Evaluate 3(6)-(4|-6|)÷8+|-8|

$3 (6) - 4 | - 6 | \div 8 + | - 8 |$

Step 1

Find the common denominator.

Write $3 (6)$ as a fraction with denominator $1$ .

$\frac{3 (6)}{1} - 4 | - 6 | \div 8 + | - 8 |$

Multiply $\frac{3 (6)}{1}$ by $\frac{8}{8}$ .

$\frac{3 (6)}{1} \cdot \frac{8}{8} - 4 | - 6 | \div 8 + | - 8 |$

Multiply $\frac{3 (6)}{1}$ by $\frac{8}{8}$ .

$\frac{3 (6) \cdot 8}{8} - 4 | - 6 | \div 8 + | - 8 |$

Write $| - 8 |$ as a fraction with denominator $1$ .

$\frac{3 (6) \cdot 8}{8} - 4 | - 6 | \div 8 + \frac{| - 8 |}{1}$

Multiply $\frac{| - 8 |}{1}$ by $\frac{8}{8}$ .

$\frac{3 (6) \cdot 8}{8} - 4 | - 6 | \div 8 + \frac{| - 8 |}{1} \cdot \frac{8}{8}$

Multiply $\frac{| - 8 |}{1}$ by $\frac{8}{8}$ .

$\frac{3 (6) \cdot 8}{8} - 4 | - 6 | \div 8 + \frac{| - 8 | \cdot 8}{8}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 (6) \cdot 8 - 4 | - 6 | + | - 8 | \cdot 8}{8}$

Step 3

Simplify each term.

Multiply $3 (6) \cdot 8$ .

Multiply $3$ by $6$ .

$\frac{18 \cdot 8 - 4 | - 6 | + | - 8 | \cdot 8}{8}$

Multiply $18$ by $8$ .

$\frac{144 - 4 | - 6 | + | - 8 | \cdot 8}{8}$

The absolute value is the distance between a number and zero. The distance between $- 6$ and $0$ is $6$ .

$\frac{144 - 4 \cdot 6 + | - 8 | \cdot 8}{8}$

Multiply $- 4$ by $6$ .

$\frac{144 - 24 + | - 8 | \cdot 8}{8}$

The absolute value is the distance between a number and zero. The distance between $- 8$ and $0$ is $8$ .

$\frac{144 - 24 + 8 \cdot 8}{8}$

Multiply $8$ by $8$ .

$\frac{144 - 24 + 64}{8}$

Step 4

Simplify the expression.

Subtract $24$ from $144$ .

$\frac{120 + 64}{8}$

Add $120$ and $64$ .

$\frac{184}{8}$

Divide $184$ by $8$ .

$23$