Solve 139/31:9/6+frac{1{6}}

$$\frac { 139 } { 31 } : \frac { 9 } { 6 + \frac { 1 } { 6 } }$$

Evaluate

$$\frac{5143}{1674}\approx 3.072281959$$

Solution Steps

Divide \frac{139}{31} by \frac{9}{6+\frac{1}{6}} by multiplying \frac{139}{31} by the reciprocal of \frac{9}{6+\frac{1}{6}}.

$$\frac{139\left(6+\frac{1}{6}\right)}{31\times 9}$$

Convert 6 to fraction \frac{36}{6}.

$$\frac{139\left(\frac{36}{6}+\frac{1}{6}\right)}{31\times 9}$$

Since \frac{36}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{139\times \frac{36+1}{6}}{31\times 9}$$

Add 36 and 1 to get 37.

$$\frac{139\times \frac{37}{6}}{31\times 9}$$

Express 139\times \frac{37}{6} as a single fraction.

$$\frac{\frac{139\times 37}{6}}{31\times 9}$$

Multiply 139 and 37 to get 5143.

$$\frac{\frac{5143}{6}}{31\times 9}$$

Multiply 31 and 9 to get 279.

$$\frac{\frac{5143}{6}}{279}$$

Express \frac{\frac{5143}{6}}{279} as a single fraction.

$$\frac{5143}{6\times 279}$$

Multiply 6 and 279 to get 1674.

$$\frac{5143}{1674}$$

Factor

$$\frac{37 \cdot 139}{2 \cdot 3 ^ {3} \cdot 31} = 3\frac{121}{1674} = 3.0722819593787336$$