Solve {2-[(1+4/3):(14/8*2)]}:{[(2^3-3/5)-(13/2-frac{3}{4})]:[(frac{3}{2}):frac{1}{2}-frac{17}{5}]}

$$\{ 2 - [ ( 1 + \frac { 4 } { 3 } ) : ( \frac { 14 } { 8 } \cdot 2 ) ] \} : \{ [ ( 2 ^ { 3 } - \frac { 3 } { 5 } ) - ( \frac { 13 } { 2 } - \frac { 3 } { 4 } ) ] : [ ( \frac { 3 } { 2 } ) : \frac { 1 } { 2 } - \frac { 17 } { 5 } ] \}$$

Evaluate

$$-\frac{32}{99}\approx -0.323232323$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{2-\frac{\frac{3}{3}+\frac{4}{3}}{\frac{14}{8}\times 2}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Since \frac{3}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{2-\frac{\frac{3+4}{3}}{\frac{14}{8}\times 2}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Add 3 and 4 to get 7.

$$\frac{2-\frac{\frac{7}{3}}{\frac{14}{8}\times 2}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Reduce the fraction \frac{14}{8} to lowest terms by extracting and canceling out 2.

$$\frac{2-\frac{\frac{7}{3}}{\frac{7}{4}\times 2}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Express \frac{7}{4}\times 2 as a single fraction.

$$\frac{2-\frac{\frac{7}{3}}{\frac{7\times 2}{4}}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Multiply 7 and 2 to get 14.

$$\frac{2-\frac{\frac{7}{3}}{\frac{14}{4}}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{2-\frac{\frac{7}{3}}{\frac{7}{2}}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Divide \frac{7}{3} by \frac{7}{2} by multiplying \frac{7}{3} by the reciprocal of \frac{7}{2}.

$$\frac{2-\frac{7}{3}\times \frac{2}{7}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Multiply \frac{7}{3} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2-\frac{7\times 2}{3\times 7}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{2-\frac{2}{3}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

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

$$\frac{\frac{6}{3}-\frac{2}{3}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6-2}{3}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Subtract 2 from 6 to get 4.

$$\frac{\frac{4}{3}}{\frac{2^{3}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{4}{3}}{\frac{8-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Convert 8 to fraction \frac{40}{5}.

$$\frac{\frac{4}{3}}{\frac{\frac{40}{5}-\frac{3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Since \frac{40}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{3}}{\frac{\frac{40-3}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Subtract 3 from 40 to get 37.

$$\frac{\frac{4}{3}}{\frac{\frac{37}{5}-\left(\frac{13}{2}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{13}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{\frac{4}{3}}{\frac{\frac{37}{5}-\left(\frac{26}{4}-\frac{3}{4}\right)}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Since \frac{26}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{3}}{\frac{\frac{37}{5}-\frac{26-3}{4}}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Subtract 3 from 26 to get 23.

$$\frac{\frac{4}{3}}{\frac{\frac{37}{5}-\frac{23}{4}}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{37}{5} and \frac{23}{4} to fractions with denominator 20.

$$\frac{\frac{4}{3}}{\frac{\frac{148}{20}-\frac{115}{20}}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Since \frac{148}{20} and \frac{115}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{3}}{\frac{\frac{148-115}{20}}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

Subtract 115 from 148 to get 33.

$$\frac{\frac{4}{3}}{\frac{\frac{33}{20}}{\frac{\frac{3}{2}}{\frac{1}{2}}-\frac{17}{5}}}$$

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

$$\frac{\frac{4}{3}}{\frac{\frac{33}{20}}{\frac{3}{2}\times 2-\frac{17}{5}}}$$

Cancel out 2 and 2.

$$\frac{\frac{4}{3}}{\frac{\frac{33}{20}}{3-\frac{17}{5}}}$$

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

$$\frac{\frac{4}{3}}{\frac{\frac{33}{20}}{\frac{15}{5}-\frac{17}{5}}}$$

Since \frac{15}{5} and \frac{17}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{3}}{\frac{\frac{33}{20}}{\frac{15-17}{5}}}$$

Subtract 17 from 15 to get -2.

$$\frac{\frac{4}{3}}{\frac{\frac{33}{20}}{-\frac{2}{5}}}$$

Divide \frac{33}{20} by -\frac{2}{5} by multiplying \frac{33}{20} by the reciprocal of -\frac{2}{5}.

$$\frac{\frac{4}{3}}{\frac{33}{20}\left(-\frac{5}{2}\right)}$$

Multiply \frac{33}{20} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4}{3}}{\frac{33\left(-5\right)}{20\times 2}}$$

Do the multiplications in the fraction \frac{33\left(-5\right)}{20\times 2}.

$$\frac{\frac{4}{3}}{\frac{-165}{40}}$$

Reduce the fraction \frac{-165}{40} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{4}{3}}{-\frac{33}{8}}$$

Divide \frac{4}{3} by -\frac{33}{8} by multiplying \frac{4}{3} by the reciprocal of -\frac{33}{8}.

$$\frac{4}{3}\left(-\frac{8}{33}\right)$$

Multiply \frac{4}{3} times -\frac{8}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-8\right)}{3\times 33}$$

Do the multiplications in the fraction \frac{4\left(-8\right)}{3\times 33}.

$$\frac{-32}{99}$$

Fraction \frac{-32}{99} can be rewritten as -\frac{32}{99} by extracting the negative sign.

$$-\frac{32}{99}$$

Factor

$$-\frac{32}{99} = -0.32323232323232326$$