Solve (16div7div6)div(32div14div5)

$$(16 \div 7 \div 6) \div (32 \div 14 \div 5)$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Divide \frac{\frac{16}{7}}{6} by \frac{\frac{32}{14}}{5} by multiplying \frac{\frac{16}{7}}{6} by the reciprocal of \frac{\frac{32}{14}}{5}.

$$\frac{\frac{16}{7}\times 5}{6\times \frac{32}{14}}$$

Express \frac{16}{7}\times 5 as a single fraction.

$$\frac{\frac{16\times 5}{7}}{6\times \frac{32}{14}}$$

Multiply 16 and 5 to get 80.

$$\frac{\frac{80}{7}}{6\times \frac{32}{14}}$$

Reduce the fraction \frac{32}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{80}{7}}{6\times \frac{16}{7}}$$

Express 6\times \frac{16}{7} as a single fraction.

$$\frac{\frac{80}{7}}{\frac{6\times 16}{7}}$$

Multiply 6 and 16 to get 96.

$$\frac{\frac{80}{7}}{\frac{96}{7}}$$

Divide \frac{80}{7} by \frac{96}{7} by multiplying \frac{80}{7} by the reciprocal of \frac{96}{7}.

$$\frac{80}{7}\times \frac{7}{96}$$

Multiply \frac{80}{7} times \frac{7}{96} by multiplying numerator times numerator and denominator times denominator.

$$\frac{80\times 7}{7\times 96}$$

Cancel out 7 in both numerator and denominator.

$$\frac{80}{96}$$

Reduce the fraction \frac{80}{96} to lowest terms by extracting and canceling out 16.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$