Solve 90div[9div8div(7div6div5)div4)div3div2]

$$90 \div [ 9 \div 8 \div ( 7 \div 6 \div 5 ) \div 4 ) \div 3 \div 2 ]$$

Evaluate

$$\frac{112}{9}\approx 12.444444444$$

Solution Steps

Express \frac{\frac{\frac{90}{\frac{\frac{\frac{9}{8}}{\frac{\frac{7}{6}}{5}}}{4}}}{3}}{2} as a single fraction.

$$\frac{\frac{90}{\frac{\frac{\frac{9}{8}}{\frac{\frac{7}{6}}{5}}}{4}}}{3\times 2}$$

Divide 90 by \frac{\frac{\frac{9}{8}}{\frac{\frac{7}{6}}{5}}}{4} by multiplying 90 by the reciprocal of \frac{\frac{\frac{9}{8}}{\frac{\frac{7}{6}}{5}}}{4}.

$$\frac{\frac{90\times 4}{\frac{\frac{9}{8}}{\frac{\frac{7}{6}}{5}}}}{3\times 2}$$

Multiply 90 and 4 to get 360.

$$\frac{\frac{360}{\frac{\frac{9}{8}}{\frac{\frac{7}{6}}{5}}}}{3\times 2}$$

Divide \frac{9}{8} by \frac{\frac{7}{6}}{5} by multiplying \frac{9}{8} by the reciprocal of \frac{\frac{7}{6}}{5}.

$$\frac{\frac{360}{\frac{9\times 5}{8\times \frac{7}{6}}}}{3\times 2}$$

Multiply 9 and 5 to get 45.

$$\frac{\frac{360}{\frac{45}{8\times \frac{7}{6}}}}{3\times 2}$$

Express 8\times \frac{7}{6} as a single fraction.

$$\frac{\frac{360}{\frac{45}{\frac{8\times 7}{6}}}}{3\times 2}$$

Multiply 8 and 7 to get 56.

$$\frac{\frac{360}{\frac{45}{\frac{56}{6}}}}{3\times 2}$$

Reduce the fraction \frac{56}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{360}{\frac{45}{\frac{28}{3}}}}{3\times 2}$$

Divide 45 by \frac{28}{3} by multiplying 45 by the reciprocal of \frac{28}{3}.

$$\frac{\frac{360}{45\times \frac{3}{28}}}{3\times 2}$$

Express 45\times \frac{3}{28} as a single fraction.

$$\frac{\frac{360}{\frac{45\times 3}{28}}}{3\times 2}$$

Multiply 45 and 3 to get 135.

$$\frac{\frac{360}{\frac{135}{28}}}{3\times 2}$$

Divide 360 by \frac{135}{28} by multiplying 360 by the reciprocal of \frac{135}{28}.

$$\frac{360\times \frac{28}{135}}{3\times 2}$$

Express 360\times \frac{28}{135} as a single fraction.

$$\frac{\frac{360\times 28}{135}}{3\times 2}$$

Multiply 360 and 28 to get 10080.

$$\frac{\frac{10080}{135}}{3\times 2}$$

Reduce the fraction \frac{10080}{135} to lowest terms by extracting and canceling out 45.

$$\frac{\frac{224}{3}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{224}{3}}{6}$$

Express \frac{\frac{224}{3}}{6} as a single fraction.

$$\frac{224}{3\times 6}$$

Multiply 3 and 6 to get 18.

$$\frac{224}{18}$$

Reduce the fraction \frac{224}{18} to lowest terms by extracting and canceling out 2.

$$\frac{112}{9}$$

Factor

$$\frac{2 ^ {4} \cdot 7}{3 ^ {2}} = 12\frac{4}{9} = 12.444444444444445$$