, x' = $\frac{50}{100}$ x

or, x' = $\dfrac{x}{2}$              .........A

Again

The new denominator = y' = y - 25% of y

i.e y' = y (1 - $\frac{25}{100}$)

Or, y' = y ($\frac{100-25}{100}$)

Or, y' = y ($\frac{75}{100}$)

Or, y' = $\frac{3 y}{4}$              ............B

So, The new fraction = $\frac{x'}{y'}$ = $\frac{\frac{x}{2}}{\frac{3 y}{4}}$

Or, $\frac{x'}{y'}$ = $\frac{2 x}{3 y}$

So, The fractional change = $\frac{1-\frac{2}{3} }{1}$ × 100

Or, The fractional change = $\frac{1}{3}$× 100

Hence, The fractional change is $\frac{1}{3}$ % . Answer