0.4 times 97.5 plus 0.25 tiies 99.34

Understanding the Calculation: $0.4\times 97.5+0.25\times 99.34$

When solving mathematical expressions like $0.4\times 97.5+0.25\times 99.34$, it is important to break the calculation into smaller steps to ensure accuracy. Here’s a step-by-step guide to understanding and solving the equation.

Step 1: Analyze the Expression

The given expression consists of two terms:

1. $0.4\times 97.5$
   This involves multiplying 97.5 by 0.4.
2. $0.25\times 99.34$
   This involves multiplying 99.34 by 0.25.

Finally, these two results will be added together.

Step 2: Perform Individual Calculations

Part 1: Calculate $0.4\times 97.5$

To find $0.4\times 97.5$:

$$0.4\times 97.5=39.0$$

Part 2: Calculate $0.25\times 99.34$

To find $0.25\times 99.34$:

$$0.25\times 99.34=24.835$$

Step 3: Add the Results

Now, add the two results from the previous steps:

$$39.0+24.835=63.835$$

Final Result

The value of the expression $0.4\times 97.5+0.25\times 99.34$ is:

63.835\boxed{63.835}63.835​

Practical Applications of Such Calculations

Expressions like these are commonly used in real-life scenarios, such as:

• Financial Calculations: For instance, calculating weighted averages or allocating resources.
• Science and Engineering: To combine measurements or analyze data with given weights.
• Everyday Math: When determining proportions or combining quantities.

By breaking down the problem into smaller steps, you can solve such expressions quickly and accurately!

A Detailed Exploration of the Calculation: $0.4\times 97.5+0.25\times 99.34$

When dealing with mathematical operations like $0.4\times 97.5+0.25\times 99.34$, it’s essential to understand the purpose and process behind each part of the calculation. This kind of expression often appears in weighted averages, financial scenarios, or scientific applications. Let’s dive deeper into the calculation.

Breaking Down the Problem

The expression consists of two weighted multiplications, followed by their sum:

1. $0.4\times 97.5$: This part signifies multiplying a weight of 0.4 with a value of 97.5.
2. $0.25\times 99.34$: Similarly, this part multiplies a weight of 0.25 with a value of 99.34.
3. Finally, adding the results combines the weighted contributions.

This is a straightforward arithmetic operation but can become complex when applied in larger contexts.

Detailed Step-by-Step Solution

Step 1: Calculate $0.4\times 97.5$

The first term is:

$$0.4\times 97.5$$Here, $0.4$ represents 40% of $97.5$. Multiplying these gives:

$$0.4\times 97.5=39.0$$

Step 2: Calculate $0.25\times 99.34$

The second term is:

$$0.25\times 99.34$$Here, $0.25$ represents 25% of $99.34$. Multiplying these gives:

$$0.25\times 99.34=24.835$$

Step 3: Add the Results

Now, add the results from the two calculations:

$$39.0+24.835=63.835$$

Final Answer

The total value of the expression is:

63.835\boxed{63.835}63.835​

Why Is This Calculation Useful?

This kind of arithmetic operation has practical applications in various fields, including:

1. Weighted Averages in Statistics

• For example, if $97.5$ represents a score weighted at 40% and $99.34$ a score weighted at 25%, this calculation finds the combined weighted score.

2. Financial Analysis

• Such equations are used to determine weighted investments or returns, where each investment is multiplied by its proportion in the portfolio.

3. Business and Economics

• Weighted costs or profits are often calculated using similar expressions to assess overall performance.

4. Real-Life Examples

• Imagine you are calculating a blended fuel efficiency score where $97.5$ is the mileage of one type of fuel and $99.34$ is the mileage of another, and the respective proportions are 40% and 25%.

Verification and Accuracy

To ensure accuracy, calculations can be verified using different methods:

Manual Verification

Repeat the multiplication and addition steps by hand to confirm the results.

Calculator or Spreadsheet

Use a scientific calculator or software like Excel to double-check the computations.

Extending the Calculation

If additional weights or values were added, the expression could grow more complex:

$$0.4\times 97.5+0.25\times 99.34+0.35\times 98.2$$Such extensions are common in weighted averages, where the sum of weights (e.g., $0.4+0.25+0.35$) must equal 1.

Conclusion

The expression $0.4\times 97.5+0.25\times 99.34$ simplifies to $63.835$, a straightforward yet versatile calculation with numerous applications. Whether for academics, finance, or real-life decisions, understanding the process ensures precision and confidence in problem-solving.