Solve 1/frac{1{700}+1/8900}

$$\frac { 1 } { \frac { 1 } { 700 } + \frac { 1 } { 8900 } }$$

Evaluate

$$\frac{15575}{24}\approx 648.958333333$$

Solution Steps

Least common multiple of 700 and 8900 is 62300. Convert \frac{1}{700} and \frac{1}{8900} to fractions with denominator 62300.

$$\frac{1}{\frac{89}{62300}+\frac{7}{62300}}$$

Since \frac{89}{62300} and \frac{7}{62300} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{89+7}{62300}}$$

Add 89 and 7 to get 96.

$$\frac{1}{\frac{96}{62300}}$$

Reduce the fraction \frac{96}{62300} to lowest terms by extracting and canceling out 4.

$$\frac{1}{\frac{24}{15575}}$$

Divide 1 by \frac{24}{15575} by multiplying 1 by the reciprocal of \frac{24}{15575}.

$$1\times \frac{15575}{24}$$

Multiply 1 and \frac{15575}{24} to get \frac{15575}{24}.

$$\frac{15575}{24}$$

Factor

$$\frac{5 ^ {2} \cdot 7 \cdot 89}{2 ^ {3} \cdot 3} = 648\frac{23}{24} = 648.9583333333334$$