Solve -12*(-1/6+1/48)-177/16div(-3)^2=

$$- 12 \times ( - \frac { 1 } { 6 } + \frac { 1 } { 48 } ) - 17 \frac { 7 } { 16 } \div ( - 3 ) ^ { 2 } =$$

Evaluate

$$-\frac{3}{16}=-0.1875$$

Solution Steps

Least common multiple of 6 and 48 is 48. Convert -\frac{1}{6} and \frac{1}{48} to fractions with denominator 48.

$$-12\left(-\frac{8}{48}+\frac{1}{48}\right)-\frac{\frac{17\times 16+7}{16}}{\left(-3\right)^{2}}$$

Since -\frac{8}{48} and \frac{1}{48} have the same denominator, add them by adding their numerators.

$$-12\times \frac{-8+1}{48}-\frac{\frac{17\times 16+7}{16}}{\left(-3\right)^{2}}$$

Add -8 and 1 to get -7.

$$-12\left(-\frac{7}{48}\right)-\frac{\frac{17\times 16+7}{16}}{\left(-3\right)^{2}}$$

Express -12\left(-\frac{7}{48}\right) as a single fraction.

$$\frac{-12\left(-7\right)}{48}-\frac{\frac{17\times 16+7}{16}}{\left(-3\right)^{2}}$$

Multiply -12 and -7 to get 84.

$$\frac{84}{48}-\frac{\frac{17\times 16+7}{16}}{\left(-3\right)^{2}}$$

Reduce the fraction \frac{84}{48} to lowest terms by extracting and canceling out 12.

$$\frac{7}{4}-\frac{\frac{17\times 16+7}{16}}{\left(-3\right)^{2}}$$

Multiply 17 and 16 to get 272.

$$\frac{7}{4}-\frac{\frac{272+7}{16}}{\left(-3\right)^{2}}$$

Add 272 and 7 to get 279.

$$\frac{7}{4}-\frac{\frac{279}{16}}{\left(-3\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{7}{4}-\frac{\frac{279}{16}}{9}$$

Express \frac{\frac{279}{16}}{9} as a single fraction.

$$\frac{7}{4}-\frac{279}{16\times 9}$$

Multiply 16 and 9 to get 144.

$$\frac{7}{4}-\frac{279}{144}$$

Reduce the fraction \frac{279}{144} to lowest terms by extracting and canceling out 9.

$$\frac{7}{4}-\frac{31}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{7}{4} and \frac{31}{16} to fractions with denominator 16.

$$\frac{28}{16}-\frac{31}{16}$$

Since \frac{28}{16} and \frac{31}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-31}{16}$$

Subtract 31 from 28 to get -3.

$$-\frac{3}{16}$$

Factor

$$-\frac{3}{16} = -0.1875$$