Solve (5/3+1/2+3/5):(1/2+frac{2}{15})

$$( \frac { 5 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } ) : ( \frac { 1 } { 2 } + \frac { 2 } { 15 } )$$

Evaluate

$$\frac{83}{19}\approx 4.368421053$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{10}{6}+\frac{3}{6}+\frac{3}{5}}{\frac{1}{2}+\frac{2}{15}}$$

Since \frac{10}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+3}{6}+\frac{3}{5}}{\frac{1}{2}+\frac{2}{15}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{13}{6}+\frac{3}{5}}{\frac{1}{2}+\frac{2}{15}}$$

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

$$\frac{\frac{65}{30}+\frac{18}{30}}{\frac{1}{2}+\frac{2}{15}}$$

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

$$\frac{\frac{65+18}{30}}{\frac{1}{2}+\frac{2}{15}}$$

Add 65 and 18 to get 83.

$$\frac{\frac{83}{30}}{\frac{1}{2}+\frac{2}{15}}$$

Least common multiple of 2 and 15 is 30. Convert \frac{1}{2} and \frac{2}{15} to fractions with denominator 30.

$$\frac{\frac{83}{30}}{\frac{15}{30}+\frac{4}{30}}$$

Since \frac{15}{30} and \frac{4}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{83}{30}}{\frac{15+4}{30}}$$

Add 15 and 4 to get 19.

$$\frac{\frac{83}{30}}{\frac{19}{30}}$$

Divide \frac{83}{30} by \frac{19}{30} by multiplying \frac{83}{30} by the reciprocal of \frac{19}{30}.

$$\frac{83}{30}\times \frac{30}{19}$$

Multiply \frac{83}{30} times \frac{30}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{83\times 30}{30\times 19}$$

Cancel out 30 in both numerator and denominator.

$$\frac{83}{19}$$

Factor

$$\frac{83}{19} = 4\frac{7}{19} = 4.368421052631579$$