Solve 3-4/7*{9/16-1/36div(-1/3)^3}+(-frac{2}{3})*(-1^101)

$$3 - \frac { 4 } { 7 } \times \{ \frac { 9 } { 16 } - \frac { 1 } { 36 } \div ( - \frac { 1 } { 3 } ) ^ { 3 } \} + ( - \frac { 2 } { 3 } ) \times ( - 1 ^ { 101 } )$$

Evaluate

$$\frac{35}{12}\approx 2.916666667$$

Solution Steps

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$3-\frac{4}{7}\left(\frac{9}{16}-\frac{\frac{1}{36}}{-\frac{1}{27}}\right)-\frac{2}{3}\left(-1^{101}\right)$$

Divide \frac{1}{36} by -\frac{1}{27} by multiplying \frac{1}{36} by the reciprocal of -\frac{1}{27}.

$$3-\frac{4}{7}\left(\frac{9}{16}-\frac{1}{36}\left(-27\right)\right)-\frac{2}{3}\left(-1^{101}\right)$$

Multiply \frac{1}{36} and -27 to get \frac{-27}{36}.

$$3-\frac{4}{7}\left(\frac{9}{16}-\frac{-27}{36}\right)-\frac{2}{3}\left(-1^{101}\right)$$

Reduce the fraction \frac{-27}{36} to lowest terms by extracting and canceling out 9.

$$3-\frac{4}{7}\left(\frac{9}{16}-\left(-\frac{3}{4}\right)\right)-\frac{2}{3}\left(-1^{101}\right)$$

The opposite of -\frac{3}{4} is \frac{3}{4}.

$$3-\frac{4}{7}\left(\frac{9}{16}+\frac{3}{4}\right)-\frac{2}{3}\left(-1^{101}\right)$$

Least common multiple of 16 and 4 is 16. Convert \frac{9}{16} and \frac{3}{4} to fractions with denominator 16.

$$3-\frac{4}{7}\left(\frac{9}{16}+\frac{12}{16}\right)-\frac{2}{3}\left(-1^{101}\right)$$

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

$$3-\frac{4}{7}\times \frac{9+12}{16}-\frac{2}{3}\left(-1^{101}\right)$$

Add 9 and 12 to get 21.

$$3-\frac{4}{7}\times \frac{21}{16}-\frac{2}{3}\left(-1^{101}\right)$$

Multiply \frac{4}{7} times \frac{21}{16} by multiplying numerator times numerator and denominator times denominator.

$$3-\frac{4\times 21}{7\times 16}-\frac{2}{3}\left(-1^{101}\right)$$

Do the multiplications in the fraction \frac{4\times 21}{7\times 16}.

$$3-\frac{84}{112}-\frac{2}{3}\left(-1^{101}\right)$$

Reduce the fraction \frac{84}{112} to lowest terms by extracting and canceling out 28.

$$3-\frac{3}{4}-\frac{2}{3}\left(-1^{101}\right)$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{12}{4}-\frac{3}{4}-\frac{2}{3}\left(-1^{101}\right)$$

Since \frac{12}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-3}{4}-\frac{2}{3}\left(-1^{101}\right)$$

Subtract 3 from 12 to get 9.

$$\frac{9}{4}-\frac{2}{3}\left(-1^{101}\right)$$

Calculate 1 to the power of 101 and get 1.

$$\frac{9}{4}-\frac{2}{3}\left(-1\right)$$

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

$$\frac{9}{4}+\frac{2}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{9}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{27}{12}+\frac{8}{12}$$

Since \frac{27}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{27+8}{12}$$

Add 27 and 8 to get 35.

$$\frac{35}{12}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2} \cdot 3} = 2\frac{11}{12} = 2.9166666666666665$$