0.4 times 97.5 plus 0.25 tiies 99.34

Solving the Equation: 0.4 × 97.5 + 0.25 × 99.34

In mathematics, solving expressions like this requires following the order of operations, commonly known as BODMAS or PEMDAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). Let us carefully compute the given equation step by step:

Expression:

$0.4\times 97.5+0.25\times 99.34$

Step 1: Solve the multiplication parts first.

1. Calculate $0.4\times 97.5$: $$0.4\times 97.5=39.0$$
2. Calculate $0.25\times 99.34$: $$0.25\times 99.34=24.835$$

Step 2: Add the results.

Now, add the two products:

$$39.0+24.835=63.835$$

Final Answer:

The result of the equation $0.4\times 97.5+0.25\times 99.34$ is:

63.835\boxed{63.835}63.835

Breaking Down the Equation: 0.4 × 97.5 + 0.25 × 99.34

Mathematics is the foundation of many practical applications, from finance to engineering. Today, we delve into a seemingly simple equation:

0.4×97.5+0.25×99.340.4 \times 97.5 + 0.25 \times 99.340.4×97.5+0.25×99.34

This expression demonstrates how operations like multiplication and addition work together to provide a solution. Let’s explore the steps in greater detail, along with possible applications of such calculations.

Step 1: The First Multiplication

We start by calculating the first part of the equation:

0.4×97.50.4 \times 97.50.4×97.5

To compute this, we multiply:

0.4×97.5=39.00.4 \times 97.5 = 39.00.4×97.5=39.0

This step may represent a situation where 40% of a quantity (97.5) is taken. For instance, in financial terms, this could be a 40% discount on an item priced at $97.50.

Step 2: The Second Multiplication

Next, we calculate the second part:

0.25×99.340.25 \times 99.340.25×99.34

Here, $0.25$ represents 25%, which we apply to $99.34$. Performing the multiplication:

0.25×99.34=24.8350.25 \times 99.34 = 24.8350.25×99.34=24.835

This step might reflect a situation like a 25% bonus on a value of $99.34. These types of calculations are common in payroll systems, taxes, or profit-sharing schemes.

Step 3: Adding the Results

Finally, we add the results from the two calculations:

39.0+24.835=63.83539.0 + 24.835 = 63.83539.0+24.835=63.835

This represents the total combined effect of applying $0.4\times 97.5$ and $0.25\times 99.34$.

Applications of Such Calculations

These types of equations frequently appear in real-world scenarios, including:

1. Budgeting and Financial Planning:
   • Calculating discounts, taxes, or interest rates often requires multiplying percentages with base amounts and then summing the results.
2. Engineering and Physics:
   • Weighted averages or combined forces often involve similar calculations.
3. Data Analysis:
   • In statistical calculations, weighted averages like these help determine overall trends.

Tips for Accuracy in Calculations

To ensure precision, especially with decimals:

• Use a reliable calculator or software for detailed computations.
• Double-check your work by performing the steps separately.

For those who work in finance, commerce, or science, mastering these principles is essential for error-free results.

Conclusion

The solution to $0.4\times 97.5+0.25\times 99.34$ is:

63.835\boxed{63.835}63.835​

This calculation not only provides a numerical answer but also emphasizes the importance of understanding how basic arithmetic operations apply in practical situations. From discounts to data analysis, such skills are universally valuable. Keep practicing to enhance your problem-solving abilities!

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