Solve 1/2:(1/4+1/3)=

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

Evaluate

$$\frac{6}{7}\approx 0.857142857$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

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

Since \frac{3}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

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

Add 3 and 4 to get 7.

$$\frac{\frac{1}{2}}{\frac{7}{12}}$$

Divide \frac{1}{2} by \frac{7}{12} by multiplying \frac{1}{2} by the reciprocal of \frac{7}{12}.

$$\frac{1}{2}\times \frac{12}{7}$$

Multiply \frac{1}{2} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 12}{2\times 7}$$

Do the multiplications in the fraction \frac{1\times 12}{2\times 7}.

$$\frac{12}{14}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$\frac{6}{7}$$

Factor

$$\frac{2 \cdot 3}{7} = 0.8571428571428571$$