Percentage of a percentage

[Generator]

If someone could help me work this out I would greatly appreciate it.
Basically
Ok I have value x
I want to take away 25% of value x
75% of value x = value y
value y multiplied by 0.7 = value I wanna get (or value z)
how do i get value z from value x in one calculation?
Thanks

[capsulecorpjx]

If someone could help me work this out I would greatly appreciate it.
Basically
Ok I have value x
I want to take away 25% of value x
75% of value x = value y
value y multiplied by 0.7 = value I wanna get (or value z)
how do i get value z from value x in one calculation?
Thanks

.75 x = y
.7 y = z

.7 ( .75 x) = z
0.525 = z
Or 52.5% of x = z.

[jemidiah]

Percentages "stack" multiplicatively. It's very similar to what's happening in fractions: half (1/2, 50%) of a fourth (1/4, 25%) of something is 1/8th of that something (12.5%), except that you don't have to convert fractions before you multiply them. Also, 3/4ths (75%) of 7/10ths (70%) of something is 21/40ths of that something--and 21/40ths is 52.5%. Just another way of saying what Capsule already said (and it's set-up for my next point...)

More generally, percent of a percent is multiplicative--that is, a% of b% of c% of d% of ... of z% of some number N is (a/100)*(b/100)*(c/100)*...*(z/100)*N, or [(a/100)*...*(z/100)]*100 % of N. You have to divide and multiply by 100 to convert between percentages and pure numbers (decimals and fractions).

Ex: 50% of 25% of 10% of 2000 = 0.5*0.25*0.1 * 2000 = 0.0125 * 2000 = 1.25% of 2000 = 25.

In doing all the multiplications, you just have to remember to convert the percentage to a pure number (decimal or fraction). You can then convert the result back to a percent if needed.

Hope this helps with something :)

[Sean12345]

25% off the original value means 75% of the original value so,

y = 75% of x
y = (3/4)x
z = 0.7y
Therefore z = 0.7((3/4)x)
z = (21/40)x OR 0.525x

So to find a percentage of a percentage, z = m(Mx) where M = first percentage multiplier and m = second percentage multiplier. By percentage multiplier i mean the decimal you multiply by to get the new value e.g. 75% = 0.75, 70% = 0.7

Hope this helps.

(Just like jemidiah and capsule said come to think of it ^^)

[krtxmrtz]

Straying somewhat off the actual thread subject, maybe this example can help you to further clarify the concept of percents.

Some people unfamiliar with basic math are puzzled by the fact that increasing a quantity by a certain percentage and then decreasing the result by the same percentage does not yield the original value.

For exmple, you start with 800, increase by 10% to obtain 880 and decrease by 10% to obtain 792. Of course, the 10% calculation applies to a different number each time:

10% of 800 is 800 * 10 / 100 = 80 -> Add to 800 and get 880
10% of 880 is 880 * 10 / 100 = 88 -> Substract from 880 and get 792

HTH :)