Solve 3/4+7/8/frac{2{5}-8/9}

$$\frac{ \frac{ 3 }{ 4 } + \frac{ 7 }{ 8 } }{ \frac{ 2 }{ 5 } - \frac{ 8 }{ 9 } }$$

Evaluate

$$-\frac{585}{176}\approx -3.323863636$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{7}{8} to fractions with denominator 8.

$$\frac{\frac{6}{8}+\frac{7}{8}}{\frac{2}{5}-\frac{8}{9}}$$

Since \frac{6}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6+7}{8}}{\frac{2}{5}-\frac{8}{9}}$$

Add 6 and 7 to get 13.

$$\frac{\frac{13}{8}}{\frac{2}{5}-\frac{8}{9}}$$

Least common multiple of 5 and 9 is 45. Convert \frac{2}{5} and \frac{8}{9} to fractions with denominator 45.

$$\frac{\frac{13}{8}}{\frac{18}{45}-\frac{40}{45}}$$

Since \frac{18}{45} and \frac{40}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{8}}{\frac{18-40}{45}}$$

Subtract 40 from 18 to get -22.

$$\frac{\frac{13}{8}}{-\frac{22}{45}}$$

Divide \frac{13}{8} by -\frac{22}{45} by multiplying \frac{13}{8} by the reciprocal of -\frac{22}{45}.

$$\frac{13}{8}\left(-\frac{45}{22}\right)$$

Multiply \frac{13}{8} times -\frac{45}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\left(-45\right)}{8\times 22}$$

Do the multiplications in the fraction \frac{13\left(-45\right)}{8\times 22}.

$$\frac{-585}{176}$$

Fraction \frac{-585}{176} can be rewritten as -\frac{585}{176} by extracting the negative sign.

$$-\frac{585}{176}$$

Factor

$$-\frac{585}{176} = -3\frac{57}{176} = -3.3238636363636362$$