Solve 3/5+1/6/frac{2{3}}

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

Evaluate

$$\frac{23}{20}=1.15$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert \frac{3}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{\frac{18}{30}+\frac{5}{30}}{\frac{2}{3}}$$

Since \frac{18}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{18+5}{30}}{\frac{2}{3}}$$

Add 18 and 5 to get 23.

$$\frac{\frac{23}{30}}{\frac{2}{3}}$$

Divide \frac{23}{30} by \frac{2}{3} by multiplying \frac{23}{30} by the reciprocal of \frac{2}{3}.

$$\frac{23}{30}\times \frac{3}{2}$$

Multiply \frac{23}{30} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 3}{30\times 2}$$

Do the multiplications in the fraction \frac{23\times 3}{30\times 2}.

$$\frac{69}{60}$$

Reduce the fraction \frac{69}{60} to lowest terms by extracting and canceling out 3.

$$\frac{23}{20}$$

Factor

$$\frac{23}{2 ^ {2} \cdot 5} = 1\frac{3}{20} = 1.15$$