Solve -2/33/5-1/2/frac{3{7}+-frac{2}{9}}

$$- \frac{ 2 }{ 3 } \frac{ \frac{ 3 }{ 5 } - \frac{ 1 }{ 2 } }{ \frac{ 3 }{ 7 } +- \frac{ 2 }{ 9 } }$$

Evaluate

$$-\frac{21}{65}\approx -0.323076923$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$-\frac{2}{3}\times \frac{\frac{6}{10}-\frac{5}{10}}{\frac{3}{7}-\frac{2}{9}}$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}\times \frac{\frac{6-5}{10}}{\frac{3}{7}-\frac{2}{9}}$$

Subtract 5 from 6 to get 1.

$$-\frac{2}{3}\times \frac{\frac{1}{10}}{\frac{3}{7}-\frac{2}{9}}$$

Least common multiple of 7 and 9 is 63. Convert \frac{3}{7} and \frac{2}{9} to fractions with denominator 63.

$$-\frac{2}{3}\times \frac{\frac{1}{10}}{\frac{27}{63}-\frac{14}{63}}$$

Since \frac{27}{63} and \frac{14}{63} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}\times \frac{\frac{1}{10}}{\frac{27-14}{63}}$$

Subtract 14 from 27 to get 13.

$$-\frac{2}{3}\times \frac{\frac{1}{10}}{\frac{13}{63}}$$

Divide \frac{1}{10} by \frac{13}{63} by multiplying \frac{1}{10} by the reciprocal of \frac{13}{63}.

$$-\frac{2}{3}\times \frac{1}{10}\times \frac{63}{13}$$

Multiply \frac{1}{10} times \frac{63}{13} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{2}{3}\times \frac{63}{10\times 13}$$

Do the multiplications in the fraction \frac{1\times 63}{10\times 13}.

$$-\frac{2}{3}\times \frac{63}{130}$$

Multiply -\frac{2}{3} times \frac{63}{130} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 63}{3\times 130}$$

Do the multiplications in the fraction \frac{-2\times 63}{3\times 130}.

$$\frac{-126}{390}$$

Reduce the fraction \frac{-126}{390} to lowest terms by extracting and canceling out 6.

$$-\frac{21}{65}$$

Factor

$$-\frac{21}{65} = -0.3230769230769231$$