Solve {[(+1/2-3/4+2/3):(+6/5)]*(+frac{0}{5})}+frac{3}{4}-frac{1}{3}+frac{1}{1}*(+frac{9}{4})

$$\{ [ ( + \frac { 1 } { 2 } - \frac { 3 } { 4 } + \frac { 2 } { 3 } ) : ( + \frac { 6 } { 5 } ) ] \cdot ( + \frac { 0 } { 5 } ) \} + \frac { 3 } { 4 } - \frac { 1 } { 3 } + \frac { 1 } { 1 } \cdot ( + \frac { 9 } { 4 } )$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{1}{2}-\frac{3}{4}+\frac{2}{3}}{\frac{6}{5}}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{\frac{2}{4}-\frac{3}{4}+\frac{2}{3}}{\frac{6}{5}}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

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

$$\frac{\frac{2-3}{4}+\frac{2}{3}}{\frac{6}{5}}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Subtract 3 from 2 to get -1.

$$\frac{-\frac{1}{4}+\frac{2}{3}}{\frac{6}{5}}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{1}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{-\frac{3}{12}+\frac{8}{12}}{\frac{6}{5}}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Since -\frac{3}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-3+8}{12}}{\frac{6}{5}}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Add -3 and 8 to get 5.

$$\frac{\frac{5}{12}}{\frac{6}{5}}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Divide \frac{5}{12} by \frac{6}{5} by multiplying \frac{5}{12} by the reciprocal of \frac{6}{5}.

$$\frac{5}{12}\times \frac{5}{6}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Multiply \frac{5}{12} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 5}{12\times 6}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Do the multiplications in the fraction \frac{5\times 5}{12\times 6}.

$$\frac{25}{72}\times \frac{0}{5}+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Zero divided by any non-zero number gives zero.

$$\frac{25}{72}\times 0+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Multiply \frac{25}{72} and 0 to get 0.

$$0+\frac{3}{4}-\frac{1}{3}+1\times \frac{9}{4}$$

Add 0 and \frac{3}{4} to get \frac{3}{4}.

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

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{9}{12}-\frac{4}{12}+1\times \frac{9}{4}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-4}{12}+1\times \frac{9}{4}$$

Subtract 4 from 9 to get 5.

$$\frac{5}{12}+1\times \frac{9}{4}$$

Multiply 1 and \frac{9}{4} to get \frac{9}{4}.

$$\frac{5}{12}+\frac{9}{4}$$

Least common multiple of 12 and 4 is 12. Convert \frac{5}{12} and \frac{9}{4} to fractions with denominator 12.

$$\frac{5}{12}+\frac{27}{12}$$

Since \frac{5}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{5+27}{12}$$

Add 5 and 27 to get 32.

$$\frac{32}{12}$$

Reduce the fraction \frac{32}{12} to lowest terms by extracting and canceling out 4.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$