Solve (7/10+1/2)+[11/3-(7/3+frac{3}{5})]+frac{2}{3}*(1-frac{2}{5})-frac{33}{99}

$$( \frac { 7 } { 10 } + \frac { 1 } { 2 } ) + [ \frac { 11 } { 3 } - ( \frac { 7 } { 3 } + \frac { 3 } { 5 } ) ] + \frac { 2 } { 3 } \cdot ( 1 - \frac { 2 } { 5 } ) - \frac { 33 } { 99 }$$

Evaluate

$$2$$

Solution Steps

Least common multiple of 10 and 2 is 10. Convert \frac{7}{10} and \frac{1}{2} to fractions with denominator 10.

$$\frac{7}{10}+\frac{5}{10}+\frac{11}{3}-\left(\frac{7}{3}+\frac{3}{5}\right)+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Since \frac{7}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{7+5}{10}+\frac{11}{3}-\left(\frac{7}{3}+\frac{3}{5}\right)+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Add 7 and 5 to get 12.

$$\frac{12}{10}+\frac{11}{3}-\left(\frac{7}{3}+\frac{3}{5}\right)+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

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

$$\frac{6}{5}+\frac{11}{3}-\left(\frac{7}{3}+\frac{3}{5}\right)+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{6}{5}+\frac{11}{3}-\left(\frac{35}{15}+\frac{9}{15}\right)+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Since \frac{35}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{6}{5}+\frac{11}{3}-\frac{35+9}{15}+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Add 35 and 9 to get 44.

$$\frac{6}{5}+\frac{11}{3}-\frac{44}{15}+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Least common multiple of 3 and 15 is 15. Convert \frac{11}{3} and \frac{44}{15} to fractions with denominator 15.

$$\frac{6}{5}+\frac{55}{15}-\frac{44}{15}+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Since \frac{55}{15} and \frac{44}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6}{5}+\frac{55-44}{15}+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Subtract 44 from 55 to get 11.

$$\frac{6}{5}+\frac{11}{15}+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Least common multiple of 5 and 15 is 15. Convert \frac{6}{5} and \frac{11}{15} to fractions with denominator 15.

$$\frac{18}{15}+\frac{11}{15}+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Since \frac{18}{15} and \frac{11}{15} have the same denominator, add them by adding their numerators.

$$\frac{18+11}{15}+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Add 18 and 11 to get 29.

$$\frac{29}{15}+\frac{2}{3}\left(1-\frac{2}{5}\right)-\frac{33}{99}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{29}{15}+\frac{2}{3}\left(\frac{5}{5}-\frac{2}{5}\right)-\frac{33}{99}$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29}{15}+\frac{2}{3}\times \frac{5-2}{5}-\frac{33}{99}$$

Subtract 2 from 5 to get 3.

$$\frac{29}{15}+\frac{2}{3}\times \frac{3}{5}-\frac{33}{99}$$

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

$$\frac{29}{15}+\frac{2\times 3}{3\times 5}-\frac{33}{99}$$

Cancel out 3 in both numerator and denominator.

$$\frac{29}{15}+\frac{2}{5}-\frac{33}{99}$$

Least common multiple of 15 and 5 is 15. Convert \frac{29}{15} and \frac{2}{5} to fractions with denominator 15.

$$\frac{29}{15}+\frac{6}{15}-\frac{33}{99}$$

Since \frac{29}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{29+6}{15}-\frac{33}{99}$$

Add 29 and 6 to get 35.

$$\frac{35}{15}-\frac{33}{99}$$

Reduce the fraction \frac{35}{15} to lowest terms by extracting and canceling out 5.

$$\frac{7}{3}-\frac{33}{99}$$

Reduce the fraction \frac{33}{99} to lowest terms by extracting and canceling out 33.

$$\frac{7}{3}-\frac{1}{3}$$

Since \frac{7}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-1}{3}$$

Subtract 1 from 7 to get 6.

$$\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2$$

Factor

$$2$$