Solve (-7)*(2^2/3-3/4+1/2)*(-6)-0.25^2div(-1/4)div(-1)

$$( - 7 ) \times ( \frac { 2 ^ { 2 } } { 3 } - \frac { 3 } { 4 } + \frac { 1 } { 2 } ) \times ( - 6 ) - 0.25 ^ { 2 } \div ( - \frac { 1 } { 4 } ) \div ( - 1 )$$

Evaluate

$$45.25$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$-7\left(\frac{4}{3}-\frac{3}{4}+\frac{1}{2}\right)\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

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

$$-7\left(\frac{16}{12}-\frac{9}{12}+\frac{1}{2}\right)\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Since \frac{16}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$-7\left(\frac{16-9}{12}+\frac{1}{2}\right)\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Subtract 9 from 16 to get 7.

$$-7\left(\frac{7}{12}+\frac{1}{2}\right)\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Least common multiple of 12 and 2 is 12. Convert \frac{7}{12} and \frac{1}{2} to fractions with denominator 12.

$$-7\left(\frac{7}{12}+\frac{6}{12}\right)\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Since \frac{7}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$-7\times \frac{7+6}{12}\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Add 7 and 6 to get 13.

$$-7\times \frac{13}{12}\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Express -7\times \frac{13}{12} as a single fraction.

$$\frac{-7\times 13}{12}\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Multiply -7 and 13 to get -91.

$$\frac{-91}{12}\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Fraction \frac{-91}{12} can be rewritten as -\frac{91}{12} by extracting the negative sign.

$$-\frac{91}{12}\left(-6\right)-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Express -\frac{91}{12}\left(-6\right) as a single fraction.

$$\frac{-91\left(-6\right)}{12}-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Multiply -91 and -6 to get 546.

$$\frac{546}{12}-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Reduce the fraction \frac{546}{12} to lowest terms by extracting and canceling out 6.

$$\frac{91}{2}-\frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1}$$

Express \frac{\frac{0.25^{2}}{-\frac{1}{4}}}{-1} as a single fraction.

$$\frac{91}{2}-\frac{0.25^{2}}{-\frac{1}{4}\left(-1\right)}$$

Calculate 0.25 to the power of 2 and get 0.0625.

$$\frac{91}{2}-\frac{0.0625}{-\frac{1}{4}\left(-1\right)}$$

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

$$\frac{91}{2}-\frac{0.0625}{\frac{1}{4}}$$

Divide 0.0625 by \frac{1}{4} by multiplying 0.0625 by the reciprocal of \frac{1}{4}.

$$\frac{91}{2}-0.0625\times 4$$

Multiply 0.0625 and 4 to get 0.25.

$$\frac{91}{2}-0.25$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{91}{2}-\frac{1}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{91}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{182}{4}-\frac{1}{4}$$

Since \frac{182}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{182-1}{4}$$

Subtract 1 from 182 to get 181.

$$\frac{181}{4}$$

Factor

$$\frac{181}{2 ^ {2}} = 45\frac{1}{4} = 45.25$$