Solve -5/3div{5/6+(3/5-(4/7divfrac{2}{9}))+6}

$$- \frac { 5 } { 3 } \div \{ \frac { 5 } { 6 } + ( \frac { 3 } { 5 } - ( \frac { 4 } { 7 } \div \frac { 2 } { 9 } ) ) + 6 \}$$

Evaluate

$$-\frac{350}{1021}\approx -0.342801175$$

Solution Steps

Least common multiple of 6 and 5 is 30. Convert \frac{5}{6} and \frac{3}{5} to fractions with denominator 30.

$$\frac{-\frac{5}{3}}{\frac{25}{30}+\frac{18}{30}-\frac{\frac{4}{7}}{\frac{2}{9}}+6}$$

Since \frac{25}{30} and \frac{18}{30} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{5}{3}}{\frac{25+18}{30}-\frac{\frac{4}{7}}{\frac{2}{9}}+6}$$

Add 25 and 18 to get 43.

$$\frac{-\frac{5}{3}}{\frac{43}{30}-\frac{\frac{4}{7}}{\frac{2}{9}}+6}$$

Divide \frac{4}{7} by \frac{2}{9} by multiplying \frac{4}{7} by the reciprocal of \frac{2}{9}.

$$\frac{-\frac{5}{3}}{\frac{43}{30}-\frac{4}{7}\times \frac{9}{2}+6}$$

Multiply \frac{4}{7} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{5}{3}}{\frac{43}{30}-\frac{4\times 9}{7\times 2}+6}$$

Do the multiplications in the fraction \frac{4\times 9}{7\times 2}.

$$\frac{-\frac{5}{3}}{\frac{43}{30}-\frac{36}{14}+6}$$

Reduce the fraction \frac{36}{14} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{5}{3}}{\frac{43}{30}-\frac{18}{7}+6}$$

Least common multiple of 30 and 7 is 210. Convert \frac{43}{30} and \frac{18}{7} to fractions with denominator 210.

$$\frac{-\frac{5}{3}}{\frac{301}{210}-\frac{540}{210}+6}$$

Since \frac{301}{210} and \frac{540}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{5}{3}}{\frac{301-540}{210}+6}$$

Subtract 540 from 301 to get -239.

$$\frac{-\frac{5}{3}}{-\frac{239}{210}+6}$$

Convert 6 to fraction \frac{1260}{210}.

$$\frac{-\frac{5}{3}}{-\frac{239}{210}+\frac{1260}{210}}$$

Since -\frac{239}{210} and \frac{1260}{210} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{5}{3}}{\frac{-239+1260}{210}}$$

Add -239 and 1260 to get 1021.

$$\frac{-\frac{5}{3}}{\frac{1021}{210}}$$

Divide -\frac{5}{3} by \frac{1021}{210} by multiplying -\frac{5}{3} by the reciprocal of \frac{1021}{210}.

$$-\frac{5}{3}\times \frac{210}{1021}$$

Multiply -\frac{5}{3} times \frac{210}{1021} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 210}{3\times 1021}$$

Do the multiplications in the fraction \frac{-5\times 210}{3\times 1021}.

$$\frac{-1050}{3063}$$

Reduce the fraction \frac{-1050}{3063} to lowest terms by extracting and canceling out 3.

$$-\frac{350}{1021}$$

Factor

$$-\frac{350}{1021} = -0.3428011753183154$$