Solve 1/2[(16/9-8/10-7/9)*frac{12}{10}-frac{44}{10}]+(7-frac{42}{99}:frac{7}{99})*frac{5}{10}3*frac{3}{1}=

$$\frac { 1 } { 2 } [ ( \frac { 16 } { 9 } - \frac { 8 } { 10 } - \frac { 7 } { 9 } ) \cdot \frac { 12 } { 10 } - \frac { 44 } { 10 } ] + ( 7 - \frac { 42 } { 99 } : \frac { 7 } { 99 } ) \cdot \frac { 5 } { 10 } 3 \cdot \frac { 3 } { 1 } =$$

Evaluate

$$\frac{121}{50}=2.42$$

Solution Steps

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\left(\left(\frac{16}{9}-\frac{4}{5}-\frac{7}{9}\right)\times \frac{12}{10}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Least common multiple of 9 and 5 is 45. Convert \frac{16}{9} and \frac{4}{5} to fractions with denominator 45.

$$\frac{1}{2}\left(\left(\frac{80}{45}-\frac{36}{45}-\frac{7}{9}\right)\times \frac{12}{10}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Since \frac{80}{45} and \frac{36}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\left(\left(\frac{80-36}{45}-\frac{7}{9}\right)\times \frac{12}{10}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Subtract 36 from 80 to get 44.

$$\frac{1}{2}\left(\left(\frac{44}{45}-\frac{7}{9}\right)\times \frac{12}{10}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Least common multiple of 45 and 9 is 45. Convert \frac{44}{45} and \frac{7}{9} to fractions with denominator 45.

$$\frac{1}{2}\left(\left(\frac{44}{45}-\frac{35}{45}\right)\times \frac{12}{10}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Since \frac{44}{45} and \frac{35}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\left(\frac{44-35}{45}\times \frac{12}{10}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Subtract 35 from 44 to get 9.

$$\frac{1}{2}\left(\frac{9}{45}\times \frac{12}{10}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

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

$$\frac{1}{2}\left(\frac{1}{5}\times \frac{12}{10}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

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

$$\frac{1}{2}\left(\frac{1}{5}\times \frac{6}{5}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Multiply \frac{1}{5} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}\left(\frac{1\times 6}{5\times 5}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Do the multiplications in the fraction \frac{1\times 6}{5\times 5}.

$$\frac{1}{2}\left(\frac{6}{25}-\frac{44}{10}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Reduce the fraction \frac{44}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\left(\frac{6}{25}-\frac{22}{5}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Least common multiple of 25 and 5 is 25. Convert \frac{6}{25} and \frac{22}{5} to fractions with denominator 25.

$$\frac{1}{2}\left(\frac{6}{25}-\frac{110}{25}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Since \frac{6}{25} and \frac{110}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{6-110}{25}+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Subtract 110 from 6 to get -104.

$$\frac{1}{2}\left(-\frac{104}{25}\right)+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Multiply \frac{1}{2} times -\frac{104}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-104\right)}{2\times 25}+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Do the multiplications in the fraction \frac{1\left(-104\right)}{2\times 25}.

$$\frac{-104}{50}+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Reduce the fraction \frac{-104}{50} to lowest terms by extracting and canceling out 2.

$$-\frac{52}{25}+\left(7-\frac{\frac{42}{99}}{\frac{7}{99}}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Divide \frac{42}{99} by \frac{7}{99} by multiplying \frac{42}{99} by the reciprocal of \frac{7}{99}.

$$-\frac{52}{25}+\left(7-\frac{42\times 99}{99\times 7}\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Cancel out 3\times 7\times 33 in both numerator and denominator.

$$-\frac{52}{25}+\left(7-2\times 3\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Multiply 2 and 3 to get 6.

$$-\frac{52}{25}+\left(7-6\right)\times \frac{5}{10}\times 3\times \frac{3}{1}$$

Subtract 6 from 7 to get 1.

$$-\frac{52}{25}+1\times \frac{5}{10}\times 3\times \frac{3}{1}$$

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

$$-\frac{52}{25}+1\times \frac{1}{2}\times 3\times \frac{3}{1}$$

Multiply 1 and \frac{1}{2} to get \frac{1}{2}.

$$-\frac{52}{25}+\frac{1}{2}\times 3\times \frac{3}{1}$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$-\frac{52}{25}+\frac{3}{2}\times \frac{3}{1}$$

Anything divided by one gives itself.

$$-\frac{52}{25}+\frac{3}{2}\times 3$$

Express \frac{3}{2}\times 3 as a single fraction.

$$-\frac{52}{25}+\frac{3\times 3}{2}$$

Multiply 3 and 3 to get 9.

$$-\frac{52}{25}+\frac{9}{2}$$

Least common multiple of 25 and 2 is 50. Convert -\frac{52}{25} and \frac{9}{2} to fractions with denominator 50.

$$-\frac{104}{50}+\frac{225}{50}$$

Since -\frac{104}{50} and \frac{225}{50} have the same denominator, add them by adding their numerators.

$$\frac{-104+225}{50}$$

Add -104 and 225 to get 121.

$$\frac{121}{50}$$

Factor

$$\frac{11 ^ {2}}{2 \cdot 5 ^ {2}} = 2\frac{21}{50} = 2.42$$