Solve -[1/2div92-1/2(1/2-1/3-1)]

$$- [ \frac { 1 } { 2 } \div 92 - \frac { 1 } { 2 } ( \frac { 1 } { 2 } - \frac { 1 } { 3 } - 1 ) ]$$

Evaluate

$$-\frac{233}{552}\approx -0.422101449$$

Solution Steps

Express \frac{\frac{1}{2}}{92} as a single fraction.

$$-\left(\frac{1}{2\times 92}-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{3}-1\right)\right)$$

Multiply 2 and 92 to get 184.

$$-\left(\frac{1}{184}-\frac{1}{2}\left(\frac{1}{2}-\frac{1}{3}-1\right)\right)$$

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

$$-\left(\frac{1}{184}-\frac{1}{2}\left(\frac{3}{6}-\frac{2}{6}-1\right)\right)$$

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

$$-\left(\frac{1}{184}-\frac{1}{2}\left(\frac{3-2}{6}-1\right)\right)$$

Subtract 2 from 3 to get 1.

$$-\left(\frac{1}{184}-\frac{1}{2}\left(\frac{1}{6}-1\right)\right)$$

Convert 1 to fraction \frac{6}{6}.

$$-\left(\frac{1}{184}-\frac{1}{2}\left(\frac{1}{6}-\frac{6}{6}\right)\right)$$

Since \frac{1}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\left(\frac{1}{184}-\frac{1}{2}\times \frac{1-6}{6}\right)$$

Subtract 6 from 1 to get -5.

$$-\left(\frac{1}{184}-\frac{1}{2}\left(-\frac{5}{6}\right)\right)$$

Multiply \frac{1}{2} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\left(\frac{1}{184}-\frac{1\left(-5\right)}{2\times 6}\right)$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{2\times 6}.

$$-\left(\frac{1}{184}-\frac{-5}{12}\right)$$

Fraction \frac{-5}{12} can be rewritten as -\frac{5}{12} by extracting the negative sign.

$$-\left(\frac{1}{184}-\left(-\frac{5}{12}\right)\right)$$

The opposite of -\frac{5}{12} is \frac{5}{12}.

$$-\left(\frac{1}{184}+\frac{5}{12}\right)$$

Least common multiple of 184 and 12 is 552. Convert \frac{1}{184} and \frac{5}{12} to fractions with denominator 552.

$$-\left(\frac{3}{552}+\frac{230}{552}\right)$$

Since \frac{3}{552} and \frac{230}{552} have the same denominator, add them by adding their numerators.

$$-\frac{3+230}{552}$$

Add 3 and 230 to get 233.

$$-\frac{233}{552}$$

Factor

$$-\frac{233}{552} = -0.4221014492753623$$