What Does Decreased By Mean

Understanding "Decreased By": A Comprehensive Guide

"Decreased by" is a phrase commonly used to describe a reduction in a quantity or value. Understanding its meaning is crucial in various contexts, from interpreting financial reports and scientific data to solving everyday math problems. This article will provide a comprehensive explanation of what "decreased by" means, exploring its mathematical implications, real-world applications, and common points of confusion. We'll delve into different scenarios, offering practical examples to solidify your understanding.

What "Decreased By" Means Mathematically

At its core, "decreased by" signifies subtraction. When a value is "decreased by" a certain amount, that amount is subtracted from the original value. This simple concept underlies many complex calculations.

For example:

• "The price decreased by $10." This means the new price is the original price minus $10. If the original price was $50, the new price is $50 - $10 = $40.

• "The population decreased by 5%." This involves calculating a percentage decrease. If the initial population was 1000, a 5% decrease would be 1000 * 0.05 = 50. The new population is 1000 - 50 = 950.

The key takeaway is that the phrase always indicates a reduction from an initial value. The "by" part specifies the amount or percentage of the reduction.

Distinguishing "Decreased By" from "Decreased To"

A common source of confusion arises when comparing "decreased by" with "decreased to." These phrases represent different mathematical operations:

• Decreased by: Involves subtraction. You subtract the given amount from the original value to find the new value.

• Decreased to: Indicates the final value after the reduction. To find the amount of decrease, you subtract the final value from the original value.

Example:

Let's say the temperature was initially 25°C.

• "The temperature decreased by 5°C." The new temperature is 25°C - 5°C = 20°C.

• "The temperature decreased to 20°C." This tells us the final temperature. The decrease is 25°C - 20°C = 5°C.

Understanding this distinction is crucial for accurate interpretation and calculation. Always pay close attention to the wording to determine whether you're dealing with a subtraction problem or finding the difference between two given values.

Real-World Applications of "Decreased By"

The phrase "decreased by" appears in numerous real-world contexts:

• Finance: Analyzing stock prices, reporting profit margins, tracking company expenses, understanding interest rate changes. For instance, "The company's profits decreased by 15% this quarter."

• Science: Measuring changes in physical quantities like temperature, pressure, or volume. A scientist might record, "The water level decreased by 2 centimeters after evaporation."

• Demographics: Tracking population changes, birth rates, or mortality rates. A report might state, "The city's population decreased by 3% over the past decade."

• Economics: Describing changes in GDP, inflation rates, or unemployment figures. An economic report might show, "Unemployment decreased by 1 percentage point last month."

• Everyday Life: Tracking weight loss ("I decreased my weight by 5 pounds."), measuring the reduction in fuel consumption ("My car's fuel consumption decreased by 2 miles per gallon after the tune-up."), or even calculating savings ("I decreased my monthly expenses by $100.").

Solving Problems Involving "Decreased By"

Let's look at some example problems to illustrate how to work with "decreased by" in different scenarios:

Example 1: Percentage Decrease

A shop owner reduced the price of a dress by 20%. If the original price was $80, what is the new price?

1. Calculate the decrease: 20% of $80 is (20/100) * $80 = $16.
2. Subtract the decrease from the original price: $80 - $16 = $64.
3. The new price is $64.

Example 2: Unknown Original Value

A company's sales decreased by 10% to $90,000. What were the original sales?

This problem requires working backward. Let's use algebra:

Let x be the original sales.

• The decrease is 10% of x, which is 0.1x.
• The new sales are x - 0.1x = 0.9x.
• We know 0.9x = $90,000.
• Solving for x: x = $90,000 / 0.9 = $100,000.
• The original sales were $100,000.

Example 3: Combined Decreases

The price of a product decreased by 15% in the first month and then by 5% in the second month. If the original price was $100, what is the final price?

1. First month decrease: 15% of $100 is $15. The price becomes $100 - $15 = $85.
2. Second month decrease: 5% of $85 is $4.25. The price becomes $85 - $4.25 = $80.75.
3. The final price is $80.75. Note that the total decrease is not simply 20%. Percentage decreases are calculated sequentially.

Dealing with Negative Values

While less common in everyday scenarios, understanding how "decreased by" works with negative numbers is crucial for a complete understanding. Subtracting a negative number is equivalent to adding its positive counterpart.

Example:

A temperature of -5°C decreased by -2°C. The new temperature is -5°C - (-2°C) = -5°C + 2°C = -3°C.

Frequently Asked Questions (FAQs)

Q: Can a value decrease by more than its original value?

A: No. A value cannot decrease by more than its original value. If a value decreases by 100%, it becomes zero. Any further decrease would result in a negative value, implying a gain rather than a decrease.

Q: What is the difference between "decreased by a factor of" and "decreased by"?

A: "Decreased by a factor of" implies multiplication, not subtraction. If something decreases by a factor of 2, it means the final value is half the original value. "Decreased by" always involves subtraction.

Q: How do I calculate the percentage decrease?

A: Percentage decrease = [(Original Value - New Value) / Original Value] * 100

Conclusion

Understanding the meaning of "decreased by" is essential for correctly interpreting information and solving problems in various fields. This phrase represents a simple yet powerful mathematical concept—subtraction—that plays a crucial role in analyzing data, understanding trends, and making informed decisions. By mastering the difference between "decreased by" and "decreased to," and by practicing solving different types of problems, you can confidently navigate any scenario involving this common phrase. Remember to always pay careful attention to the context and the specific numbers involved to ensure accurate calculations.