Solve 1/2div(5+12/8div6/5)

$$\frac{ 1 }{ 2 } \div (5+1 \frac{ 2 }{ 8 } \div \frac{ 6 }{ 5 } )$$

Evaluate

$$\frac{12}{145}\approx 0.082758621$$

Solution Steps

Divide \frac{1\times 8+2}{8} by \frac{6}{5} by multiplying \frac{1\times 8+2}{8} by the reciprocal of \frac{6}{5}.

$$\frac{\frac{1}{2}}{5+\frac{\left(1\times 8+2\right)\times 5}{8\times 6}}$$

Multiply 1 and 8 to get 8.

$$\frac{\frac{1}{2}}{5+\frac{\left(8+2\right)\times 5}{8\times 6}}$$

Add 8 and 2 to get 10.

$$\frac{\frac{1}{2}}{5+\frac{10\times 5}{8\times 6}}$$

Multiply 10 and 5 to get 50.

$$\frac{\frac{1}{2}}{5+\frac{50}{8\times 6}}$$

Multiply 8 and 6 to get 48.

$$\frac{\frac{1}{2}}{5+\frac{50}{48}}$$

Reduce the fraction \frac{50}{48} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{2}}{5+\frac{25}{24}}$$

Convert 5 to fraction \frac{120}{24}.

$$\frac{\frac{1}{2}}{\frac{120}{24}+\frac{25}{24}}$$

Since \frac{120}{24} and \frac{25}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{\frac{120+25}{24}}$$

Add 120 and 25 to get 145.

$$\frac{\frac{1}{2}}{\frac{145}{24}}$$

Divide \frac{1}{2} by \frac{145}{24} by multiplying \frac{1}{2} by the reciprocal of \frac{145}{24}.

$$\frac{1}{2}\times \frac{24}{145}$$

Multiply \frac{1}{2} times \frac{24}{145} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 24}{2\times 145}$$

Do the multiplications in the fraction \frac{1\times 24}{2\times 145}.

$$\frac{24}{290}$$

Reduce the fraction \frac{24}{290} to lowest terms by extracting and canceling out 2.

$$\frac{12}{145}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{5 \cdot 29} = 0.08275862068965517$$