Pregunta
Evaluate \( \frac{1}{5-\frac{1}{3-\frac{1}{1-\frac{1}{2}}}} \) without a calculato
Ask by Norton Higgins. in Australia
Feb 06,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The value of the expression is \( \frac{1}{4} \).
Solución
To evaluate the expression:
\[
\frac{1}{5 - \frac{1}{3 - \frac{1}{1 - \frac{1}{2}}}}
\]
We'll work from the innermost part outward.
1. **Innermost Fraction:**
\[
1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}
\]
2. **Next Layer:**
\[
3 - \frac{1}{\frac{1}{2}} = 3 - 2 = 1
\]
3. **Substitute Back:**
\[
5 - \frac{1}{1} = 5 - 1 = 4
\]
4. **Final Calculation:**
\[
\frac{1}{4}
\]
So, the value of the expression is:
\(\boxed{\dfrac{1}{4}}\)
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Extra Insights
To evaluate the expression \( \frac{1}{5-\frac{1}{3-\frac{1}{1-\frac{1}{2}}}} \), we will work from the innermost fraction outwards. First, let's start with the innermost part: 1. Calculate \( 1 - \frac{1}{2} \): \[ 1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2} \] 2. Now, we substitute this result into the next layer: \[ 3 - \frac{1}{\frac{1}{2}} = 3 - 2 = 1 \] 3. Substitute this back into the next layer: \[ 5 - \frac{1}{1} = 5 - 1 = 4 \] Now we can compute the original expression: \[ \frac{1}{4} \] Thus, the final result is: \[ \boxed{\frac{1}{4}} \]
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