Solve [(25/9-2/3):38/19-12/10]*frac{5}{1}:{[frac{14}{9}+frac{3}{2}-(frac{1}{3}+frac{2}{9})]:frac{45}{99}}

$$[ ( \frac { 25 } { 9 } - \frac { 2 } { 3 } ) : \frac { 38 } { 19 } - \frac { 12 } { 10 } ] \cdot \frac { 5 } { 1 } : \{ [ \frac { 14 } { 9 } + \frac { 3 } { 2 } - ( \frac { 1 } { 3 } + \frac { 2 } { 9 } ) ] : \frac { 45 } { 99 } \}$$

Evaluate

$$-\frac{13}{99}\approx -0.131313131$$

Solution Steps

Least common multiple of 9 and 3 is 9. Convert \frac{25}{9} and \frac{2}{3} to fractions with denominator 9.

$$\frac{\left(\frac{\frac{25}{9}-\frac{6}{9}}{\frac{38}{19}}-\frac{12}{10}\right)\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Since \frac{25}{9} and \frac{6}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{\frac{25-6}{9}}{\frac{38}{19}}-\frac{12}{10}\right)\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Subtract 6 from 25 to get 19.

$$\frac{\left(\frac{\frac{19}{9}}{\frac{38}{19}}-\frac{12}{10}\right)\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Divide 38 by 19 to get 2.

$$\frac{\left(\frac{\frac{19}{9}}{2}-\frac{12}{10}\right)\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Express \frac{\frac{19}{9}}{2} as a single fraction.

$$\frac{\left(\frac{19}{9\times 2}-\frac{12}{10}\right)\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Multiply 9 and 2 to get 18.

$$\frac{\left(\frac{19}{18}-\frac{12}{10}\right)\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\left(\frac{19}{18}-\frac{6}{5}\right)\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Least common multiple of 18 and 5 is 90. Convert \frac{19}{18} and \frac{6}{5} to fractions with denominator 90.

$$\frac{\left(\frac{95}{90}-\frac{108}{90}\right)\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Since \frac{95}{90} and \frac{108}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{95-108}{90}\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Subtract 108 from 95 to get -13.

$$\frac{-\frac{13}{90}\times \frac{5}{1}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Anything divided by one gives itself.

$$\frac{-\frac{13}{90}\times 5}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Express -\frac{13}{90}\times 5 as a single fraction.

$$\frac{\frac{-13\times 5}{90}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Multiply -13 and 5 to get -65.

$$\frac{\frac{-65}{90}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Reduce the fraction \frac{-65}{90} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{13}{18}}{\frac{\frac{14}{9}+\frac{3}{2}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Least common multiple of 9 and 2 is 18. Convert \frac{14}{9} and \frac{3}{2} to fractions with denominator 18.

$$\frac{-\frac{13}{18}}{\frac{\frac{28}{18}+\frac{27}{18}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Since \frac{28}{18} and \frac{27}{18} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{13}{18}}{\frac{\frac{28+27}{18}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Add 28 and 27 to get 55.

$$\frac{-\frac{13}{18}}{\frac{\frac{55}{18}-\left(\frac{1}{3}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{2}{9} to fractions with denominator 9.

$$\frac{-\frac{13}{18}}{\frac{\frac{55}{18}-\left(\frac{3}{9}+\frac{2}{9}\right)}{\frac{45}{99}}}$$

Since \frac{3}{9} and \frac{2}{9} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{13}{18}}{\frac{\frac{55}{18}-\frac{3+2}{9}}{\frac{45}{99}}}$$

Add 3 and 2 to get 5.

$$\frac{-\frac{13}{18}}{\frac{\frac{55}{18}-\frac{5}{9}}{\frac{45}{99}}}$$

Least common multiple of 18 and 9 is 18. Convert \frac{55}{18} and \frac{5}{9} to fractions with denominator 18.

$$\frac{-\frac{13}{18}}{\frac{\frac{55}{18}-\frac{10}{18}}{\frac{45}{99}}}$$

Since \frac{55}{18} and \frac{10}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{13}{18}}{\frac{\frac{55-10}{18}}{\frac{45}{99}}}$$

Subtract 10 from 55 to get 45.

$$\frac{-\frac{13}{18}}{\frac{\frac{45}{18}}{\frac{45}{99}}}$$

Reduce the fraction \frac{45}{18} to lowest terms by extracting and canceling out 9.

$$\frac{-\frac{13}{18}}{\frac{\frac{5}{2}}{\frac{45}{99}}}$$

Reduce the fraction \frac{45}{99} to lowest terms by extracting and canceling out 9.

$$\frac{-\frac{13}{18}}{\frac{\frac{5}{2}}{\frac{5}{11}}}$$

Divide \frac{5}{2} by \frac{5}{11} by multiplying \frac{5}{2} by the reciprocal of \frac{5}{11}.

$$\frac{-\frac{13}{18}}{\frac{5}{2}\times \frac{11}{5}}$$

Multiply \frac{5}{2} times \frac{11}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{13}{18}}{\frac{5\times 11}{2\times 5}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-\frac{13}{18}}{\frac{11}{2}}$$

Divide -\frac{13}{18} by \frac{11}{2} by multiplying -\frac{13}{18} by the reciprocal of \frac{11}{2}.

$$-\frac{13}{18}\times \frac{2}{11}$$

Multiply -\frac{13}{18} times \frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-13\times 2}{18\times 11}$$

Do the multiplications in the fraction \frac{-13\times 2}{18\times 11}.

$$\frac{-26}{198}$$

Reduce the fraction \frac{-26}{198} to lowest terms by extracting and canceling out 2.

$$-\frac{13}{99}$$

Factor

$$-\frac{13}{99} = -0.13131313131313133$$