\frac{35\times 6+36\times 6+37\times 2+38\times 12+39\times 14}{6+6+2+12+14}

asked by guest
on Oct 21, 2024 at 9:19 pm



You asked:

Evaluate the expression: \(\frac{35 \cdot 6 + 36 \cdot 6 + 37 \cdot 2 + 38 \cdot 12 + 39 \cdot 14}{6 + 6 + 2 + 12 + 14}\)

MathBot Answer:

\[\frac{35 \cdot 6 + 36 \cdot 6 + 37 \cdot 2 + 38 \cdot 12 + 39 \cdot 14}{6 + 6 + 2 + 12 + 14} = \frac{751}{20} = 37.55\]

\[\begin{aligned}\frac{35 \cdot 6 + 36 \cdot 6 + 37 \cdot 2 + 38 \cdot 12 + 39 \cdot 14}{6 + 6 + 2 + 12 + 14}& = \left(35 \cdot 6 + 36 \cdot 6 + 37 \cdot 2 + 38 \cdot 12 + 39 \cdot 14\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = \left(210 + 36 \cdot 6 + 37 \cdot 2 + 38 \cdot 12 + 39 \cdot 14\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = \left(210 + 216 + 37 \cdot 2 + 38 \cdot 12 + 39 \cdot 14\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = \left(210 + 216 + 74 + 38 \cdot 12 + 39 \cdot 14\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = \left(210 + 216 + 74 + 456 + 39 \cdot 14\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = \left(210 + 216 + 74 + 456 + 546\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = \left(426 + 74 + 456 + 546\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = \left(500 + 456 + 546\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = \left(956 + 546\right) \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = 1502 \cdot \frac{1}{6 + 6 + 2 + 12 + 14}\\& = 1502 \cdot \frac{1}{12 + 2 + 12 + 14}\\& = 1502 \cdot \frac{1}{14 + 12 + 14}\\& = 1502 \cdot \frac{1}{26 + 14}\\& = \frac{1502}{40}\\& = \frac{751}{20}\end{aligned}\]

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