Solve 6/4+9{3-3/2+frac{1{1-frac{1/2}}}}=?

$$\frac { 6 } { 4 + \frac { 9 } { 3 - \frac { 3 } { 2 + \frac { 1 } { 1 - \frac { 1 } { 2 } } } } } = ?$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

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

$$\frac{6}{4+\frac{9}{3-\frac{3}{2+\frac{1}{\frac{2}{2}-\frac{1}{2}}}}}$$

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

$$\frac{6}{4+\frac{9}{3-\frac{3}{2+\frac{1}{\frac{2-1}{2}}}}}$$

Subtract 1 from 2 to get 1.

$$\frac{6}{4+\frac{9}{3-\frac{3}{2+\frac{1}{\frac{1}{2}}}}}$$

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

$$\frac{6}{4+\frac{9}{3-\frac{3}{2+1\times 2}}}$$

Multiply 1 and 2 to get 2.

$$\frac{6}{4+\frac{9}{3-\frac{3}{2+2}}}$$

Add 2 and 2 to get 4.

$$\frac{6}{4+\frac{9}{3-\frac{3}{4}}}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{6}{4+\frac{9}{\frac{12}{4}-\frac{3}{4}}}$$

Since \frac{12}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6}{4+\frac{9}{\frac{12-3}{4}}}$$

Subtract 3 from 12 to get 9.

$$\frac{6}{4+\frac{9}{\frac{9}{4}}}$$

Divide 9 by \frac{9}{4} by multiplying 9 by the reciprocal of \frac{9}{4}.

$$\frac{6}{4+9\times \frac{4}{9}}$$

Cancel out 9 and 9.

$$\frac{6}{4+4}$$

Add 4 and 4 to get 8.

$$\frac{6}{8}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$