Solve 3/4/5{frac{8/frac{5{12}}}}

$$\frac{ \frac{ 3 }{ 4 } }{ \frac{ 5 }{ \frac{ 8 }{ \frac{ 5 }{ 12 } } } }$$

Evaluate

$$\frac{72}{25}=2.88$$

Solution Steps

Divide \frac{3}{4} by \frac{5}{\frac{8}{\frac{5}{12}}} by multiplying \frac{3}{4} by the reciprocal of \frac{5}{\frac{8}{\frac{5}{12}}}.

$$\frac{3\times \frac{8}{\frac{5}{12}}}{4\times 5}$$

Divide 8 by \frac{5}{12} by multiplying 8 by the reciprocal of \frac{5}{12}.

$$\frac{3\times 8\times \frac{12}{5}}{4\times 5}$$

Express 8\times \frac{12}{5} as a single fraction.

$$\frac{3\times \frac{8\times 12}{5}}{4\times 5}$$

Multiply 8 and 12 to get 96.

$$\frac{3\times \frac{96}{5}}{4\times 5}$$

Express 3\times \frac{96}{5} as a single fraction.

$$\frac{\frac{3\times 96}{5}}{4\times 5}$$

Multiply 3 and 96 to get 288.

$$\frac{\frac{288}{5}}{4\times 5}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{288}{5}}{20}$$

Express \frac{\frac{288}{5}}{20} as a single fraction.

$$\frac{288}{5\times 20}$$

Multiply 5 and 20 to get 100.

$$\frac{288}{100}$$

Reduce the fraction \frac{288}{100} to lowest terms by extracting and canceling out 4.

$$\frac{72}{25}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {2}}{5 ^ {2}} = 2\frac{22}{25} = 2.88$$