Simplify: 1/4 + 1/4 * (1/4) / (1/4 + 1/4 * 1/4)
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
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Identify the Expression
We start with simplifying the expression: $$ \frac{\frac{1}{4} + \frac{1}{4}}{\frac{1}{4} + \left(\frac{1}{4} \times \frac{1}{4}\right)} $$
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Simplify the Numerator
The numerator is: $$ \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $$
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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: $$ \frac{1}{4} + \frac{1}{16} = \frac{4}{16} + \frac{1}{16} = \frac{5}{16} $$
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Combine the Results
Now, substitute the simplified numerator and denominator into the expression: $$ \frac{\frac{1}{2}}{\frac{5}{16}} $$
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Simplify the Fraction
To divide by a fraction, multiply by its reciprocal: $$ \frac{1}{2} \times \frac{16}{5} = \frac{16}{10} = \frac{8}{5} $$
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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.
