Solve 409/{283quad5/{153quad5/2}}

$$\frac { 409 } { \frac { { 283 } \quad 5 } { \frac { { 153 } \quad 5 } { 2 } } }$$

Evaluate

$$\frac{62577}{566}\approx 110.560070671$$

Solution Steps

Divide 409 by \frac{283\times 5}{\frac{153\times 5}{2}} by multiplying 409 by the reciprocal of \frac{283\times 5}{\frac{153\times 5}{2}}.

$$\frac{409\times \frac{153\times 5}{2}}{283\times 5}$$

Multiply 153 and 5 to get 765.

$$\frac{409\times \frac{765}{2}}{283\times 5}$$

Express 409\times \frac{765}{2} as a single fraction.

$$\frac{\frac{409\times 765}{2}}{283\times 5}$$

Multiply 409 and 765 to get 312885.

$$\frac{\frac{312885}{2}}{283\times 5}$$

Multiply 283 and 5 to get 1415.

$$\frac{\frac{312885}{2}}{1415}$$

Express \frac{\frac{312885}{2}}{1415} as a single fraction.

$$\frac{312885}{2\times 1415}$$

Multiply 2 and 1415 to get 2830.

$$\frac{312885}{2830}$$

Reduce the fraction \frac{312885}{2830} to lowest terms by extracting and canceling out 5.

$$\frac{62577}{566}$$

Factor

$$\frac{3 ^ {2} \cdot 17 \cdot 409}{2 \cdot 283} = 110\frac{317}{566} = 110.56007067137809$$