Solve 12/5div36/84/3/frac{frac{3{2}}{frac{4}{3}}}

$$\frac{ \frac{ 12 }{ 5 } \div \frac{ 36 }{ 8 } \frac{ 4 }{ 3 } }{ \frac{ \frac{ 3 }{ 2 } }{ \frac{ 4 }{ 3 } } }$$

Evaluate

$$\frac{256}{405}\approx 0.632098765$$

Solution Steps

Divide \frac{12}{5} by \frac{36}{8} by multiplying \frac{12}{5} by the reciprocal of \frac{36}{8}.

$$\frac{\frac{12\times 8}{5\times 36}\times \frac{4}{3}}{\frac{\frac{3}{2}}{\frac{4}{3}}}$$

Cancel out 12 in both numerator and denominator.

$$\frac{\frac{8}{3\times 5}\times \frac{4}{3}}{\frac{\frac{3}{2}}{\frac{4}{3}}}$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{8}{15}\times \frac{4}{3}}{\frac{\frac{3}{2}}{\frac{4}{3}}}$$

Multiply \frac{8}{15} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8\times 4}{15\times 3}}{\frac{\frac{3}{2}}{\frac{4}{3}}}$$

Do the multiplications in the fraction \frac{8\times 4}{15\times 3}.

$$\frac{\frac{32}{45}}{\frac{\frac{3}{2}}{\frac{4}{3}}}$$

Divide \frac{3}{2} by \frac{4}{3} by multiplying \frac{3}{2} by the reciprocal of \frac{4}{3}.

$$\frac{\frac{32}{45}}{\frac{3}{2}\times \frac{3}{4}}$$

Multiply \frac{3}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{32}{45}}{\frac{3\times 3}{2\times 4}}$$

Do the multiplications in the fraction \frac{3\times 3}{2\times 4}.

$$\frac{\frac{32}{45}}{\frac{9}{8}}$$

Divide \frac{32}{45} by \frac{9}{8} by multiplying \frac{32}{45} by the reciprocal of \frac{9}{8}.

$$\frac{32}{45}\times \frac{8}{9}$$

Multiply \frac{32}{45} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32\times 8}{45\times 9}$$

Do the multiplications in the fraction \frac{32\times 8}{45\times 9}.

$$\frac{256}{405}$$

Factor

$$\frac{2 ^ {8}}{3 ^ {4} \cdot 5} = 0.6320987654320988$$