Solve -63/8-[2+(-4/7)div111/21]_{-2}

$$- 6 \frac { 3 } { 8 } - [ 2 + ( - \frac { 4 } { 7 } ) \div 1 \frac { 11 } { 21 } ] _ { - 2 }$$

Evaluate

$$-8$$

Solution Steps

Multiply 6 and 8 to get 48.

$$-\frac{48+3}{8}-\left(2+\frac{-\frac{4}{7}}{\frac{1\times 21+11}{21}}\right)$$

Add 48 and 3 to get 51.

$$-\frac{51}{8}-\left(2+\frac{-\frac{4}{7}}{\frac{1\times 21+11}{21}}\right)$$

Divide -\frac{4}{7} by \frac{1\times 21+11}{21} by multiplying -\frac{4}{7} by the reciprocal of \frac{1\times 21+11}{21}.

$$-\frac{51}{8}-\left(2+\frac{-4\times 21}{7\left(1\times 21+11\right)}\right)$$

Cancel out 7 in both numerator and denominator.

$$-\frac{51}{8}-\left(2+\frac{-4\times 3}{11+21}\right)$$

Multiply -4 and 3 to get -12.

$$-\frac{51}{8}-\left(2+\frac{-12}{11+21}\right)$$

Add 11 and 21 to get 32.

$$-\frac{51}{8}-\left(2+\frac{-12}{32}\right)$$

Reduce the fraction \frac{-12}{32} to lowest terms by extracting and canceling out 4.

$$-\frac{51}{8}-\left(2-\frac{3}{8}\right)$$

Convert 2 to fraction \frac{16}{8}.

$$-\frac{51}{8}-\left(\frac{16}{8}-\frac{3}{8}\right)$$

Since \frac{16}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{51}{8}-\frac{16-3}{8}$$

Subtract 3 from 16 to get 13.

$$-\frac{51}{8}-\frac{13}{8}$$

Since -\frac{51}{8} and \frac{13}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-51-13}{8}$$

Subtract 13 from -51 to get -64.

$$\frac{-64}{8}$$

Divide -64 by 8 to get -8.

$$-8$$

Factor

$$-8$$