Solve (10div5/6)div109/32

$$( 10 \div \frac { 5 } { 6 } ) \div 10 \frac { 9 } { 32 }$$

Evaluate

$$\frac{384}{329}\approx 1.167173252$$

Solution Steps

Divide \frac{10}{\frac{5}{6}} by \frac{10\times 32+9}{32} by multiplying \frac{10}{\frac{5}{6}} by the reciprocal of \frac{10\times 32+9}{32}.

$$\frac{10\times 32}{\frac{5}{6}\left(10\times 32+9\right)}$$

Multiply 10 and 32 to get 320.

$$\frac{320}{\frac{5}{6}\left(10\times 32+9\right)}$$

Multiply 10 and 32 to get 320.

$$\frac{320}{\frac{5}{6}\left(320+9\right)}$$

Add 320 and 9 to get 329.

$$\frac{320}{\frac{5}{6}\times 329}$$

Express \frac{5}{6}\times 329 as a single fraction.

$$\frac{320}{\frac{5\times 329}{6}}$$

Multiply 5 and 329 to get 1645.

$$\frac{320}{\frac{1645}{6}}$$

Divide 320 by \frac{1645}{6} by multiplying 320 by the reciprocal of \frac{1645}{6}.

$$320\times \frac{6}{1645}$$

Express 320\times \frac{6}{1645} as a single fraction.

$$\frac{320\times 6}{1645}$$

Multiply 320 and 6 to get 1920.

$$\frac{1920}{1645}$$

Reduce the fraction \frac{1920}{1645} to lowest terms by extracting and canceling out 5.

$$\frac{384}{329}$$

Factor

$$\frac{2 ^ {7} \cdot 3}{7 \cdot 47} = 1\frac{55}{329} = 1.1671732522796352$$