Answer: The new number is 1.44% smaller than the original.
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Step-by-step explanation:
To increase by 12%, we involve the multiplier 1.12
Think of 1.12 as 100% + 12% = 1 + 0.12 = 1.12
We go from x to 1.12x
To decrease by 12%, we will use the multiplier 0.88 because 1 - 0.12 = 0.88
Think of it like a discount. If you save 12%, then you pay the remaining 88%
So 0.88*1.12x = 0.9856x
The value 0.9856 is smaller than 1, meaning that overall we have a net discount going on.
The discount rate is 1 - 0.9856 = 0.0144 = 1.44%
In other words, x ultimately goes down by exactly 1.44%
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If you want to use an actual number to see an example, let's go for x = 100
Increasing 100 by 12% means we increase by 0.12*100 = 12
We go from 100 to 112
Then decreasing by 12% means the value goes down by 0.12*112 = 13.44 and drops to 112-13.44 = 98.56
The original value 100 becomes the final value 98.56
This is a percent decrease of (100-98.56)/100 = 0.0144 = 1.44%