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

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

Evaluate

$$\frac{56}{123}\approx 0.455284553$$

Solution Steps

Least common multiple of 4 and 7 is 28. Convert \frac{3}{4} and \frac{5}{7} to fractions with denominator 28.

$$\frac{\frac{2}{3}}{\frac{21}{28}+\frac{20}{28}}$$

Since \frac{21}{28} and \frac{20}{28} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{3}}{\frac{21+20}{28}}$$

Add 21 and 20 to get 41.

$$\frac{\frac{2}{3}}{\frac{41}{28}}$$

Divide \frac{2}{3} by \frac{41}{28} by multiplying \frac{2}{3} by the reciprocal of \frac{41}{28}.

$$\frac{2}{3}\times \frac{28}{41}$$

Multiply \frac{2}{3} times \frac{28}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 28}{3\times 41}$$

Do the multiplications in the fraction \frac{2\times 28}{3\times 41}.

$$\frac{56}{123}$$

Factor

$$\frac{2 ^ {3} \cdot 7}{3 \cdot 41} = 0.45528455284552843$$