Solve x\div1\times(31)/(35)=9\times(1)/(3)

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Question

$$x \div 1 \times \frac{ 31 }{ 35 } =9 \times \frac{ 1 }{ 3 }$$

$x = \frac{105}{31} = 3\frac{12}{31} \approx 3.387096774$

Multiply both sides of the equation by $105$, the least common multiple of $35,3$.

$$105x\times \frac{31}{35}=945\times \frac{1}{3}$$

Express $105\times \frac{31}{35}$ as a single fraction.

$$\frac{105\times 31}{35}x=945\times \frac{1}{3}$$

Multiply $105$ and $31$ to get $3255$.

$$\frac{3255}{35}x=945\times \frac{1}{3}$$

Divide $3255$ by $35$ to get $93$.

$$93x=945\times \frac{1}{3}$$

Multiply $945$ and $\frac{1}{3}$ to get $\frac{945}{3}$.

$$93x=\frac{945}{3}$$

Divide $945$ by $3$ to get $315$.

$$93x=315$$

Divide both sides by $93$.

$$x=\frac{315}{93}$$

Reduce the fraction $\frac{315}{93}$ to lowest terms by extracting and canceling out $3$.

$$x=\frac{105}{31}$$