Solve 1/3/frac{2{3}}+2/15+3/5

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

Evaluate

$$\frac{37}{30}\approx 1.233333333$$

Solution Steps

Divide \frac{1}{3} by \frac{2}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{2}{3}.

$$\frac{1}{3}\times \frac{3}{2}+\frac{2}{15}+\frac{3}{5}$$

Multiply \frac{1}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{3\times 2}+\frac{2}{15}+\frac{3}{5}$$

Cancel out 3 in both numerator and denominator.

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

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

$$\frac{15}{30}+\frac{4}{30}+\frac{3}{5}$$

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

$$\frac{15+4}{30}+\frac{3}{5}$$

Add 15 and 4 to get 19.

$$\frac{19}{30}+\frac{3}{5}$$

Least common multiple of 30 and 5 is 30. Convert \frac{19}{30} and \frac{3}{5} to fractions with denominator 30.

$$\frac{19}{30}+\frac{18}{30}$$

Since \frac{19}{30} and \frac{18}{30} have the same denominator, add them by adding their numerators.

$$\frac{19+18}{30}$$

Add 19 and 18 to get 37.

$$\frac{37}{30}$$

Factor

$$\frac{37}{2 \cdot 3 \cdot 5} = 1\frac{7}{30} = 1.2333333333333334$$