Solve 1/frac{1{10}+1/20}

$$\frac { 1 } { \frac { 1 } { 10 } + \frac { 1 } { 20 } }$$

Evaluate

$$\frac{20}{3}\approx 6.666666667$$

Solution Steps

Least common multiple of 10 and 20 is 20. Convert \frac{1}{10} and \frac{1}{20} to fractions with denominator 20.

$$\frac{1}{\frac{2}{20}+\frac{1}{20}}$$

Since \frac{2}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{2+1}{20}}$$

Add 2 and 1 to get 3.

$$\frac{1}{\frac{3}{20}}$$

Divide 1 by \frac{3}{20} by multiplying 1 by the reciprocal of \frac{3}{20}.

$$1\times \frac{20}{3}$$

Multiply 1 and \frac{20}{3} to get \frac{20}{3}.

$$\frac{20}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3} = 6\frac{2}{3} = 6.666666666666667$$