Solve 12/7:3/14+6/11-18/5*frac{20}{9}

$$\frac { 12 } { 7 } : \frac { 3 } { 14 } + \frac { 6 } { 11 } - \frac { 18 } { 5 } \cdot \frac { 20 } { 9 }$$

Evaluate

$$\frac{6}{11}\approx 0.545454545$$

Solution Steps

Divide \frac{12}{7} by \frac{3}{14} by multiplying \frac{12}{7} by the reciprocal of \frac{3}{14}.

$$\frac{12}{7}\times \frac{14}{3}+\frac{6}{11}-\frac{18}{5}\times \frac{20}{9}$$

Multiply \frac{12}{7} times \frac{14}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 14}{7\times 3}+\frac{6}{11}-\frac{18}{5}\times \frac{20}{9}$$

Do the multiplications in the fraction \frac{12\times 14}{7\times 3}.

$$\frac{168}{21}+\frac{6}{11}-\frac{18}{5}\times \frac{20}{9}$$

Divide 168 by 21 to get 8.

$$8+\frac{6}{11}-\frac{18}{5}\times \frac{20}{9}$$

Convert 8 to fraction \frac{88}{11}.

$$\frac{88}{11}+\frac{6}{11}-\frac{18}{5}\times \frac{20}{9}$$

Since \frac{88}{11} and \frac{6}{11} have the same denominator, add them by adding their numerators.

$$\frac{88+6}{11}-\frac{18}{5}\times \frac{20}{9}$$

Add 88 and 6 to get 94.

$$\frac{94}{11}-\frac{18}{5}\times \frac{20}{9}$$

Multiply \frac{18}{5} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{94}{11}-\frac{18\times 20}{5\times 9}$$

Do the multiplications in the fraction \frac{18\times 20}{5\times 9}.

$$\frac{94}{11}-\frac{360}{45}$$

Divide 360 by 45 to get 8.

$$\frac{94}{11}-8$$

Convert 8 to fraction \frac{88}{11}.

$$\frac{94}{11}-\frac{88}{11}$$

Since \frac{94}{11} and \frac{88}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{94-88}{11}$$

Subtract 88 from 94 to get 6.

$$\frac{6}{11}$$

Factor

$$\frac{2 \cdot 3}{11} = 0.5454545454545454$$