Solve 1/2frac{4/3/frac{frac{1{2}}{6}}}{1/2+frac{1}{4}}

$$\frac{ \frac{ \frac{ 1 }{ 2 } \frac{ 4 }{ 3 } }{ \frac{ \frac{ 1 }{ 2 } }{ 6 } } }{ \frac{ 1 }{ 2 } + \frac{ 1 }{ 4 } }$$

Evaluate

$$\frac{32}{3}\approx 10.666666667$$

Solution Steps

Multiply \frac{1}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{1\times 4}{2\times 3}}{\frac{\frac{1}{2}}{6}}}{\frac{1}{2}+\frac{1}{4}}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 3}.

$$\frac{\frac{\frac{4}{6}}{\frac{\frac{1}{2}}{6}}}{\frac{1}{2}+\frac{1}{4}}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{\frac{2}{3}}{\frac{\frac{1}{2}}{6}}}{\frac{1}{2}+\frac{1}{4}}$$

Express \frac{\frac{1}{2}}{6} as a single fraction.

$$\frac{\frac{\frac{2}{3}}{\frac{1}{2\times 6}}}{\frac{1}{2}+\frac{1}{4}}$$

Multiply 2 and 6 to get 12.

$$\frac{\frac{\frac{2}{3}}{\frac{1}{12}}}{\frac{1}{2}+\frac{1}{4}}$$

Divide \frac{2}{3} by \frac{1}{12} by multiplying \frac{2}{3} by the reciprocal of \frac{1}{12}.

$$\frac{\frac{2}{3}\times 12}{\frac{1}{2}+\frac{1}{4}}$$

Express \frac{2}{3}\times 12 as a single fraction.

$$\frac{\frac{2\times 12}{3}}{\frac{1}{2}+\frac{1}{4}}$$

Multiply 2 and 12 to get 24.

$$\frac{\frac{24}{3}}{\frac{1}{2}+\frac{1}{4}}$$

Divide 24 by 3 to get 8.

$$\frac{8}{\frac{1}{2}+\frac{1}{4}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{8}{\frac{2}{4}+\frac{1}{4}}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{8}{\frac{2+1}{4}}$$

Add 2 and 1 to get 3.

$$\frac{8}{\frac{3}{4}}$$

Divide 8 by \frac{3}{4} by multiplying 8 by the reciprocal of \frac{3}{4}.

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

Express 8\times \frac{4}{3} as a single fraction.

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

Multiply 8 and 4 to get 32.

$$\frac{32}{3}$$

Factor

$$\frac{2 ^ {5}}{3} = 10\frac{2}{3} = 10.666666666666666$$