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

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

Evaluate

$$\frac{43}{42}\approx 1.023809524$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

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

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

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

Add 3 and 4 to get 7.

$$\frac{1}{\frac{7}{6}}+\frac{1}{6}$$

Divide 1 by \frac{7}{6} by multiplying 1 by the reciprocal of \frac{7}{6}.

$$1\times \frac{6}{7}+\frac{1}{6}$$

Multiply 1 and \frac{6}{7} to get \frac{6}{7}.

$$\frac{6}{7}+\frac{1}{6}$$

Least common multiple of 7 and 6 is 42. Convert \frac{6}{7} and \frac{1}{6} to fractions with denominator 42.

$$\frac{36}{42}+\frac{7}{42}$$

Since \frac{36}{42} and \frac{7}{42} have the same denominator, add them by adding their numerators.

$$\frac{36+7}{42}$$

Add 36 and 7 to get 43.

$$\frac{43}{42}$$

Factor

$$\frac{43}{2 \cdot 3 \cdot 7} = 1\frac{1}{42} = 1.0238095238095237$$