Solve 1/frac{7{3600}+8/4600}=

$$\frac { 1 } { \frac { 7 } { 3600 } + \frac { 8 } { 4600 } } =$$

Evaluate

$$\frac{16560}{61}\approx 271.475409836$$

Solution Steps

Reduce the fraction \frac{8}{4600} to lowest terms by extracting and canceling out 8.

$$\frac{1}{\frac{7}{3600}+\frac{1}{575}}$$

Least common multiple of 3600 and 575 is 82800. Convert \frac{7}{3600} and \frac{1}{575} to fractions with denominator 82800.

$$\frac{1}{\frac{161}{82800}+\frac{144}{82800}}$$

Since \frac{161}{82800} and \frac{144}{82800} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{161+144}{82800}}$$

Add 161 and 144 to get 305.

$$\frac{1}{\frac{305}{82800}}$$

Reduce the fraction \frac{305}{82800} to lowest terms by extracting and canceling out 5.

$$\frac{1}{\frac{61}{16560}}$$

Divide 1 by \frac{61}{16560} by multiplying 1 by the reciprocal of \frac{61}{16560}.

$$1\times \frac{16560}{61}$$

Multiply 1 and \frac{16560}{61} to get \frac{16560}{61}.

$$\frac{16560}{61}$$

Factor

$$\frac{2 ^ {4} \cdot 3 ^ {2} \cdot 5 \cdot 23}{61} = 271\frac{29}{61} = 271.4754098360656$$