Pregunta
General revision 10) If \( 1 \frac{7}{14}-k=1 \), then the value of \( k=\ldots \ldots \ldots \) \( \begin{array}{llll}\text { a. } \frac{8}{14} & \text { b. } \frac{1}{2} & \text { c. } \frac{5}{14} & \text { d. } \frac{5}{7}\end{array} \)
Ask by Moran Gough. in Egypt
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( k = \frac{1}{2} \)
Solución
1. Convert the mixed number to an improper fraction:
\[
1 \frac{7}{14} = 1 + \frac{7}{14} = 1 + \frac{1}{2} = \frac{3}{2}
\]
2. Substitute into the equation:
\[
\frac{3}{2} - k = 1
\]
3. Solve for \( k \):
\[
k = \frac{3}{2} - 1 = \frac{3}{2} - \frac{2}{2} = \frac{1}{2}
\]
4. Therefore, the value of \( k \) is:
\[
k = \frac{1}{2}
\]
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Simplifique esta solución Beyond the Answer
To solve the equation \( 1 \frac{7}{14} - k = 1 \), first convert the mixed number to an improper fraction. This gives you \( 1 \frac{7}{14} = \frac{14}{14} + \frac{7}{14} = \frac{21}{14} \). Now, rewrite the equation as \( \frac{21}{14} - k = 1 \). Next, express \( 1 \) as a fraction with a denominator of \( 14 \), which is \( \frac{14}{14} \). Thus, your equation becomes \( \frac{21}{14} - k = \frac{14}{14} \). Subtract \( \frac{14}{14} \) from \( \frac{21}{14} \) to find \( k \): \[ k = \frac{21}{14} - \frac{14}{14} = \frac{7}{14} = \frac{1}{2}. \] So, the value of \( k \) is \( \frac{1}{2} \), which corresponds to option **b**.
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