-5/6:(-3+7/2)-1/2*[-3*(-(1/2-frac{1}{1})+1]-এর সমাধান করুন

$$- \frac { 5 } { 6 } : ( - 3 + \frac { 7 } { 2 } ) - \frac { 1 } { 2 } \cdot [ - 3 \cdot ( - ( \frac { 1 } { 2 } - \frac { 1 } { 1 } ) + 1 ]$$

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{-\frac{5}{6}}{-3+\frac{7}{2}}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)$$

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

$$\frac{-\frac{5}{6}}{-\frac{6}{2}+\frac{7}{2}}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)$$

Since -\frac{6}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{5}{6}}{\frac{-6+7}{2}}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)$$

Add -6 and 7 to get 1.

$$\frac{-\frac{5}{6}}{\frac{1}{2}}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)$$

Divide -\frac{5}{6} by \frac{1}{2} by multiplying -\frac{5}{6} by the reciprocal of \frac{1}{2}.

$$-\frac{5}{6}\times 2-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)$$

Express -\frac{5}{6}\times 2 as a single fraction.

$$\frac{-5\times 2}{6}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)$$

Multiply -5 and 2 to get -10.

$$\frac{-10}{6}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{3}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)$$

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

$$-\frac{5}{3}-\frac{-3}{2}\left(-\left(\frac{1}{2}-1\right)+1\right)$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-\frac{5}{3}-\left(-\frac{3}{2}\left(-\left(\frac{1}{2}-1\right)+1\right)\right)$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{5}{3}-\left(-\frac{3}{2}\left(-\left(\frac{1}{2}-\frac{2}{2}\right)+1\right)\right)$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{3}-\left(-\frac{3}{2}\left(-\frac{1-2}{2}+1\right)\right)$$

Subtract 2 from 1 to get -1.

$$-\frac{5}{3}-\left(-\frac{3}{2}\left(-\left(-\frac{1}{2}\right)+1\right)\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$-\frac{5}{3}-\left(-\frac{3}{2}\left(\frac{1}{2}+1\right)\right)$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{5}{3}-\left(-\frac{3}{2}\left(\frac{1}{2}+\frac{2}{2}\right)\right)$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$-\frac{5}{3}-\left(-\frac{3}{2}\times \frac{1+2}{2}\right)$$

Add 1 and 2 to get 3.

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

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

$$-\frac{5}{3}-\frac{-3\times 3}{2\times 2}$$

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

$$-\frac{5}{3}-\frac{-9}{4}$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$-\frac{5}{3}-\left(-\frac{9}{4}\right)$$

The opposite of -\frac{9}{4} is \frac{9}{4}.

$$-\frac{5}{3}+\frac{9}{4}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{5}{3} and \frac{9}{4} to fractions with denominator 12.

$$-\frac{20}{12}+\frac{27}{12}$$

Since -\frac{20}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{-20+27}{12}$$

Add -20 and 27 to get 7.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$