Simplify (-1|2/3-4|)÷(5/6)

$- 1 | \frac{2}{3} - 4 | \div \frac{5}{6}$

To divide by a fraction, multiply by its reciprocal.

$- 1 | \frac{2}{3} - 4 | \frac{6}{5}$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 1 | \frac{2}{3} - 4 \cdot \frac{3}{3} | \frac{6}{5}$

Combine $- 4$ and $\frac{3}{3}$ .

$- 1 | \frac{2}{3} + \frac{- 4 \cdot 3}{3} | \frac{6}{5}$

Combine the numerators over the common denominator.

$- 1 | \frac{2 - 4 \cdot 3}{3} | \frac{6}{5}$

Simplify the numerator.

Multiply $- 4$ by $3$ .

$- 1 | \frac{2 - 12}{3} | \frac{6}{5}$

Subtract $12$ from $2$ .

$- 1 | \frac{- 10}{3} | \frac{6}{5}$

Move the negative in front of the fraction.

$- 1 | - \frac{10}{3} | \frac{6}{5}$

$- \frac{10}{3}$ is approximately $- 3.\overline{3}$ which is negative so negate $- \frac{10}{3}$ and remove the absolute value

$- 1 (\frac{10}{3}) \frac{6}{5}$

Rewrite $- 1 (\frac{10}{3})$ as $- (\frac{10}{3})$ .

$- (\frac{10}{3}) \frac{6}{5}$

Cancel the common factor of $5$ .

Move the leading negative in $- (\frac{10}{3})$ into the numerator.

$\frac{- 10}{3} \cdot \frac{6}{5}$

Factor $5$ out of $- 10$ .

$\frac{5 (- 2)}{3} \cdot \frac{6}{5}$

Cancel the common factor.

$\frac{5 \cdot - 2}{3} \cdot \frac{6}{5}$

Rewrite the expression.

$\frac{- 2}{3} \cdot 6$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{- 2}{3} \cdot (3 (2))$

Cancel the common factor.

$\frac{- 2}{3} \cdot (3 \cdot 2)$

Rewrite the expression.

$- 2 \cdot 2$

Multiply $- 2$ by $2$ .

$- 4$