why does % go up even though both Num. increase by the same

[Guest]

not sure if this right board to ask but i have question around percentages. If i have the following calculation

1047/1523

I get 68.7%

if I increase both figures by an extra 300. my % total increase

1347/1823 73.8%

Can someone explain why?

It might be common sense to most but I would have thought the % should be the same since both values are increase by the same amount

[Baltuilhe]

Good night!

If you have a fraction [tex]\dfrac{a}{b}[/tex] and add 'k' to numerator and denominator, simultaneously.
[tex]\dfrac{a+k}{b+k}[/tex]

This fraction is bigger or smaller than original one?

Let's calculate the difference!
[tex]\dfrac{a+k}{b+k}-\dfrac{a}{b}=\dfrac{b(a+k)-a(b+k)}{b(b+k)}=\dfrac{ba+bk-ab-ak}{b(b+k)}=\dfrac{k(b-a)}{b(b+k)}[/tex]

So, if you have b > a, the difference is bigger than zero. So, it increases the final value!

I hope to have helped!