Solve 100/frac{30{5}+10/8+60/50}

$$\frac { 100 } { \frac { 30 } { 5 } + \frac { 10 } { 8 } + \frac { 60 } { 50 } }$$

Evaluate

$$\frac{2000}{169}\approx 11.834319527$$

Solution Steps

Divide 30 by 5 to get 6.

$$\frac{100}{6+\frac{10}{8}+\frac{60}{50}}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{100}{6+\frac{5}{4}+\frac{60}{50}}$$

Convert 6 to fraction \frac{24}{4}.

$$\frac{100}{\frac{24}{4}+\frac{5}{4}+\frac{60}{50}}$$

Since \frac{24}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{100}{\frac{24+5}{4}+\frac{60}{50}}$$

Add 24 and 5 to get 29.

$$\frac{100}{\frac{29}{4}+\frac{60}{50}}$$

Reduce the fraction \frac{60}{50} to lowest terms by extracting and canceling out 10.

$$\frac{100}{\frac{29}{4}+\frac{6}{5}}$$

Least common multiple of 4 and 5 is 20. Convert \frac{29}{4} and \frac{6}{5} to fractions with denominator 20.

$$\frac{100}{\frac{145}{20}+\frac{24}{20}}$$

Since \frac{145}{20} and \frac{24}{20} have the same denominator, add them by adding their numerators.

$$\frac{100}{\frac{145+24}{20}}$$

Add 145 and 24 to get 169.

$$\frac{100}{\frac{169}{20}}$$

Divide 100 by \frac{169}{20} by multiplying 100 by the reciprocal of \frac{169}{20}.

$$100\times \frac{20}{169}$$

Express 100\times \frac{20}{169} as a single fraction.

$$\frac{100\times 20}{169}$$

Multiply 100 and 20 to get 2000.

$$\frac{2000}{169}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {3}}{13 ^ {2}} = 11\frac{141}{169} = 11.834319526627219$$