Solve 1/frac{1{3}+1/9}

$$\frac { 1 } { \frac { 1 } { 3 } + \frac { 1 } { 9 } }$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{1}{\frac{3}{9}+\frac{1}{9}}$$

Since \frac{3}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{3+1}{9}}$$

Add 3 and 1 to get 4.

$$\frac{1}{\frac{4}{9}}$$

Divide 1 by \frac{4}{9} by multiplying 1 by the reciprocal of \frac{4}{9}.

$$1\times \frac{9}{4}$$

Multiply 1 and \frac{9}{4} to get \frac{9}{4}.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$