Solve (5/10+6/9+75/100):(1-6/9+frac{25}{100}-frac{16-1}{90})+frac{4}{10}*frac{33-3}{9}=

$$( \frac { 5 } { 10 } + \frac { 6 } { 9 } + \frac { 75 } { 100 } ) : ( 1 - \frac { 6 } { 9 } + \frac { 25 } { 100 } - \frac { 16 - 1 } { 90 } ) + \frac { 4 } { 10 } \times \frac { 33 - 3 } { 9 } =$$

Evaluate

$$\frac{89}{15}\approx 5.933333333$$

Solution Steps

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{2}+\frac{6}{9}+\frac{75}{100}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{2}+\frac{2}{3}+\frac{75}{100}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{3}{6}+\frac{4}{6}+\frac{75}{100}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+4}{6}+\frac{75}{100}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Add 3 and 4 to get 7.

$$\frac{\frac{7}{6}+\frac{75}{100}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{7}{6}+\frac{3}{4}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Least common multiple of 6 and 4 is 12. Convert \frac{7}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{14}{12}+\frac{9}{12}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Since \frac{14}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14+9}{12}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Add 14 and 9 to get 23.

$$\frac{\frac{23}{12}}{1-\frac{6}{9}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{23}{12}}{1-\frac{2}{3}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{23}{12}}{\frac{3}{3}-\frac{2}{3}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23}{12}}{\frac{3-2}{3}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{23}{12}}{\frac{1}{3}+\frac{25}{100}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{23}{12}}{\frac{1}{3}+\frac{1}{4}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{23}{12}}{\frac{4}{12}+\frac{3}{12}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{23}{12}}{\frac{4+3}{12}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Add 4 and 3 to get 7.

$$\frac{\frac{23}{12}}{\frac{7}{12}-\frac{16-1}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Subtract 1 from 16 to get 15.

$$\frac{\frac{23}{12}}{\frac{7}{12}-\frac{15}{90}}+\frac{4}{10}\times \frac{33-3}{9}$$

Reduce the fraction \frac{15}{90} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{23}{12}}{\frac{7}{12}-\frac{1}{6}}+\frac{4}{10}\times \frac{33-3}{9}$$

Least common multiple of 12 and 6 is 12. Convert \frac{7}{12} and \frac{1}{6} to fractions with denominator 12.

$$\frac{\frac{23}{12}}{\frac{7}{12}-\frac{2}{12}}+\frac{4}{10}\times \frac{33-3}{9}$$

Since \frac{7}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23}{12}}{\frac{7-2}{12}}+\frac{4}{10}\times \frac{33-3}{9}$$

Subtract 2 from 7 to get 5.

$$\frac{\frac{23}{12}}{\frac{5}{12}}+\frac{4}{10}\times \frac{33-3}{9}$$

Divide \frac{23}{12} by \frac{5}{12} by multiplying \frac{23}{12} by the reciprocal of \frac{5}{12}.

$$\frac{23}{12}\times \frac{12}{5}+\frac{4}{10}\times \frac{33-3}{9}$$

Multiply \frac{23}{12} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 12}{12\times 5}+\frac{4}{10}\times \frac{33-3}{9}$$

Cancel out 12 in both numerator and denominator.

$$\frac{23}{5}+\frac{4}{10}\times \frac{33-3}{9}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{23}{5}+\frac{2}{5}\times \frac{33-3}{9}$$

Subtract 3 from 33 to get 30.

$$\frac{23}{5}+\frac{2}{5}\times \frac{30}{9}$$

Reduce the fraction \frac{30}{9} to lowest terms by extracting and canceling out 3.

$$\frac{23}{5}+\frac{2}{5}\times \frac{10}{3}$$

Multiply \frac{2}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23}{5}+\frac{2\times 10}{5\times 3}$$

Do the multiplications in the fraction \frac{2\times 10}{5\times 3}.

$$\frac{23}{5}+\frac{20}{15}$$

Reduce the fraction \frac{20}{15} to lowest terms by extracting and canceling out 5.

$$\frac{23}{5}+\frac{4}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{23}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{69}{15}+\frac{20}{15}$$

Since \frac{69}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$\frac{69+20}{15}$$

Add 69 and 20 to get 89.

$$\frac{89}{15}$$

Factor

$$\frac{89}{3 \cdot 5} = 5\frac{14}{15} = 5.933333333333334$$