Percentage Increases and Decreases

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Understanding percentage increases and decreases is crucial for analyzing financial, scientific, and statistical data. This guide explains how to calculate these changes using simple formulas. Learn to adjust values by a given percentage and analyze changes over time, with examples like price adjustments and account balance evaluations.

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Understanding Percentage Increases and Decreases

Percentage increases and decreases are fundamental mathematical concepts used to express the change in value or quantity in terms of a hundredth. A percentage is a ratio that represents a part of a whole as a fraction of 100, symbolized by the percent sign (%). To calculate the percentage of a number, one multiplies the number by the percentage and then divides by 100. For example, to find 3% of a number, multiply the number by 0.03 (since 3% equals 3/100 or 0.03). This concept is crucial for understanding how to compute the relative change in values, whether they represent growth or decline.

Calculator on wooden desk flanked by ascending and descending stacks of coins, reflecting financial calculations and value representation.

Calculating Percentage Increase

To calculate a percentage increase, identify the absolute increase by subtracting the original number from the new, higher number. Then, divide this increase by the original number and multiply by 100 to express it as a percentage. The formula for percentage increase is: Percentage Increase (%) = (Increase / Original Number) × 100. For example, if a product's price increases from £20 to £35, the increase is £15. The percentage increase is calculated as (15 / 20) × 100, resulting in a 75% increase.

Calculating Percentage Decrease

To calculate a percentage decrease, find the absolute decrease by subtracting the new, lower number from the original number. Divide this decrease by the original number and multiply by 100 to convert it to a percentage. The formula is: Percentage Decrease (%) = (Decrease / Original Number) × 100. For instance, if an account balance decreases from £2000 to £800, the decrease is £1200. The percentage decrease is (1200 / 2000) × 100, which equals a 60% decrease.

Adjusting Values by a Percentage

To adjust a value by a given percentage, calculate the percentage of the original value and then add or subtract it from the original value to increase or decrease it respectively. To increase £80 by 5%, calculate 5% of £80 (0.05 × 80 = £4) and add it to the original amount to get £84. To decrease a 70 cm piece of wood by 3%, calculate 3% of 70 cm (0.03 × 70 = 2.1 cm) and subtract it from the original length to obtain a new length of 67.9 cm.

Analyzing Percentage Change Over Time

To analyze percentage change over a period of time, use the formula: Percentage Change Over Time (%) = ((New Number / Original Number) - 1) × (100 / Time Period). This formula can indicate growth with a positive value or a decline with a negative value. For example, if the price of petrol increases from £1.99 to £2.15 over 2 years, the annual percentage increase is ((2.15 / 1.99) - 1) × (100 / 2), which is approximately 4.02% per year. If the water level in a reservoir drops from 30 liters to 15 liters in 30 minutes, the percentage decrease per minute is ((15 / 30) - 1) × (100 / 30), which is approximately -1.67% per minute.

Key Takeaways on Percentage Increase and Decrease

In conclusion, understanding percentage increases and decreases is vital for quantitatively comparing changes in values and quantities. A percentage increase reflects a rise in value, while a percentage decrease signifies a reduction. It is important to note that a negative result in these calculations indicates a decrease, and the negative sign should be omitted when expressing the final percentage change. Mastery of these concepts is not only essential for academic purposes but also has practical applications in fields such as economics, business, and science.