Solve 8/5+2/3/2+frac{4{7}}

$$\frac { \frac { 8 } { 5 } + \frac { 2 } { 3 } } { 2 + \frac { 4 } { 7 } }$$

Evaluate

$$\frac{119}{135}\approx 0.881481481$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{8}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{\frac{24}{15}+\frac{10}{15}}{2+\frac{4}{7}}$$

Since \frac{24}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{24+10}{15}}{2+\frac{4}{7}}$$

Add 24 and 10 to get 34.

$$\frac{\frac{34}{15}}{2+\frac{4}{7}}$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{\frac{34}{15}}{\frac{14}{7}+\frac{4}{7}}$$

Since \frac{14}{7} and \frac{4}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{34}{15}}{\frac{14+4}{7}}$$

Add 14 and 4 to get 18.

$$\frac{\frac{34}{15}}{\frac{18}{7}}$$

Divide \frac{34}{15} by \frac{18}{7} by multiplying \frac{34}{15} by the reciprocal of \frac{18}{7}.

$$\frac{34}{15}\times \frac{7}{18}$$

Multiply \frac{34}{15} times \frac{7}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{34\times 7}{15\times 18}$$

Do the multiplications in the fraction \frac{34\times 7}{15\times 18}.

$$\frac{238}{270}$$

Reduce the fraction \frac{238}{270} to lowest terms by extracting and canceling out 2.

$$\frac{119}{135}$$

Factor

$$\frac{7 \cdot 17}{3 ^ {3} \cdot 5} = 0.8814814814814815$$