Solve 1/frac{1{45}+1/10}

$$\frac { 1 } { \frac { 1 } { 45 } + \frac { 1 } { 10 } }$$

Evaluate

$$\frac{90}{11}\approx 8.181818182$$

Solution Steps

Least common multiple of 45 and 10 is 90. Convert \frac{1}{45} and \frac{1}{10} to fractions with denominator 90.

$$\frac{1}{\frac{2}{90}+\frac{9}{90}}$$

Since \frac{2}{90} and \frac{9}{90} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{2+9}{90}}$$

Add 2 and 9 to get 11.

$$\frac{1}{\frac{11}{90}}$$

Divide 1 by \frac{11}{90} by multiplying 1 by the reciprocal of \frac{11}{90}.

$$1\times \frac{90}{11}$$

Multiply 1 and \frac{90}{11} to get \frac{90}{11}.

$$\frac{90}{11}$$

Factor

$$\frac{2 \cdot 3 ^ {2} \cdot 5}{11} = 8\frac{2}{11} = 8.181818181818182$$