Solve (21/4-41/2-11/8)div(-11/8)-(-3)^3div3*frac{1}{3}

$$( 2 \frac { 1 } { 4 } - 4 \frac { 1 } { 2 } - 1 \frac { 1 } { 8 } ) \div ( - 1 \frac { 1 } { 8 } ) - ( - 3 ) ^ { 3 } \div 3 \times \frac { 1 } { 3 }$$

Evaluate

$$6$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{\frac{8+1}{4}-\frac{4\times 2+1}{2}-\frac{1\times 8+1}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Add 8 and 1 to get 9.

$$\frac{\frac{9}{4}-\frac{4\times 2+1}{2}-\frac{1\times 8+1}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{9}{4}-\frac{8+1}{2}-\frac{1\times 8+1}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Add 8 and 1 to get 9.

$$\frac{\frac{9}{4}-\frac{9}{2}-\frac{1\times 8+1}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

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

$$\frac{\frac{9}{4}-\frac{18}{4}-\frac{1\times 8+1}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Since \frac{9}{4} and \frac{18}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-18}{4}-\frac{1\times 8+1}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Subtract 18 from 9 to get -9.

$$\frac{-\frac{9}{4}-\frac{1\times 8+1}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Multiply 1 and 8 to get 8.

$$\frac{-\frac{9}{4}-\frac{8+1}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Add 8 and 1 to get 9.

$$\frac{-\frac{9}{4}-\frac{9}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Least common multiple of 4 and 8 is 8. Convert -\frac{9}{4} and \frac{9}{8} to fractions with denominator 8.

$$\frac{-\frac{18}{8}-\frac{9}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Since -\frac{18}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-18-9}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Subtract 9 from -18 to get -27.

$$\frac{-\frac{27}{8}}{-\frac{1\times 8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Multiply 1 and 8 to get 8.

$$\frac{-\frac{27}{8}}{-\frac{8+1}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Add 8 and 1 to get 9.

$$\frac{-\frac{27}{8}}{-\frac{9}{8}}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Divide -\frac{27}{8} by -\frac{9}{8} by multiplying -\frac{27}{8} by the reciprocal of -\frac{9}{8}.

$$-\frac{27}{8}\left(-\frac{8}{9}\right)-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Multiply -\frac{27}{8} times -\frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-27\left(-8\right)}{8\times 9}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Do the multiplications in the fraction \frac{-27\left(-8\right)}{8\times 9}.

$$\frac{216}{72}-\frac{\left(-3\right)^{3}}{3}\times \frac{1}{3}$$

Divide 216 by 72 to get 3.

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

Calculate -3 to the power of 3 and get -27.

$$3-\frac{-27}{3}\times \frac{1}{3}$$

Divide -27 by 3 to get -9.

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

Multiply -9 and \frac{1}{3} to get \frac{-9}{3}.

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

Divide -9 by 3 to get -3.

$$3-\left(-3\right)$$

The opposite of -3 is 3.

$$3+3$$

Add 3 and 3 to get 6.

$$6$$

Factor

$$2\times 3$$