Percentage decrease is a fundamental concept that measures how much a value has reduced relative to its original amount. The formula is: percentage decrease equals original value minus new value, divided by original value, then multiplied by 100 percent. This calculation is widely used in real-world scenarios such as price reductions, population decline, performance metrics, and financial analysis. For example, if a value decreases from 100 to 75, the percentage decrease would be 25 percent.
Now let's identify the given values from our specific problem. We need to find the percentage decrease from 120 to 71. The first step is to correctly identify which value is the original and which is the new value. In this case, 120 is our original value, as it's the starting amount, and 71 is our new value, as it's the ending amount. This identification is crucial because mixing up these values would give us an incorrect result.
Now let's work through the calculation step by step. Step 1: Calculate the difference between the original and new values. 120 minus 71 equals 49. Step 2: Divide this difference by the original value. 49 divided by 120 equals approximately 0.4083. Step 3: Multiply by 100 to convert to a percentage. 0.4083 times 100 equals 40.83 percent. Each step builds logically on the previous one, leading us to our final answer of 40.83 percent decrease.
Our final answer is 40.83 percent decrease from 120 to 71. This means that 71 is approximately 40.83 percent less than the original value of 120. To verify our calculation, we can check: 40.83 percent of 120 equals approximately 49, and 120 minus 49 equals 71, which confirms our answer is correct. In practical terms, this represents a significant reduction of about two-fifths of the original value.
Percentage decrease calculations have many practical applications in our daily lives. They're used for price reductions and sales, population decline studies, performance metric analysis, stock market losses, weight loss tracking, budget cuts, and energy consumption reduction. Let's look at another example to reinforce our understanding. If we want to find the percentage decrease from 80 to 56: first, we calculate 80 minus 56 equals 24. Then we divide 24 by 80 to get 0.3. Finally, we multiply by 100 to get 30 percent. The formula works universally for any values, making it a powerful tool for analyzing changes in quantities.