Solve 2(3-2/5)/2+2{2+frac{2/2+1/2}}

$$\frac { 2 ( 3 - 2 / 5 ) } { 2 + \frac { 2 } { 2 + \frac { 2 } { 2 + 1 / 2 } } }$$

Evaluate

$$\frac{182}{95}\approx 1.915789474$$

Solution Steps

Convert 3 to fraction \frac{15}{5}.

$$\frac{2\left(\frac{15}{5}-\frac{2}{5}\right)}{2+\frac{2}{2+\frac{2}{2+\frac{1}{2}}}}$$

Since \frac{15}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times \frac{15-2}{5}}{2+\frac{2}{2+\frac{2}{2+\frac{1}{2}}}}$$

Subtract 2 from 15 to get 13.

$$\frac{2\times \frac{13}{5}}{2+\frac{2}{2+\frac{2}{2+\frac{1}{2}}}}$$

Express 2\times \frac{13}{5} as a single fraction.

$$\frac{\frac{2\times 13}{5}}{2+\frac{2}{2+\frac{2}{2+\frac{1}{2}}}}$$

Multiply 2 and 13 to get 26.

$$\frac{\frac{26}{5}}{2+\frac{2}{2+\frac{2}{2+\frac{1}{2}}}}$$

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

$$\frac{\frac{26}{5}}{2+\frac{2}{2+\frac{2}{\frac{4}{2}+\frac{1}{2}}}}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{26}{5}}{2+\frac{2}{2+\frac{2}{\frac{4+1}{2}}}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{26}{5}}{2+\frac{2}{2+\frac{2}{\frac{5}{2}}}}$$

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

$$\frac{\frac{26}{5}}{2+\frac{2}{2+2\times \frac{2}{5}}}$$

Express 2\times \frac{2}{5} as a single fraction.

$$\frac{\frac{26}{5}}{2+\frac{2}{2+\frac{2\times 2}{5}}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{26}{5}}{2+\frac{2}{2+\frac{4}{5}}}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{26}{5}}{2+\frac{2}{\frac{10}{5}+\frac{4}{5}}}$$

Since \frac{10}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{26}{5}}{2+\frac{2}{\frac{10+4}{5}}}$$

Add 10 and 4 to get 14.

$$\frac{\frac{26}{5}}{2+\frac{2}{\frac{14}{5}}}$$

Divide 2 by \frac{14}{5} by multiplying 2 by the reciprocal of \frac{14}{5}.

$$\frac{\frac{26}{5}}{2+2\times \frac{5}{14}}$$

Express 2\times \frac{5}{14} as a single fraction.

$$\frac{\frac{26}{5}}{2+\frac{2\times 5}{14}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{26}{5}}{2+\frac{10}{14}}$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{26}{5}}{2+\frac{5}{7}}$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{\frac{26}{5}}{\frac{14}{7}+\frac{5}{7}}$$

Since \frac{14}{7} and \frac{5}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{26}{5}}{\frac{14+5}{7}}$$

Add 14 and 5 to get 19.

$$\frac{\frac{26}{5}}{\frac{19}{7}}$$

Divide \frac{26}{5} by \frac{19}{7} by multiplying \frac{26}{5} by the reciprocal of \frac{19}{7}.

$$\frac{26}{5}\times \frac{7}{19}$$

Multiply \frac{26}{5} times \frac{7}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{26\times 7}{5\times 19}$$

Do the multiplications in the fraction \frac{26\times 7}{5\times 19}.

$$\frac{182}{95}$$

Factor

$$\frac{2 \cdot 7 \cdot 13}{5 \cdot 19} = 1\frac{87}{95} = 1.9157894736842105$$