Solve 2/36+2/3+4/36quadquadquadquadquadquadquad8/9-frac{2}{18}-frac{2}{3}

$$\frac { 2 } { 36 } + \frac { 2 } { 3 } + \frac { 4 } { 36 } \quad \quad \quad \quad \quad \quad \quad \frac { 8 } { 9 } - \frac { 2 } { 18 } - \frac { 2 } { 3 }$$

Evaluate

$$\frac{7}{162}\approx 0.043209877$$

Solution Steps

Reduce the fraction \frac{2}{36} to lowest terms by extracting and canceling out 2.

$$\frac{1}{18}+\frac{2}{3}+\frac{4}{36}\times \frac{8}{9}-\frac{2}{18}-\frac{2}{3}$$

Least common multiple of 18 and 3 is 18. Convert \frac{1}{18} and \frac{2}{3} to fractions with denominator 18.

$$\frac{1}{18}+\frac{12}{18}+\frac{4}{36}\times \frac{8}{9}-\frac{2}{18}-\frac{2}{3}$$

Since \frac{1}{18} and \frac{12}{18} have the same denominator, add them by adding their numerators.

$$\frac{1+12}{18}+\frac{4}{36}\times \frac{8}{9}-\frac{2}{18}-\frac{2}{3}$$

Add 1 and 12 to get 13.

$$\frac{13}{18}+\frac{4}{36}\times \frac{8}{9}-\frac{2}{18}-\frac{2}{3}$$

Reduce the fraction \frac{4}{36} to lowest terms by extracting and canceling out 4.

$$\frac{13}{18}+\frac{1}{9}\times \frac{8}{9}-\frac{2}{18}-\frac{2}{3}$$

Multiply \frac{1}{9} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{18}+\frac{1\times 8}{9\times 9}-\frac{2}{18}-\frac{2}{3}$$

Do the multiplications in the fraction \frac{1\times 8}{9\times 9}.

$$\frac{13}{18}+\frac{8}{81}-\frac{2}{18}-\frac{2}{3}$$

Least common multiple of 18 and 81 is 162. Convert \frac{13}{18} and \frac{8}{81} to fractions with denominator 162.

$$\frac{117}{162}+\frac{16}{162}-\frac{2}{18}-\frac{2}{3}$$

Since \frac{117}{162} and \frac{16}{162} have the same denominator, add them by adding their numerators.

$$\frac{117+16}{162}-\frac{2}{18}-\frac{2}{3}$$

Add 117 and 16 to get 133.

$$\frac{133}{162}-\frac{2}{18}-\frac{2}{3}$$

Reduce the fraction \frac{2}{18} to lowest terms by extracting and canceling out 2.

$$\frac{133}{162}-\frac{1}{9}-\frac{2}{3}$$

Least common multiple of 162 and 9 is 162. Convert \frac{133}{162} and \frac{1}{9} to fractions with denominator 162.

$$\frac{133}{162}-\frac{18}{162}-\frac{2}{3}$$

Since \frac{133}{162} and \frac{18}{162} have the same denominator, subtract them by subtracting their numerators.

$$\frac{133-18}{162}-\frac{2}{3}$$

Subtract 18 from 133 to get 115.

$$\frac{115}{162}-\frac{2}{3}$$

Least common multiple of 162 and 3 is 162. Convert \frac{115}{162} and \frac{2}{3} to fractions with denominator 162.

$$\frac{115}{162}-\frac{108}{162}$$

Since \frac{115}{162} and \frac{108}{162} have the same denominator, subtract them by subtracting their numerators.

$$\frac{115-108}{162}$$

Subtract 108 from 115 to get 7.

$$\frac{7}{162}$$

Factor

$$\frac{7}{2 \cdot 3 ^ {4}} = 0.043209876543209874$$