Solve 1/2div(2/3+3/4)

$$\frac{ 1 }{ 2 } \div ( \frac{ 2 }{ 3 } + \frac{ 3 }{ 4 } )$$

Evaluate

$$\frac{6}{17}\approx 0.352941176$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{1}{2}}{\frac{8}{12}+\frac{9}{12}}$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{\frac{8+9}{12}}$$

Add 8 and 9 to get 17.

$$\frac{\frac{1}{2}}{\frac{17}{12}}$$

Divide \frac{1}{2} by \frac{17}{12} by multiplying \frac{1}{2} by the reciprocal of \frac{17}{12}.

$$\frac{1}{2}\times \frac{12}{17}$$

Multiply \frac{1}{2} times \frac{12}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 12}{2\times 17}$$

Do the multiplications in the fraction \frac{1\times 12}{2\times 17}.

$$\frac{12}{34}$$

Reduce the fraction \frac{12}{34} to lowest terms by extracting and canceling out 2.

$$\frac{6}{17}$$

Factor

$$\frac{2 \cdot 3}{17} = 0.35294117647058826$$