What is this voodoo?! It doesn't make any sense

[Debugger]

Say we have a result, z.
The result is determined by dividing x over y (i.e. x/y)

If the numerator (x) increases by 10%, the result (z) increases by 10%.

However if the denominator (y) decreases by 10%, why does that result (z) not increase by 10% too?


For a more specific example:
The break-even point (in units) is calculated as: Fixed Costs, divided by the unit selling price minus the unit variable cost.
If fixed costs increase by 10%, the break-even point increases by 10%.
However, if unit variable cost increases by 10% (i.e. thus decreasing the denominator by 10%), why doesn't the break-even point also increase by 10%?


Any help would be great, thank you

 

[lookagain]

Say we have a result, z.
The result is determined by dividing x over y (i.e. x/y)

If the numerator (x) increases by 10%, the result (z) increases by 10%.

However if the denominator (y) decreases by 10%, why does that result (z) not increase by 10% too?

Why should it? Decreasing a denominator (for instance in the case where the
numer. and the denom. are both positive, and you decrease the denominator until it still
remains positive), increases the value of the fraction.

What would have been a "voodoo" for further looking into, is if you had decreased
the numerator (with no change in the denominator), but z had not decreased, or had
not decreased by the proper percent.

 

[ksdhart2]

Alright, so if I'm reading your post correctly, you've noted that increasing a numerator by 10% increases the overall fraction by 10%. Now, you're wondering why decreasing the denominator of a fraction by 10% does not decrease the overall fraction by exactly 10%. If your supposition was true, you'd essentially be saying the following:

Original equation: \(\displaystyle \frac{x}{y}=z\)

Increasing the numerator: \(\displaystyle \frac{1.1x}{y}=1.1z\)

Decreasing the numerator: \(\displaystyle \frac{x}{0.9y}=1.1z\)

Equating the two, we have: \(\displaystyle \frac{1.1x}{y}=\frac{x}{0.9y}=1.1z\)

You'll find that last equation is only true for some values of x and y, rather than being an identity. Your job is to determine why it's not true. I'd further note that this principle holds true for any scalar multiple n, rather than being something specific about 10%.

 

[Debugger]

Alright, so if I'm reading your post correctly, you've noted that increasing a numerator by 10% increases the overall fraction by 10%. Now, you're wondering why decreasing the denominator of a fraction by 10% does not decrease the overall fraction by exactly 10%. If your supposition was true, you'd essentially be saying the following:

Original equation: \(\displaystyle \frac{x}{y}=z\)

Increasing the numerator: \(\displaystyle \frac{1.1x}{y}=1.1z\)

Decreasing the numerator: \(\displaystyle \frac{x}{0.9y}=1.1z\)

Equating the two, we have: \(\displaystyle \frac{1.1x}{y}=\frac{x}{0.9y}=1.1z\)

You'll find that last equation is only true for some values of x and y, rather than being an identity. Your job is to determine why it's not true. I'd further note that this principle holds true for any scalar multiple n, rather than being something specific about 10%.

Thank you.

My ultimate aim was to determine if it was possible to ascertain how much z would be affected (i.e. %), as a result of a particular % change in the denominator. Is it possible to do this?