Question

by what percent will the fraction change if its numerator decreased by 20 and its denominator is decreased by 60

Answer 1

I consider the original fraction: x/y.

If the numerator "x" increases by 20%, it can be interpreted in this way:

"x" represents 100% (the unit) and when increasing by 20% we have that the value of "x" becomes 120%

120% of "x" is
`\bf{(120*x)/(100)=1,2x }`

This is what we have left in the numerator.

By the same reasoning, in the denominator "y" remains:

100% - 40% = 60% of "and"

60% of "y" is...
`\bf{(60*y)/(100)=0.6 y }`

The new fraction is: 1,2x / 1,6y.

...simplifying by dividing top and bottom by 0.6,... 2x / y

To find out the percentage by which the original fraction has changed, we first find the relationship or ratio between the original fraction and the new fraction with the fraction quotient:

`\bf{((2x)/(y) )/((x)/(y) )=(2xy)/(xy)=2 }`

... that is to say that the new fraction has doubled in relation to the original.

Therefore, the percentage of variation per increase is 100%.

Pisces04