$\frac{\(3(4)+3(3)+3(3)+3(4)+3(2)+3(2.7)+3(2.3)+3(2.7)+3(3.3)+2(3.3)+2(3.7)) }{\31}$

asked by guest
on Mar 18, 2025 at 9:38 pm



You asked:

Evaluate the expression: 3⋅4+3⋅3+3⋅3+3⋅4+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731\frac{3 \cdot 4 + 3 \cdot 3 + 3 \cdot 3 + 3 \cdot 4 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}

MathBot Answer:

3⋅4+3⋅3+3⋅3+3⋅4+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=9531=3.064516129032258‾\frac{3 \cdot 4 + 3 \cdot 3 + 3 \cdot 3 + 3 \cdot 4 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31} = \frac{95}{31} = 3.\overline{064516129032258}

3⋅4+3⋅3+3⋅3+3⋅4+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=12+3⋅3+3⋅3+3⋅4+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=12+9+3⋅3+3⋅4+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=21+3⋅3+3⋅4+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=21+9+3⋅4+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=30+3⋅4+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=30+12+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=42+3⋅2+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=42+6+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=48+3⋅2.7+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=48+3⋅2710+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=48+8110+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=56110+3⋅2.3+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=56110+3⋅2310+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=56110+6910+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=63+3⋅2.7+3⋅3.3+2⋅3.3+2⋅3.731=63+3⋅2710+3⋅3.3+2⋅3.3+2⋅3.731=63+8110+3⋅3.3+2⋅3.3+2⋅3.731=71110+3⋅3.3+2⋅3.3+2⋅3.731=71110+3⋅3310+2⋅3.3+2⋅3.731=71110+9910+2⋅3.3+2⋅3.731=81+2⋅3.3+2⋅3.731=81+2⋅3310+2⋅3.731=81+335+2⋅3.731=4385+2⋅3.731=4385+2⋅371031=4385+37531=9531\begin{aligned}\frac{3 \cdot 4 + 3 \cdot 3 + 3 \cdot 3 + 3 \cdot 4 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}&=\frac{12 + 3 \cdot 3 + 3 \cdot 3 + 3 \cdot 4 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{12 + 9 + 3 \cdot 3 + 3 \cdot 4 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{21 + 3 \cdot 3 + 3 \cdot 4 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{21 + 9 + 3 \cdot 4 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{30 + 3 \cdot 4 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{30 + 12 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{42 + 3 \cdot 2 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{42 + 6 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{48 + 3 \cdot 2.7 + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{48 + 3 \cdot \frac{27}{10} + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{48 + \frac{81}{10} + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{\frac{561}{10} + 3 \cdot 2.3 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{\frac{561}{10} + 3 \cdot \frac{23}{10} + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{\frac{561}{10} + \frac{69}{10} + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{63 + 3 \cdot 2.7 + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{63 + 3 \cdot \frac{27}{10} + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{63 + \frac{81}{10} + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{\frac{711}{10} + 3 \cdot 3.3 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{\frac{711}{10} + 3 \cdot \frac{33}{10} + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{\frac{711}{10} + \frac{99}{10} + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{81 + 2 \cdot 3.3 + 2 \cdot 3.7}{31}\\&=\frac{81 + 2 \cdot \frac{33}{10} + 2 \cdot 3.7}{31}\\&=\frac{81 + \frac{33}{5} + 2 \cdot 3.7}{31}\\&=\frac{\frac{438}{5} + 2 \cdot 3.7}{31}\\&=\frac{\frac{438}{5} + 2 \cdot \frac{37}{10}}{31}\\&=\frac{\frac{438}{5} + \frac{37}{5}}{31}\\&=\frac{95}{31}\end{aligned}

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