Math Antics - Calculating Percent Change

Summary

The video script from Math Antics teaches viewers how to calculate percent change, which is the relative change in value expressed as a percentage. It explains that percent change is always related to the original amount, and provides a formula: (change / original amount) x 100. The script uses various examples, including an increase in the number of dogs at a daycare and a decrease in the price of shoes with a coupon, to illustrate the concept. It also discusses how to handle situations where the absolute change is not given, and emphasizes the importance of using intuition and understanding the meaning behind the formula.

Takeaways

• 📈 Percent change is a way to express the relative change in value, comparing the amount of change to the original amount.
• 🔢 The formula for calculating percent change is: (Absolute change / Original amount) * 100.
• 💡 Understanding percent change involves relating the amount of change to the original amount, often visualized as a fraction with 100 as the denominator.
• 📚 To find the percent increase or decrease, you can use a diagram to represent the original value and the change, or use algebraic methods.
• 💡 When the original amount is exactly 100, calculating the percent change is straightforward, as any increase or decrease directly represents the percentage.
• 📉 In cases where the original amount is not 100, you can find the equivalent fraction that has 100 as the denominator to determine the percent change.
• 🛒 Examples in the script include calculating percent change for a Doggie Day Care's customer increase and a discount on a pair of shoes, illustrating practical applications.
• 🧮 When given an original and a new value, you must first calculate the absolute change by subtraction before applying the percent change formula.
• 🤔 The order of subtraction matters in determining whether the percent change is an increase or a decrease, with the new amount minus the original amount indicating an increase.
• 📉 Percent change can exceed 100%, as shown when starting with 1 and ending with 3, which is a 200% increase, demonstrating that the change can be more than the original amount.

Q & A

What is percent change and how is it different from absolute change?

Percent change is a way to express the change in a value relative to the original value, using percentages. Unlike absolute change, which shows the exact amount of increase or decrease, percent change relates the change to the original amount by dividing the absolute change by the original value and multiplying by 100.

How do you calculate the percent increase if you start with $750 and your value increases by $150?

To calculate the percent increase, you divide the increase amount ($150) by the original amount ($750) and then multiply by 100. So, the calculation is (150 / 750) * 100, which equals 20%.

What is the formula for calculating percent change?

The formula for calculating percent change is: (Absolute Change / Original Amount) * 100. This formula helps you find the percentage by which a value has increased or decreased from its original amount.

Can you give an example of calculating percent change with a Doggie Day Care scenario?

Sure. If a Doggie Day Care takes care of 25 dogs on Friday and 3 more dogs join on Saturday, the percent increase in the number of dogs is calculated as (3 / 25) * 100, which equals 12%.

How would you calculate the percent decrease if a pair of shoes originally costs $65 but is reduced by $15 with a coupon?

To find the percent decrease, you use the formula: (-15 / 65) * 100. This calculation results in -23%, indicating a 23% decrease in the price of the shoes.

What if you're given the original and new values but not the absolute change? How do you calculate percent change then?

If you're given the original and new values, you first calculate the absolute change by subtracting the original value from the new value. Then, apply the percent change formula: (Absolute Change / Original Amount) * 100.

Why is it important to consider the order of subtraction when calculating percent change?

The order of subtraction is important because it determines whether the result is positive (indicating an increase) or negative (indicating a decrease). Subtracting the original amount from the new amount ensures that you're calculating the change from the baseline value.

Can you explain why a percent change can be greater than 100%?

A percent change can be greater than 100% when the new value is more than double the original value. For example, if you start with 1 and end up with 3, the increase is 200% because (2 / 1) * 100 equals 200.

What is the significance of the term 'percent' in the context of percent change?

The term 'percent' means 'per 100' and is used in percent change to relate the amount of change to the original value. It allows for a standardized way of expressing how much a value has increased or decreased relative to its original amount.

How does the original amount affect the calculation of percent change?

The original amount is crucial in calculating percent change because it serves as the baseline for comparison. The same absolute change can result in different percent changes depending on the original amount due to the relative nature of percentage calculations.