Answer: 12.5%
Step-by-step explanation:
Let the original fraction is [tex]\frac{x}{y}[/tex]
After decreasing its numerator by 30% and denominator by 20%,
New fraction = [tex]\frac{x-30\%\text{ of} x}{y-20\%\text{ of} y}[/tex]
= [tex]\frac{x-\frac{30x}{100}}{y-\frac{20x}{100}}[/tex]
= [tex]\frac{\frac{100x}{100}-\frac{30x}{100}}{\frac{100y}{100}-\frac{20x}{100}}[/tex]
= [tex]\frac{\frac{100x-30x}{100}}{\frac{100y-20y}{100}}[/tex]
= [tex]\frac{\frac{70x}{100}}{\frac{80y}{100}}[/tex]
= [tex]\frac{70x}{80y}[/tex]
= [tex]\frac{7x}{8y}[/tex]
Thus, the total percentage change in the original fraction,
= [tex]\frac{\text{original fraction-new fraction}}{\text{original fraction}} \times 100[/tex]
= [tex]\frac{\frac{x}{y} -\frac{7x}{8y} }{\frac{x}{y} } \times 100[/tex]
= [tex]\frac{1 -\frac{7}{8} }{1 } \times 100[/tex]
= [tex]\frac{8-7}{8}\times 100[/tex]
= [tex]\frac{100}{8} = 12.5\%[/tex]
