Solve 1/10/frac{frac{1{3}}{2/3}}div45

$$\frac{ \frac{ 1 }{ 10 } }{ \frac{ \frac{ 1 }{ 3 } }{ \frac{ 2 }{ 3 } } } \div 45$$

Evaluate

$$\frac{1}{225}\approx 0.004444444$$

Solution Steps

Express \frac{\frac{\frac{1}{10}}{\frac{\frac{1}{3}}{\frac{2}{3}}}}{45} as a single fraction.

$$\frac{\frac{1}{10}}{\frac{\frac{1}{3}}{\frac{2}{3}}\times 45}$$

Divide \frac{1}{3} by \frac{2}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{2}{3}.

$$\frac{\frac{1}{10}}{\frac{1}{3}\times \frac{3}{2}\times 45}$$

Multiply \frac{1}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{10}}{\frac{1\times 3}{3\times 2}\times 45}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{10}}{\frac{1}{2}\times 45}$$

Multiply \frac{1}{2} and 45 to get \frac{45}{2}.

$$\frac{\frac{1}{10}}{\frac{45}{2}}$$

Divide \frac{1}{10} by \frac{45}{2} by multiplying \frac{1}{10} by the reciprocal of \frac{45}{2}.

$$\frac{1}{10}\times \frac{2}{45}$$

Multiply \frac{1}{10} times \frac{2}{45} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{10\times 45}$$

Do the multiplications in the fraction \frac{1\times 2}{10\times 45}.

$$\frac{2}{450}$$

Reduce the fraction \frac{2}{450} to lowest terms by extracting and canceling out 2.

$$\frac{1}{225}$$

Factor

$$\frac{1}{3 ^ {2} \cdot 5 ^ {2}} = 0.0044444444444444444$$