Solve 92/3*2-11/2/2frac{1{2}+3/1+frac{1{2}}}

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

Evaluate

$$\frac{29}{27}\approx 1.074074074$$

Solution Steps

Multiply 9 and 3 to get 27.

$$\frac{27+2}{3}\times \frac{2-\frac{1\times 2+1}{2}}{\frac{2\times 2+1}{2}+\frac{3}{1+\frac{1}{2}}}$$

Add 27 and 2 to get 29.

$$\frac{29}{3}\times \frac{2-\frac{1\times 2+1}{2}}{\frac{2\times 2+1}{2}+\frac{3}{1+\frac{1}{2}}}$$

Multiply 1 and 2 to get 2.

$$\frac{29}{3}\times \frac{2-\frac{2+1}{2}}{\frac{2\times 2+1}{2}+\frac{3}{1+\frac{1}{2}}}$$

Add 2 and 1 to get 3.

$$\frac{29}{3}\times \frac{2-\frac{3}{2}}{\frac{2\times 2+1}{2}+\frac{3}{1+\frac{1}{2}}}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{29}{3}\times \frac{\frac{4}{2}-\frac{3}{2}}{\frac{2\times 2+1}{2}+\frac{3}{1+\frac{1}{2}}}$$

Since \frac{4}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29}{3}\times \frac{\frac{4-3}{2}}{\frac{2\times 2+1}{2}+\frac{3}{1+\frac{1}{2}}}$$

Subtract 3 from 4 to get 1.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{2\times 2+1}{2}+\frac{3}{1+\frac{1}{2}}}$$

Multiply 2 and 2 to get 4.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{4+1}{2}+\frac{3}{1+\frac{1}{2}}}$$

Add 4 and 1 to get 5.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{5}{2}+\frac{3}{1+\frac{1}{2}}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{5}{2}+\frac{3}{\frac{2}{2}+\frac{1}{2}}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{5}{2}+\frac{3}{\frac{2+1}{2}}}$$

Add 2 and 1 to get 3.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{5}{2}+\frac{3}{\frac{3}{2}}}$$

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

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{5}{2}+3\times \frac{2}{3}}$$

Cancel out 3 and 3.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{5}{2}+2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{5}{2}+\frac{4}{2}}$$

Since \frac{5}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{5+4}{2}}$$

Add 5 and 4 to get 9.

$$\frac{29}{3}\times \frac{\frac{1}{2}}{\frac{9}{2}}$$

Divide \frac{1}{2} by \frac{9}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{9}{2}.

$$\frac{29}{3}\times \frac{1}{2}\times \frac{2}{9}$$

Multiply \frac{1}{2} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29}{3}\times \frac{1\times 2}{2\times 9}$$

Cancel out 2 in both numerator and denominator.

$$\frac{29}{3}\times \frac{1}{9}$$

Multiply \frac{29}{3} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 1}{3\times 9}$$

Do the multiplications in the fraction \frac{29\times 1}{3\times 9}.

$$\frac{29}{27}$$

Factor

$$\frac{29}{3 ^ {3}} = 1\frac{2}{27} = 1.0740740740740742$$