How to solve this problem

A step by step guide

Calculating percentage increase or decrease is a useful way to track data points over time. If you have two numbers, their relationship can be described by the percentage change between them. The reason this is an important metric is because it is normalized. Percentage increases and decreases can be slightly confusing at first, but become much more simple once you understand how they are calculated. To calculate percentage change, we will use three operations. As usual with percentage problems, these operations will involve basic arithmetic. In this case, we want to calculate the percentage increase or decrease from 829 to 178. Here are the steps:

Step 1: Subtract 829 from 178
The first step is to find the difference between the new number (the second input, 178) and the old number (the first input, 829). We can do this by simply subtracting 829 from 178: $$ 178 - 829 = -651 $$

Step 2: Divide -651 by 829
The second step is to divide the result of step 1 by the original number. This is done to compare the difference to the original number. The equation for this is quite simply: $$ \frac{-651}{829} = -651 \div 829 = -0.78528347406514 $$

Step 3: Multiply -0.78528347406514 by 100
The final step of this calculation is to multiply the result of step 2 by 100 to turn it into a percentage (%). This equation for this is simple: $$ -0.78528347406514 \times 100 = -78.53 $$

And there you have it! These three steps can be used to calculate the percentage increase or decrease of any two numbers. Give it a try with another set of numbers.