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

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

Evaluate

$$\frac{13}{6}\approx 2.166666667$$

Solution Steps

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

$$\frac{\frac{4}{12}+\frac{9}{12}}{\frac{1}{2}}$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+9}{12}}{\frac{1}{2}}$$

Add 4 and 9 to get 13.

$$\frac{\frac{13}{12}}{\frac{1}{2}}$$

Divide \frac{13}{12} by \frac{1}{2} by multiplying \frac{13}{12} by the reciprocal of \frac{1}{2}.

$$\frac{13}{12}\times 2$$

Express \frac{13}{12}\times 2 as a single fraction.

$$\frac{13\times 2}{12}$$

Multiply 13 and 2 to get 26.

$$\frac{26}{12}$$

Reduce the fraction \frac{26}{12} to lowest terms by extracting and canceling out 2.

$$\frac{13}{6}$$

Factor

$$\frac{13}{2 \cdot 3} = 2\frac{1}{6} = 2.1666666666666665$$