Solve 5/9+1+3/9(4+21/99-2/3)

$$\frac { 5 } { 9 } + 1 + \frac { 3 } { 9 } ( 4 + \frac { 21 } { 99 } - \frac { 2 } { 3 } )$$

Evaluate

$$\frac{271}{99}\approx 2.737373737$$

Solution Steps

Convert 1 to fraction \frac{9}{9}.

$$\frac{5}{9}+\frac{9}{9}+\frac{3}{9}\left(4+\frac{21}{99}-\frac{2}{3}\right)$$

Since \frac{5}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{5+9}{9}+\frac{3}{9}\left(4+\frac{21}{99}-\frac{2}{3}\right)$$

Add 5 and 9 to get 14.

$$\frac{14}{9}+\frac{3}{9}\left(4+\frac{21}{99}-\frac{2}{3}\right)$$

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

$$\frac{14}{9}+\frac{1}{3}\left(4+\frac{21}{99}-\frac{2}{3}\right)$$

Reduce the fraction \frac{21}{99} to lowest terms by extracting and canceling out 3.

$$\frac{14}{9}+\frac{1}{3}\left(4+\frac{7}{33}-\frac{2}{3}\right)$$

Convert 4 to fraction \frac{132}{33}.

$$\frac{14}{9}+\frac{1}{3}\left(\frac{132}{33}+\frac{7}{33}-\frac{2}{3}\right)$$

Since \frac{132}{33} and \frac{7}{33} have the same denominator, add them by adding their numerators.

$$\frac{14}{9}+\frac{1}{3}\left(\frac{132+7}{33}-\frac{2}{3}\right)$$

Add 132 and 7 to get 139.

$$\frac{14}{9}+\frac{1}{3}\left(\frac{139}{33}-\frac{2}{3}\right)$$

Least common multiple of 33 and 3 is 33. Convert \frac{139}{33} and \frac{2}{3} to fractions with denominator 33.

$$\frac{14}{9}+\frac{1}{3}\left(\frac{139}{33}-\frac{22}{33}\right)$$

Since \frac{139}{33} and \frac{22}{33} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14}{9}+\frac{1}{3}\times \frac{139-22}{33}$$

Subtract 22 from 139 to get 117.

$$\frac{14}{9}+\frac{1}{3}\times \frac{117}{33}$$

Reduce the fraction \frac{117}{33} to lowest terms by extracting and canceling out 3.

$$\frac{14}{9}+\frac{1}{3}\times \frac{39}{11}$$

Multiply \frac{1}{3} times \frac{39}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14}{9}+\frac{1\times 39}{3\times 11}$$

Do the multiplications in the fraction \frac{1\times 39}{3\times 11}.

$$\frac{14}{9}+\frac{39}{33}$$

Reduce the fraction \frac{39}{33} to lowest terms by extracting and canceling out 3.

$$\frac{14}{9}+\frac{13}{11}$$

Least common multiple of 9 and 11 is 99. Convert \frac{14}{9} and \frac{13}{11} to fractions with denominator 99.

$$\frac{154}{99}+\frac{117}{99}$$

Since \frac{154}{99} and \frac{117}{99} have the same denominator, add them by adding their numerators.

$$\frac{154+117}{99}$$

Add 154 and 117 to get 271.

$$\frac{271}{99}$$

Factor

$$\frac{271}{3 ^ {2} \cdot 11} = 2\frac{73}{99} = 2.7373737373737375$$