Solve 11/2[31/2div21/3{11/4div(2+3frac{2}{3})}]

$$1 \frac { 1 } { 2 } [ 3 \frac { 1 } { 2 } \div 2 \frac { 1 } { 3 } \{ 1 \frac { 1 } { 4 } \div ( 2 + 3 \frac { 2 } { 3 } ) \} ]$$

Evaluate

$$\frac{135}{272}\approx 0.496323529$$

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.

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

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

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

Cancel out 1+2\times 3 in both numerator and denominator.

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

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

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

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

$$\frac{9}{4}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Multiply 1 and 4 to get 4.

$$\frac{9}{4}\times \frac{\frac{4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Add 4 and 1 to get 5.

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

Multiply 3 and 3 to get 9.

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

Add 9 and 2 to get 11.

$$\frac{9}{4}\times \frac{\frac{5}{4}}{2+\frac{11}{3}}$$

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

$$\frac{9}{4}\times \frac{\frac{5}{4}}{\frac{6}{3}+\frac{11}{3}}$$

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

$$\frac{9}{4}\times \frac{\frac{5}{4}}{\frac{6+11}{3}}$$

Add 6 and 11 to get 17.

$$\frac{9}{4}\times \frac{\frac{5}{4}}{\frac{17}{3}}$$

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

$$\frac{9}{4}\times \frac{5}{4}\times \frac{3}{17}$$

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

$$\frac{9}{4}\times \frac{5\times 3}{4\times 17}$$

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

$$\frac{9}{4}\times \frac{15}{68}$$

Multiply \frac{9}{4} times \frac{15}{68} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 15}{4\times 68}$$

Do the multiplications in the fraction \frac{9\times 15}{4\times 68}.

$$\frac{135}{272}$$

Factor

$$\frac{3 ^ {3} \cdot 5}{2 ^ {4} \cdot 17} = 0.4963235294117647$$