Solve 3/2+2/3+3/5/frac{20{3}+frac{3-12}{5}+frac{3}{3+2}}

$$\frac{ \frac{ 3 }{ 2 } + \frac{ 2 }{ 3 } + \frac{ 3 }{ 5 } }{ \frac{ 20 }{ 3 } + \frac{ 3-12 }{ 5 } + \frac{ 3 }{ 3+2 } }$$

Evaluate

$$\frac{83}{164}\approx 0.506097561$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{9}{6}+\frac{4}{6}+\frac{3}{5}}{\frac{20}{3}+\frac{3-12}{5}+\frac{3}{3+2}}$$

Since \frac{9}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+4}{6}+\frac{3}{5}}{\frac{20}{3}+\frac{3-12}{5}+\frac{3}{3+2}}$$

Add 9 and 4 to get 13.

$$\frac{\frac{13}{6}+\frac{3}{5}}{\frac{20}{3}+\frac{3-12}{5}+\frac{3}{3+2}}$$

Least common multiple of 6 and 5 is 30. Convert \frac{13}{6} and \frac{3}{5} to fractions with denominator 30.

$$\frac{\frac{65}{30}+\frac{18}{30}}{\frac{20}{3}+\frac{3-12}{5}+\frac{3}{3+2}}$$

Since \frac{65}{30} and \frac{18}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{65+18}{30}}{\frac{20}{3}+\frac{3-12}{5}+\frac{3}{3+2}}$$

Add 65 and 18 to get 83.

$$\frac{\frac{83}{30}}{\frac{20}{3}+\frac{3-12}{5}+\frac{3}{3+2}}$$

Subtract 12 from 3 to get -9.

$$\frac{\frac{83}{30}}{\frac{20}{3}+\frac{-9}{5}+\frac{3}{3+2}}$$

Fraction \frac{-9}{5} can be rewritten as -\frac{9}{5} by extracting the negative sign.

$$\frac{\frac{83}{30}}{\frac{20}{3}-\frac{9}{5}+\frac{3}{3+2}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{20}{3} and \frac{9}{5} to fractions with denominator 15.

$$\frac{\frac{83}{30}}{\frac{100}{15}-\frac{27}{15}+\frac{3}{3+2}}$$

Since \frac{100}{15} and \frac{27}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{83}{30}}{\frac{100-27}{15}+\frac{3}{3+2}}$$

Subtract 27 from 100 to get 73.

$$\frac{\frac{83}{30}}{\frac{73}{15}+\frac{3}{3+2}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{83}{30}}{\frac{73}{15}+\frac{3}{5}}$$

Least common multiple of 15 and 5 is 15. Convert \frac{73}{15} and \frac{3}{5} to fractions with denominator 15.

$$\frac{\frac{83}{30}}{\frac{73}{15}+\frac{9}{15}}$$

Since \frac{73}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{83}{30}}{\frac{73+9}{15}}$$

Add 73 and 9 to get 82.

$$\frac{\frac{83}{30}}{\frac{82}{15}}$$

Divide \frac{83}{30} by \frac{82}{15} by multiplying \frac{83}{30} by the reciprocal of \frac{82}{15}.

$$\frac{83}{30}\times \frac{15}{82}$$

Multiply \frac{83}{30} times \frac{15}{82} by multiplying numerator times numerator and denominator times denominator.

$$\frac{83\times 15}{30\times 82}$$

Do the multiplications in the fraction \frac{83\times 15}{30\times 82}.

$$\frac{1245}{2460}$$

Reduce the fraction \frac{1245}{2460} to lowest terms by extracting and canceling out 15.

$$\frac{83}{164}$$

Factor

$$\frac{83}{2 ^ {2} \cdot 41} = 0.5060975609756098$$