Solve 9/4:{2/3-(1/4:1/2)-frac{3}{4}}+frac{1}{2}*frac{1}{3}-frac{1}{2}

$$\frac { 9 } { 4 } : \{ \frac { 2 } { 3 } - ( \frac { 1 } { 4 } : \frac { 1 } { 2 } ) - \frac { 3 } { 4 } \} + \frac { 1 } { 2 } \cdot \frac { 1 } { 3 } - \frac { 1 } { 2 }$$

Evaluate

$$-\frac{88}{21}\approx -4.19047619$$

Solution Steps

Divide \frac{1}{4} by \frac{1}{2} by multiplying \frac{1}{4} by the reciprocal of \frac{1}{2}.

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

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

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

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

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

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

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

Since \frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 4 to get 1.

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

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{9}{4}}{\frac{2}{12}-\frac{9}{12}}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Since \frac{2}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{4}}{\frac{2-9}{12}}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Subtract 9 from 2 to get -7.

$$\frac{\frac{9}{4}}{-\frac{7}{12}}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Divide \frac{9}{4} by -\frac{7}{12} by multiplying \frac{9}{4} by the reciprocal of -\frac{7}{12}.

$$\frac{9}{4}\left(-\frac{12}{7}\right)+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Multiply \frac{9}{4} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\left(-12\right)}{4\times 7}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Do the multiplications in the fraction \frac{9\left(-12\right)}{4\times 7}.

$$\frac{-108}{28}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Reduce the fraction \frac{-108}{28} to lowest terms by extracting and canceling out 4.

$$-\frac{27}{7}+\frac{1}{2}\times \frac{1}{3}-\frac{1}{2}$$

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{27}{7}+\frac{1\times 1}{2\times 3}-\frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

$$-\frac{27}{7}+\frac{1}{6}-\frac{1}{2}$$

Least common multiple of 7 and 6 is 42. Convert -\frac{27}{7} and \frac{1}{6} to fractions with denominator 42.

$$-\frac{162}{42}+\frac{7}{42}-\frac{1}{2}$$

Since -\frac{162}{42} and \frac{7}{42} have the same denominator, add them by adding their numerators.

$$\frac{-162+7}{42}-\frac{1}{2}$$

Add -162 and 7 to get -155.

$$-\frac{155}{42}-\frac{1}{2}$$

Least common multiple of 42 and 2 is 42. Convert -\frac{155}{42} and \frac{1}{2} to fractions with denominator 42.

$$-\frac{155}{42}-\frac{21}{42}$$

Since -\frac{155}{42} and \frac{21}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-155-21}{42}$$

Subtract 21 from -155 to get -176.

$$\frac{-176}{42}$$

Reduce the fraction \frac{-176}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{88}{21}$$

Factor

$$-\frac{88}{21} = -4\frac{4}{21} = -4.190476190476191$$