$1/2*12/13+1/3*12/13+1/4*12/13$

asked by guest
on Sep 20, 2024 at 8:32 am



You asked:

Evaluate the expression: \(\frac{\frac{1}{2} \cdot 12}{13} + \frac{\frac{1}{3} \cdot 12}{13} + \frac{\frac{1}{4} \cdot 12}{13}\)

MathBot Answer:

\[\frac{\frac{1}{2} \cdot 12}{13} + \frac{\frac{1}{3} \cdot 12}{13} + \frac{\frac{1}{4} \cdot 12}{13} = 1\]

\[\begin{aligned}\frac{\frac{1}{2} \cdot 12}{13} + \frac{\frac{1}{3} \cdot 12}{13} + \frac{\frac{1}{4} \cdot 12}{13}& = \frac{12}{2} \cdot \frac{1}{13} + \frac{12}{3} \cdot \frac{1}{13} + \frac{12}{4} \cdot \frac{1}{13}\\& = \frac{1}{2} \cdot \frac{12}{13} + \frac{12}{3} \cdot \frac{1}{13} + \frac{12}{4} \cdot \frac{1}{13}\\& = \frac{6}{13} + \frac{12}{3} \cdot \frac{1}{13} + \frac{12}{4} \cdot \frac{1}{13}\\& = \frac{6}{13} + \frac{1}{3} \cdot \frac{12}{13} + \frac{12}{4} \cdot \frac{1}{13}\\& = \frac{6}{13} + \frac{4}{13} + \frac{12}{4} \cdot \frac{1}{13}\\& = \frac{6}{13} + \frac{4}{13} + \frac{1}{4} \cdot \frac{12}{13}\\& = \frac{6}{13} + \frac{4}{13} + \frac{3}{13}\\& = \frac{10}{13} + \frac{3}{13}\\& = 1\end{aligned}\]

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