The TI-84 Plus calculator is a staple in classrooms and beyond, renowned for its versatility and ability to tackle a wide array of mathematical problems. Among its many functions, calculating percentages is a common and crucial skill. This guide will walk you through various percentage calculations using your TI-84 Plus, providing clear instructions and real-world examples. From basic percentage calculations to more complex applications involving percentage increase, decrease, and discounts, this article equips you with the knowledge to confidently handle percentage problems.
The Basics: Finding a Percentage of a Number
The most fundamental percentage calculation involves finding what a certain percentage represents of a given number. For instance, what is 20% of 150? The TI-84 Plus makes this incredibly straightforward.
To calculate this, simply enter the percentage as a decimal (or use the percentage symbol) multiplied by the number.
Enter: 0.20 * 150
Press ENTER.
Output: 30
Alternatively, you can utilize the percentage symbol directly.
Enter: 20% * 150
Press ENTER.
Output: 30
Key takeaway: Multiplying the decimal equivalent of the percentage by the number gives you the result. Using the percentage symbol is another efficient option.
Calculating Percentage Increase
Understanding percentage increase is vital in many scenarios, such as calculating price increases, salary raises, or growth rates. The TI-84 Plus can easily handle these calculations.
Determining the Amount of Increase
Suppose a product’s price increases from $50 to $60. What is the percentage increase? First, you need to find the amount of the increase.
Amount of Increase = New Value – Original Value
Amount of Increase = $60 – $50 = $10
Calculating the Percentage Increase
Now, divide the amount of increase by the original value and multiply by 100 to express the result as a percentage.
Percentage Increase = (Amount of Increase / Original Value) * 100
Percentage Increase = ($10 / $50) * 100
Using your TI-84 Plus:
Enter: (10 / 50) * 100
Press ENTER.
Output: 20
Therefore, the percentage increase is 20%.
Key takeaway: Percentage increase is found by dividing the amount of increase by the original value and multiplying by 100.
Calculating Percentage Decrease
Percentage decrease is the opposite of percentage increase and is used to determine the reduction in value, such as discounts, depreciation, or drops in sales. The process is similar to calculating percentage increase.
Determining the Amount of Decrease
Let’s say the price of an item decreases from $80 to $60. What is the percentage decrease? First, find the amount of the decrease.
Amount of Decrease = Original Value – New Value
Amount of Decrease = $80 – $60 = $20
Calculating the Percentage Decrease
Divide the amount of decrease by the original value and multiply by 100 to express the result as a percentage.
Percentage Decrease = (Amount of Decrease / Original Value) * 100
Percentage Decrease = ($20 / $80) * 100
Using your TI-84 Plus:
Enter: (20 / 80) * 100
Press ENTER.
Output: 25
Therefore, the percentage decrease is 25%.
Key takeaway: Percentage decrease is found by dividing the amount of decrease by the original value and multiplying by 100.
Finding the Original Value Given a Percentage and Result
Sometimes, you might know a percentage of a number and the result, but need to find the original number. For example, if 15% of a number is 45, what is the original number?
To solve this, divide the result by the percentage expressed as a decimal.
Original Value = Result / (Percentage / 100)
Original Value = 45 / (15 / 100)
Using your TI-84 Plus:
Enter: 45 / (15 / 100)
Press ENTER.
Output: 300
Therefore, the original number is 300.
Key takeaway: To find the original value, divide the result by the decimal equivalent of the percentage.
Calculating Discounts
Discounts are a practical application of percentage calculations, particularly when shopping. The TI-84 Plus can help you quickly determine the discounted price.
Calculating the Discount Amount
Suppose an item costs $120, and there is a 30% discount. First, calculate the discount amount.
Discount Amount = Original Price * (Discount Percentage / 100)
Discount Amount = $120 * (30 / 100)
Using your TI-84 Plus:
Enter: 120 * (30 / 100)
Press ENTER.
Output: 36
The discount amount is $36.
Calculating the Final Price
Subtract the discount amount from the original price to find the final price.
Final Price = Original Price – Discount Amount
Final Price = $120 – $36 = $84
Therefore, the final price after the discount is $84.
Key takeaway: Calculate the discount amount by multiplying the original price by the discount percentage (as a decimal). Then, subtract the discount amount from the original price to find the final price.
Calculating Sales Tax
Sales tax is another common application of percentage calculations. It is added to the price of goods and services and is calculated as a percentage of the original price.
Calculating the Sales Tax Amount
Suppose an item costs $50, and the sales tax rate is 8%. First, calculate the sales tax amount.
Sales Tax Amount = Original Price * (Sales Tax Rate / 100)
Sales Tax Amount = $50 * (8 / 100)
Using your TI-84 Plus:
Enter: 50 * (8 / 100)
Press ENTER.
Output: 4
The sales tax amount is $4.
Calculating the Total Price
Add the sales tax amount to the original price to find the total price.
Total Price = Original Price + Sales Tax Amount
Total Price = $50 + $4 = $54
Therefore, the total price including sales tax is $54.
Key takeaway: Calculate the sales tax amount by multiplying the original price by the sales tax rate (as a decimal). Then, add the sales tax amount to the original price to find the total price.
Percentage Change: A More Advanced Approach
Percentage change is a general term encompassing both percentage increase and percentage decrease. It represents the relative change in a quantity. The formula remains consistent.
Percentage Change = ((New Value – Original Value) / Original Value) * 100
If the result is positive, it represents a percentage increase. If the result is negative, it represents a percentage decrease.
Example: A stock’s price changes from $25 to $30. Calculate the percentage change.
Using your TI-84 Plus:
Enter: ((30 – 25) / 25) * 100
Press ENTER.
Output: 20
The percentage change is 20%, indicating a percentage increase.
Example 2: A store reduces its inventory from 500 units to 400 units. Calculate the percentage change.
Using your TI-84 Plus:
Enter: ((400 – 500) / 500) * 100
Press ENTER.
Output: -20
The percentage change is -20%, indicating a percentage decrease of 20%.
Key takeaway: The percentage change formula is universally applicable for both increases and decreases. Pay attention to the sign of the result to determine whether it’s an increase or decrease.
Tips for Efficient Percentage Calculations on Your TI-84 Plus
Using your TI-84 Plus effectively can significantly speed up your calculations. Here are some helpful tips:
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Use Parentheses: When performing calculations with multiple steps, use parentheses to ensure the correct order of operations. This is especially important when dealing with fractions within percentage calculations.
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Utilize the ANS Key: The “ANS” key (usually accessed by pressing “2nd” and then “(-)”) stores the result of the previous calculation. This can be useful for carrying over results to subsequent calculations.
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Clear the Screen: Regularly clear the screen using the “CLEAR” button to avoid accidental entries and ensure accuracy.
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Check Your Work: Always double-check your inputs and calculations to minimize errors, especially on tests or important assignments.
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Decimal vs. Percentage Symbol: Be mindful whether you are inputting the percentage as a decimal (e.g., 0.25 for 25%) or using the percentage symbol (%). Using the wrong format will lead to incorrect results.
By mastering these techniques, you’ll be able to confidently and efficiently tackle a wide range of percentage problems using your TI-84 Plus calculator. Whether you’re calculating discounts, analyzing data, or solving mathematical equations, your TI-84 Plus is a powerful tool that can help you achieve accurate and reliable results. Remember to practice regularly to reinforce your understanding and build proficiency. With consistent effort, you’ll become a percentage calculation expert in no time.
Advanced Applications: Compound Percentage Changes
While simple percentage increase or decrease is commonly encountered, sometimes you need to calculate compound percentage changes, where a percentage change is applied multiple times in succession. This is particularly relevant in finance, such as calculating compound interest.
Consider an investment that grows by 5% each year for 3 years. If the initial investment is $1000, what is the final value?
Year 1: Value = $1000 * (1 + 0.05) = $1050
Year 2: Value = $1050 * (1 + 0.05) = $1102.50
Year 3: Value = $1102.50 * (1 + 0.05) = $1157.625
A more efficient way to calculate this is using exponents.
Final Value = Initial Value * (1 + Percentage Change)^Number of Periods
Final Value = $1000 * (1 + 0.05)^3
Using your TI-84 Plus:
Enter: 1000 * (1 + 0.05)^3
Press ENTER.
Output: 1157.625
Therefore, the final value after 3 years is $1157.63 (rounded to the nearest cent).
Key takeaway: For compound percentage changes, use the formula: Final Value = Initial Value * (1 + Percentage Change)^Number of Periods. The “^” symbol on the TI-84 Plus is used for exponents.
Understanding and applying these percentage calculations on your TI-84 Plus will undoubtedly enhance your mathematical skills and provide you with a valuable tool for solving real-world problems. The key is consistent practice and a thorough understanding of the underlying concepts.
How do I calculate a percentage of a number on my TI-84 Plus?
To calculate the percentage of a number, you can use the standard multiplication operation on your TI-84 Plus calculator. Simply enter the percentage as a decimal (e.g., for 25%, enter 0.25) and multiply it by the number. The result displayed will be the percentage of that number. For example, to find 25% of 80, enter 0.25 * 80 and press ENTER. The calculator will display 20, which is 25% of 80.
You can also directly use the percentage symbol if you prefer. However, the calculator automatically converts this percentage value into its decimal equivalent. Using the previous example, enter 25% * 80. You can find the percentage symbol by pressing 2nd and then the button above the open parenthesis which has the % symbol. The calculator will once again display 20.
What is the shortcut to find the percentage increase using my TI-84 Plus?
While there isn’t a specific built-in function for percentage increase, you can easily calculate it using a simple formula. Subtract the original value from the new value, divide the result by the original value, and then multiply by 100. This will give you the percentage increase.
For example, if a price increases from $50 to $60, the calculation is as follows: (60 – 50) / 50 * 100. Input this directly into your TI-84 Plus as (60 – 50) / 50 * 100. The result, 20, indicates a 20% increase. Remember to use parentheses to ensure the subtraction is performed before the division.
How can I calculate the original price after a discount using my TI-84 Plus?
If you know the discounted price and the percentage discount, you can find the original price using the following method. Let ‘x’ be the original price. Then, discounted price = x – (discount percentage * x). Rearranging the formula, x = discounted price / (1 – discount percentage as a decimal).
For example, if an item costs $45 after a 25% discount, the original price is calculated as: 45 / (1 – 0.25). On your TI-84 Plus, enter 45 / (1 – 0.25) and press ENTER. The calculator will display 60, meaning the original price was $60.
Can I use my TI-84 Plus to convert a fraction to a percentage?
Yes, you can easily convert a fraction to a percentage using your TI-84 Plus calculator. First, enter the fraction into the calculator as a division problem. For example, to convert 3/4 to a percentage, enter 3 / 4.
Press ENTER to get the decimal equivalent, which in this case is 0.75. Then, multiply the decimal by 100 to convert it to a percentage. So, enter 0.75 * 100 and press ENTER. The result, 75, indicates that 3/4 is equal to 75%.
How do I calculate the percentage difference between two numbers on my TI-84 Plus?
To calculate the percentage difference between two numbers, use the following formula: |(Value 1 – Value 2) / ((Value 1 + Value 2) / 2)| * 100. This calculates the absolute difference between the two values, divides it by the average of the two values, and then multiplies by 100 to express the result as a percentage.
For instance, if you want to find the percentage difference between 80 and 60, enter the formula into your TI-84 Plus as abs((80 – 60) / ((80 + 60) / 2)) * 100. Note that abs() can be found under MATH, NUM. Press ENTER. The calculator will display approximately 28.57, meaning the percentage difference between 80 and 60 is approximately 28.57%.
How can I find what percentage one number is of another using my TI-84 Plus?
To determine what percentage one number is of another, divide the first number by the second number and then multiply the result by 100. This calculation will give you the percentage that the first number represents relative to the second number.
For example, if you want to find what percentage 30 is of 120, enter 30 / 120 * 100 into your TI-84 Plus and press ENTER. The calculator will display 25. This means that 30 is 25% of 120.
Is there a function to calculate compound interest which uses percentages on my TI-84 Plus calculator?
Yes, your TI-84 Plus has a built-in finance application that can calculate compound interest. Press APPS and select Finance. If it is the first option press ENTER, otherwise scroll down and press ENTER. Then select the TVM Solver.
In the TVM Solver, input the following: N (number of compounding periods), I% (annual interest rate), PV (present value, enter as a negative if it’s an initial investment), PMT (payment per period, usually 0 for compound interest), FV (future value, what you’re solving for), P/Y (payments per year), and C/Y (compounding periods per year). Place the cursor on the variable you want to solve for (FV in the case of future value) and press ALPHA, then SOLVE (ENTER). The calculator will compute and display the result. Remember to set the Begin/End setting appropriately (usually End for most problems).