Solve 11/231/2/2frac{1{3}1frac{1/4}{2+3frac{2}{3}}}

$$1 \frac{ 1 }{ 2 } \frac{ 3 \frac{ 1 }{ 2 } }{ 2 \frac{ 1 }{ 3 } \frac{ 1 \frac{ 1 }{ 4 } }{ 2+3 \frac{ 2 }{ 3 } } }$$

Evaluate

$$\frac{51}{5}=10.2$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{2+1}{2}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}}$$

Multiply 3 and 2 to get 6.

$$\frac{3}{2}\times \frac{\frac{6+1}{2}}{\frac{2\times 3+1}{3}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}}$$

Add 6 and 1 to get 7.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{2\times 3+1}{3}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}}$$

Multiply 2 and 3 to get 6.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{6+1}{3}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}}$$

Add 6 and 1 to get 7.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}}$$

Multiply 1 and 4 to get 4.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{\frac{4+1}{4}}{2+\frac{3\times 3+2}{3}}}$$

Add 4 and 1 to get 5.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{\frac{5}{4}}{2+\frac{3\times 3+2}{3}}}$$

Multiply 3 and 3 to get 9.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{\frac{5}{4}}{2+\frac{9+2}{3}}}$$

Add 9 and 2 to get 11.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{\frac{5}{4}}{2+\frac{11}{3}}}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{\frac{5}{4}}{\frac{6}{3}+\frac{11}{3}}}$$

Since \frac{6}{3} and \frac{11}{3} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{\frac{5}{4}}{\frac{6+11}{3}}}$$

Add 6 and 11 to get 17.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{\frac{5}{4}}{\frac{17}{3}}}$$

Divide \frac{5}{4} by \frac{17}{3} by multiplying \frac{5}{4} by the reciprocal of \frac{17}{3}.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{5}{4}\times \frac{3}{17}}$$

Multiply \frac{5}{4} times \frac{3}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{5\times 3}{4\times 17}}$$

Do the multiplications in the fraction \frac{5\times 3}{4\times 17}.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7}{3}\times \frac{15}{68}}$$

Multiply \frac{7}{3} times \frac{15}{68} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{7\times 15}{3\times 68}}$$

Do the multiplications in the fraction \frac{7\times 15}{3\times 68}.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{105}{204}}$$

Reduce the fraction \frac{105}{204} to lowest terms by extracting and canceling out 3.

$$\frac{3}{2}\times \frac{\frac{7}{2}}{\frac{35}{68}}$$

Divide \frac{7}{2} by \frac{35}{68} by multiplying \frac{7}{2} by the reciprocal of \frac{35}{68}.

$$\frac{3}{2}\times \frac{7}{2}\times \frac{68}{35}$$

Multiply \frac{7}{2} times \frac{68}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}\times \frac{7\times 68}{2\times 35}$$

Do the multiplications in the fraction \frac{7\times 68}{2\times 35}.

$$\frac{3}{2}\times \frac{476}{70}$$

Reduce the fraction \frac{476}{70} to lowest terms by extracting and canceling out 14.

$$\frac{3}{2}\times \frac{34}{5}$$

Multiply \frac{3}{2} times \frac{34}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 34}{2\times 5}$$

Do the multiplications in the fraction \frac{3\times 34}{2\times 5}.

$$\frac{102}{10}$$

Reduce the fraction \frac{102}{10} to lowest terms by extracting and canceling out 2.

$$\frac{51}{5}$$

Factor

$$\frac{3 \cdot 17}{5} = 10\frac{1}{5} = 10.2$$