Understanding and Simplifying Complex Mathematical Expressions

Mathematics is a fundamental discipline that underlies many aspects of technology, engineering, and everyday life. Understanding complex mathematical expressions and simplifying them is a key skill. In this article, we will break down and simplify the expression 5 x 0.2 4 x 0.5 6 x 0.5 x 5 step by step. This process not only helps in solving the problem accurately but also improves our ability to handle similar problems in the future.

Breaking Down the Expression

To solve the given mathematical expression 5 x 0.2 4 x 0.5 6 x 0.5 x 5, it's beneficial to break it down into individual multiplication operations first. Let's do this step-by-step:

Step 1: Calculate Each Multiplication

5 times 0.2: 5 x 0.2 1.0 4 times 0.5: 4 x 0.5 2.0 6 times 0.5 times 5: 6 x 0.5 3.0
3.0 x 5 15.0

Step 2: Add the Results Together

Now we add the results of these individual multiplications together: 1.0 2.0 15.0 18.0

Step 3: Multiply the Sum by 5

Finally, we multiply the sum by 5: 18.0 x 5 90.0

Simplifying the Expression

Alternatively, we can simplify the expression 5 x 0.2 4 x 0.5 6 x 0.5 x 5 by first solving the multiplications within the parentheses and then substituting these values back into the original expression:

Step 1: Simplifying the Multiplications Within Parentheses

5 x 0.2 1 4 x 0.5 2 6 x 0.5 3 3 x 5 15

Step 2: Substituting the Values Back

Now, substitute these simplified values back into the expression:

1 2 15 18

And then multiply the sum by 5:

18 x 5 90

Conclusion

The value of the expression 5 x 0.2 4 x 0.5 6 x 0.5 x 5 is 90.

Understanding and simplifying mathematical expressions is a crucial skill in various fields. If you're working on engineering projects, financial analyses, or even everyday problem-solving, mastering these techniques can be incredibly beneficial. Whether you choose to break down the expression step-by-step or simplify it first, the key is to ensure that each step is accurate and logical.

For more resources and detailed explanations, please visit our website or consult a reliable math textbook.