Solve 1/2+2/7/frac{1{5}+2/3}

$$\frac { \frac { 1 } { 2 } + \frac { 2 } { 7 } } { \frac { 1 } { 5 } + \frac { 2 } { 3 } }$$

Evaluate

$$\frac{165}{182}\approx 0.906593407$$

Solution Steps

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{2}{7} to fractions with denominator 14.

$$\frac{\frac{7}{14}+\frac{4}{14}}{\frac{1}{5}+\frac{2}{3}}$$

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

$$\frac{\frac{7+4}{14}}{\frac{1}{5}+\frac{2}{3}}$$

Add 7 and 4 to get 11.

$$\frac{\frac{11}{14}}{\frac{1}{5}+\frac{2}{3}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{\frac{11}{14}}{\frac{3}{15}+\frac{10}{15}}$$

Since \frac{3}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{14}}{\frac{3+10}{15}}$$

Add 3 and 10 to get 13.

$$\frac{\frac{11}{14}}{\frac{13}{15}}$$

Divide \frac{11}{14} by \frac{13}{15} by multiplying \frac{11}{14} by the reciprocal of \frac{13}{15}.

$$\frac{11}{14}\times \frac{15}{13}$$

Multiply \frac{11}{14} times \frac{15}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 15}{14\times 13}$$

Do the multiplications in the fraction \frac{11\times 15}{14\times 13}.

$$\frac{165}{182}$$

Factor

$$\frac{3 \cdot 5 \cdot 11}{2 \cdot 7 \cdot 13} = 0.9065934065934066$$