Solve 2/3+3/5:11/5

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

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Divide \frac{3}{5} by \frac{1\times 5+1}{5} by multiplying \frac{3}{5} by the reciprocal of \frac{1\times 5+1}{5}.

$$\frac{2}{3}+\frac{3\times 5}{5\left(1\times 5+1\right)}$$

Cancel out 5 in both numerator and denominator.

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

Add 1 and 5 to get 6.

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{4}{6}+\frac{3}{6}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{6}$$

Add 4 and 3 to get 7.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$