Solve 1/3/frac{2{3}}+2/1.5+3/5

$$\frac { \frac { 1 } { 3 } } { \frac { 2 } { 3 } } + \frac { 2 } { 1.5 } + \frac { 3 } { 5 }$$

Evaluate

$$\frac{73}{30}\approx 2.433333333$$

Solution Steps

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

$$\frac{1}{3}\times \frac{3}{2}+\frac{2}{1.5}+\frac{3}{5}$$

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

$$\frac{1\times 3}{3\times 2}+\frac{2}{1.5}+\frac{3}{5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{2}+\frac{2}{1.5}+\frac{3}{5}$$

Expand \frac{2}{1.5} by multiplying both numerator and the denominator by 10.

$$\frac{1}{2}+\frac{20}{15}+\frac{3}{5}$$

Reduce the fraction \frac{20}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}+\frac{4}{3}+\frac{3}{5}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{8}{6}+\frac{3}{5}$$

Since \frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+8}{6}+\frac{3}{5}$$

Add 3 and 8 to get 11.

$$\frac{11}{6}+\frac{3}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{11}{6} and \frac{3}{5} to fractions with denominator 30.

$$\frac{55}{30}+\frac{18}{30}$$

Since \frac{55}{30} and \frac{18}{30} have the same denominator, add them by adding their numerators.

$$\frac{55+18}{30}$$

Add 55 and 18 to get 73.

$$\frac{73}{30}$$

Factor

$$\frac{73}{2 \cdot 3 \cdot 5} = 2\frac{13}{30} = 2.433333333333333$$