Solve a=21/3-22/3:8/9/(3-4*1frac{1{4})*(-frac{5}{6})}

$$a = \frac { 2 \frac { 1 } { 3 } - 2 \frac { 2 } { 3 } : \frac { 8 } { 9 } } { ( 3 - 4 \cdot 1 \frac { 1 } { 4 } ) \cdot ( - \frac { 5 } { 6 } ) }$$

Solve for a

$$a=-\frac{2}{5}=-0.4$$

Steps for Solving Linear Equation

Multiply 2 and 3 to get 6.

$$a=\frac{\frac{6+1}{3}-\frac{\frac{2\times 3+2}{3}}{\frac{8}{9}}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Add 6 and 1 to get 7.

$$a=\frac{\frac{7}{3}-\frac{\frac{2\times 3+2}{3}}{\frac{8}{9}}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Multiply 2 and 3 to get 6.

$$a=\frac{\frac{7}{3}-\frac{\frac{6+2}{3}}{\frac{8}{9}}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Add 6 and 2 to get 8.

$$a=\frac{\frac{7}{3}-\frac{\frac{8}{3}}{\frac{8}{9}}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Divide \frac{8}{3} by \frac{8}{9} by multiplying \frac{8}{3} by the reciprocal of \frac{8}{9}.

$$a=\frac{\frac{7}{3}-\frac{8}{3}\times \frac{9}{8}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Multiply \frac{8}{3} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{\frac{7}{3}-\frac{8\times 9}{3\times 8}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Cancel out 8 in both numerator and denominator.

$$a=\frac{\frac{7}{3}-\frac{9}{3}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Divide 9 by 3 to get 3.

$$a=\frac{\frac{7}{3}-3}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Convert 3 to fraction \frac{9}{3}.

$$a=\frac{\frac{7}{3}-\frac{9}{3}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Since \frac{7}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$a=\frac{\frac{7-9}{3}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Subtract 9 from 7 to get -2.

$$a=\frac{-\frac{2}{3}}{\left(3-4\times \frac{1\times 4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Multiply 1 and 4 to get 4.

$$a=\frac{-\frac{2}{3}}{\left(3-4\times \frac{4+1}{4}\right)\left(-\frac{5}{6}\right)}$$

Add 4 and 1 to get 5.

$$a=\frac{-\frac{2}{3}}{\left(3-4\times \frac{5}{4}\right)\left(-\frac{5}{6}\right)}$$

Cancel out 4 and 4.

$$a=\frac{-\frac{2}{3}}{\left(3-5\right)\left(-\frac{5}{6}\right)}$$

Subtract 5 from 3 to get -2.

$$a=\frac{-\frac{2}{3}}{-2\left(-\frac{5}{6}\right)}$$

Express -2\left(-\frac{5}{6}\right) as a single fraction.

$$a=\frac{-\frac{2}{3}}{\frac{-2\left(-5\right)}{6}}$$

Multiply -2 and -5 to get 10.

$$a=\frac{-\frac{2}{3}}{\frac{10}{6}}$$

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

$$a=\frac{-\frac{2}{3}}{\frac{5}{3}}$$

Divide -\frac{2}{3} by \frac{5}{3} by multiplying -\frac{2}{3} by the reciprocal of \frac{5}{3}.

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

Multiply -\frac{2}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$a=\frac{-2}{5}$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$a=-\frac{2}{5}$$

Assign a

$$a≔-\frac{2}{5}$$