Solve 8/2--10/3/frac{3(-4){4}+8/8}

$$\frac{ \frac{ 8 }{ 2 } - \frac{ -10 }{ 3 } }{ \frac{ 3(-4) }{ 4 } + \frac{ 8 }{ 8 } }$$

Evaluate

$$-\frac{11}{3}\approx -3.666666667$$

Solution Steps

Divide 8 by 8 to get 1.

$$\frac{\frac{8}{2}-\frac{-10}{3}}{\frac{3\left(-4\right)}{4}+1}$$

Divide 8 by 2 to get 4.

$$\frac{4-\frac{-10}{3}}{\frac{3\left(-4\right)}{4}+1}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{4-\left(-\frac{10}{3}\right)}{\frac{3\left(-4\right)}{4}+1}$$

The opposite of -\frac{10}{3} is \frac{10}{3}.

$$\frac{4+\frac{10}{3}}{\frac{3\left(-4\right)}{4}+1}$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{\frac{12}{3}+\frac{10}{3}}{\frac{3\left(-4\right)}{4}+1}$$

Since \frac{12}{3} and \frac{10}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12+10}{3}}{\frac{3\left(-4\right)}{4}+1}$$

Add 12 and 10 to get 22.

$$\frac{\frac{22}{3}}{\frac{3\left(-4\right)}{4}+1}$$

Cancel out 4 and 4.

$$\frac{\frac{22}{3}}{3\left(-1\right)+1}$$

Multiply 3 and -1 to get -3.

$$\frac{\frac{22}{3}}{-3+1}$$

Add -3 and 1 to get -2.

$$\frac{\frac{22}{3}}{-2}$$

Express \frac{\frac{22}{3}}{-2} as a single fraction.

$$\frac{22}{3\left(-2\right)}$$

Multiply 3 and -2 to get -6.

$$\frac{22}{-6}$$

Reduce the fraction \frac{22}{-6} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{3}$$

Factor

$$-\frac{11}{3} = -3\frac{2}{3} = -3.6666666666666665$$