Solve 1/2+2/3:3/5+4/3=

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

Evaluate

$$\frac{53}{18}\approx 2.944444444$$

Solution Steps

Divide \frac{2}{3} by \frac{3}{5} by multiplying \frac{2}{3} by the reciprocal of \frac{3}{5}.

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

Multiply \frac{2}{3} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 5}{3\times 3}.

$$\frac{1}{2}+\frac{10}{9}+\frac{4}{3}$$

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{10}{9} to fractions with denominator 18.

$$\frac{9}{18}+\frac{20}{18}+\frac{4}{3}$$

Since \frac{9}{18} and \frac{20}{18} have the same denominator, add them by adding their numerators.

$$\frac{9+20}{18}+\frac{4}{3}$$

Add 9 and 20 to get 29.

$$\frac{29}{18}+\frac{4}{3}$$

Least common multiple of 18 and 3 is 18. Convert \frac{29}{18} and \frac{4}{3} to fractions with denominator 18.

$$\frac{29}{18}+\frac{24}{18}$$

Since \frac{29}{18} and \frac{24}{18} have the same denominator, add them by adding their numerators.

$$\frac{29+24}{18}$$

Add 29 and 24 to get 53.

$$\frac{53}{18}$$

Factor

$$\frac{53}{2 \cdot 3 ^ {2}} = 2\frac{17}{18} = 2.9444444444444446$$