I have the following chart that I am supposed to find the percent increase in one step. The directions specifically say not to use a two step method.
10.5
12.5
14.9
17.7
21.1
25.1
So I divide 12.5 by 10.5, 14.9 by 12.5, etc.
When I do this (and round) I get about 19% increase for each one. (we are supposed to round. )
Then I have another chart that we are supposed to find the percent decrease also using the one step method.
80.2
71.4
63.5
56.5
50.3
44.8
If I use the same method I get about 12% decrease each time but the answer says 11% each time. If I do it the opposite way, for example, 71.4/80.2 and then subtract from 1.00 I would get more like 11%.
I'm just not really certain of the methodology to get the correct 11% answer.
Thank you
In the first one you divided the 2nd by the 1st and got
12.5/10.5 = 1.19.. = 1 + .19
= 100% + 19% ---> an increase (+) of 19%
I assume that is how you got 19%
So why not do the same thing in the 2nd ?
71.4/80.2 = .8902..
= 1 - .1097
= 100% - 10.97%
= 100% - 11.97% ---> a decrease (-) of appr 11%
I see no discrepancy in the methods
Notice we divided "in the same direction"
What I'm asking about is actually about the decrease in the second chart. If I divide top to bottom (80.2/71.4, 71.4/63.5, etc), I get a different result than if I divide bottom to top (71.4/80.2, 63.5/71.4 and then subtract from 1.00). If I do the top to bottom way I get 12% which I'm told is wrong. If I do bottom to top I get 11% which I'm told is correct. I just don't understand the WHY that is correct.
I thought I explained it quite simply.
Why would you change the "direction" of your division?
I consistently divided the old one from the new one (2nd - 1st)
if the result is greater than 1 you have an increase, and the increase is the difference between 1 or 100% and your answer.
if the result is less than 1 you have a decrease, and the decrease is the difference between 1 and your answer.
I did the same thing in both cases.
in the first you correctly divided 12.5 by 10.5
but for the second you changed it to 80.2/71.4 . Why would you switch???
and not do the same as in the first question?
I apologize for asking for clarification because I did not understand.
To find the percent increase or decrease using the one-step method, you can follow these steps:
1. Start by identifying the initial value (the starting point) and the final value (the ending point).
2. For percent increase, subtract the initial value from the final value. For percent decrease, subtract the final value from the initial value.
3. Divide the result from step 2 by the initial value.
4. Multiply the quotient by 100 to get the percentage.
Let's apply these steps to the given charts:
For the percent increase chart:
Initial value = 10.5
Final value = 12.5
1. Subtract the initial value from the final value: 12.5 - 10.5 = 2
2. Divide the result by the initial value: 2 / 10.5 ≈ 0.1905
3. Multiply by 100 to get the percentage: 0.1905 * 100 ≈ 19% (rounded)
Following the same steps for the remaining values in the increase chart, you would find approximately 19% as the percent increase for each case.
For the percent decrease chart:
Initial value = 80.2
Final value = 71.4
1. Subtract the final value from the initial value: 80.2 - 71.4 = 8.8
2. Divide the result by the initial value: 8.8 / 80.2 ≈ 0.1097
3. Multiply by 100 to get the percentage: 0.1097 * 100 ≈ 10.97% (rounded)
When rounded, you get approximately 11% as the percent decrease for each case. However, it seems like the given answer of 11% is an approximation and has been rounded down, which is why you were getting around 12% when performing the calculation using the "opposite way" (dividing and subtracting from 1.00).
In conclusion, you have been correctly applying the one-step method to calculate the percent increase and decrease. The differences in the final answer may be due to variations in rounding.