Value of the expression is decreased by what percentage?

[PrudensOptimus]

A question, kind a tricky problem if you think it's easy.

$$xv^{2}z^{3}$$

if the values of x, v, and z are each decreased by 50 percent, then the value of the expression is decreased by what percentage?

$$\frac{(x(1-0.5)v(1-0.5)^{2}z(1-0.5)^{3})}{xv^{2}z^{3}}$$

Wonder if that's how you do it...

 

[HallsofIvy]

I don't see why you have divided by xv²z³.

Here's how I would do this: x decreased by 50% is (as you have it)
x(1- .5) which is then 0.5 x or x/2. Similarly v is reduce to v/2 and z is reduced to z/2.

xv²z³ is reduced to (x/2)(v/2)²(z/2)³= (xv²z³)/(2*4*8)= (xv²z³)/64. In other words xv²z³ is reduce to 1/64 of it's value.

(Oh, THAT'S why you divided by xv²z³- to get only the multiplier! Yes, you are correct!)

Reducing it to 1/64 is the same as reducing it by 63/64 which is 98.4375%.

 

[ahrkron]

Originally posted by PrudensOptimus
$$\frac{(x(1-0.5)v(1-0.5)^{2}z(1-0.5)^{3})}{xv^{2}z^{3}}$$

Just be careful with the parentheses:

$$\frac{x(1-0.5)(v(1-0.5))^{2}(z(1-0.5))^{3}}{xv^2z^3}$$