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

$$\frac{25}{72}\approx 0.347222222$$

Solution Steps

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

$$\frac{\frac{2}{4}-\frac{3}{4}+\frac{2}{3}}{\frac{6}{5}}$$

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

$$\frac{\frac{2-3}{4}+\frac{2}{3}}{\frac{6}{5}}$$

Subtract 3 from 2 to get -1.

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

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

$$\frac{-\frac{3}{12}+\frac{8}{12}}{\frac{6}{5}}$$

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

$$\frac{\frac{-3+8}{12}}{\frac{6}{5}}$$

Add -3 and 8 to get 5.

$$\frac{\frac{5}{12}}{\frac{6}{5}}$$

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

$$\frac{5}{12}\times \frac{5}{6}$$

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

$$\frac{5\times 5}{12\times 6}$$

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

$$\frac{25}{72}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {3} \cdot 3 ^ {2}} = 0.3472222222222222$$