Simplify: 1/4 + 1/4 * (1/4) / (1/4 + 1/4 * 1/4)

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Understand the Problem

The question is asking to simplify a mathematical expression involving fractions and determine its value.

Answer

The simplified value of the expression is \( \frac{8}{5} \).
Answer for screen readers

The final simplified value of the expression is ( \frac{8}{5} ).

Steps to Solve

  1. Identify the Expression

    We start with simplifying the expression: $$ \frac{\frac{1}{4} + \frac{1}{4}}{\frac{1}{4} + \left(\frac{1}{4} \times \frac{1}{4}\right)} $$

  2. Simplify the Numerator

    The numerator is: $$ \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $$

  3. Simplify the Denominator

    The denominator is: $$ \frac{1}{4} + \left(\frac{1}{4} \times \frac{1}{4}\right) $$

    Calculate ( \frac{1}{4} \times \frac{1}{4} ): $$ \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} $$

    Now combine them: $$ \frac{1}{4} + \frac{1}{16} = \frac{4}{16} + \frac{1}{16} = \frac{5}{16} $$

  4. Combine the Results

    Now, substitute the simplified numerator and denominator into the expression: $$ \frac{\frac{1}{2}}{\frac{5}{16}} $$

  5. Simplify the Fraction

    To divide by a fraction, multiply by its reciprocal: $$ \frac{1}{2} \times \frac{16}{5} = \frac{16}{10} = \frac{8}{5} $$

  6. Final Answer

    Thus, the simplified value of the original expression is: $$ \frac{8}{5} $$

The final simplified value of the expression is ( \frac{8}{5} ).

More Information

The expression simplifies to a fraction greater than 1, meaning its final value indicates that the operation involves combining fractions and results in a rational number that can be interpreted in various contexts.

Tips

  • Confusing addition and multiplication of fractions can lead to incorrect simplifications.
  • Forgetting to find a common denominator when combining fractions can cause errors.
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