Solve frac{5/6/3frac{1{4}}}{12/3}

$$\frac{ \frac{ \frac{ 5 }{ 6 } }{ 3 \frac{ 1 }{ 4 } } }{ 1 \frac{ 2 }{ 3 } }$$

Evaluate

$$\frac{2}{13}\approx 0.153846154$$

Solution Steps

Divide \frac{\frac{5}{6}}{\frac{3\times 4+1}{4}} by \frac{1\times 3+2}{3} by multiplying \frac{\frac{5}{6}}{\frac{3\times 4+1}{4}} by the reciprocal of \frac{1\times 3+2}{3}.

$$\frac{\frac{5}{6}\times 3}{\frac{3\times 4+1}{4}\left(1\times 3+2\right)}$$

Express \frac{5}{6}\times 3 as a single fraction.

$$\frac{\frac{5\times 3}{6}}{\frac{3\times 4+1}{4}\left(1\times 3+2\right)}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{15}{6}}{\frac{3\times 4+1}{4}\left(1\times 3+2\right)}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{5}{2}}{\frac{3\times 4+1}{4}\left(1\times 3+2\right)}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{5}{2}}{\frac{12+1}{4}\left(1\times 3+2\right)}$$

Add 12 and 1 to get 13.

$$\frac{\frac{5}{2}}{\frac{13}{4}\left(1\times 3+2\right)}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{5}{2}}{\frac{13}{4}\left(3+2\right)}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{2}}{\frac{13}{4}\times 5}$$

Express \frac{13}{4}\times 5 as a single fraction.

$$\frac{\frac{5}{2}}{\frac{13\times 5}{4}}$$

Multiply 13 and 5 to get 65.

$$\frac{\frac{5}{2}}{\frac{65}{4}}$$

Divide \frac{5}{2} by \frac{65}{4} by multiplying \frac{5}{2} by the reciprocal of \frac{65}{4}.

$$\frac{5}{2}\times \frac{4}{65}$$

Multiply \frac{5}{2} times \frac{4}{65} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{2\times 65}$$

Do the multiplications in the fraction \frac{5\times 4}{2\times 65}.

$$\frac{20}{130}$$

Reduce the fraction \frac{20}{130} to lowest terms by extracting and canceling out 10.

$$\frac{2}{13}$$

Factor

$$\frac{2}{13} = 0.15384615384615385$$