Solve 2/6-6/7/frac{5{4}+4/9}

$$\frac{ \frac{ 2 }{ 6 } - \frac{ 6 }{ 7 } }{ \frac{ 5 }{ 4 } + \frac{ 4 }{ 9 } }$$

Evaluate

$$-\frac{132}{427}\approx -0.309133489$$

Solution Steps

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{3}-\frac{6}{7}}{\frac{5}{4}+\frac{4}{9}}$$

Least common multiple of 3 and 7 is 21. Convert \frac{1}{3} and \frac{6}{7} to fractions with denominator 21.

$$\frac{\frac{7}{21}-\frac{18}{21}}{\frac{5}{4}+\frac{4}{9}}$$

Since \frac{7}{21} and \frac{18}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-18}{21}}{\frac{5}{4}+\frac{4}{9}}$$

Subtract 18 from 7 to get -11.

$$\frac{-\frac{11}{21}}{\frac{5}{4}+\frac{4}{9}}$$

Least common multiple of 4 and 9 is 36. Convert \frac{5}{4} and \frac{4}{9} to fractions with denominator 36.

$$\frac{-\frac{11}{21}}{\frac{45}{36}+\frac{16}{36}}$$

Since \frac{45}{36} and \frac{16}{36} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{11}{21}}{\frac{45+16}{36}}$$

Add 45 and 16 to get 61.

$$\frac{-\frac{11}{21}}{\frac{61}{36}}$$

Divide -\frac{11}{21} by \frac{61}{36} by multiplying -\frac{11}{21} by the reciprocal of \frac{61}{36}.

$$-\frac{11}{21}\times \frac{36}{61}$$

Multiply -\frac{11}{21} times \frac{36}{61} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\times 36}{21\times 61}$$

Do the multiplications in the fraction \frac{-11\times 36}{21\times 61}.

$$\frac{-396}{1281}$$

Reduce the fraction \frac{-396}{1281} to lowest terms by extracting and canceling out 3.

$$-\frac{132}{427}$$

Factor

$$-\frac{132}{427} = -0.3091334894613583$$