Solve (1/6+7/9)*36/17+4/3(frac{1}{7}-frac{1}{21})

$$( \frac { 1 } { 6 } + \frac { 7 } { 9 } ) \cdot \frac { 36 } { 17 } + \frac { 4 } { 3 } ( \frac { 1 } { 7 } - \frac { 1 } { 21 } )$$

Evaluate

$$\frac{134}{63}\approx 2.126984127$$

Solution Steps

Least common multiple of 6 and 9 is 18. Convert \frac{1}{6} and \frac{7}{9} to fractions with denominator 18.

$$\left(\frac{3}{18}+\frac{14}{18}\right)\times \frac{36}{17}+\frac{4}{3}\left(\frac{1}{7}-\frac{1}{21}\right)$$

Since \frac{3}{18} and \frac{14}{18} have the same denominator, add them by adding their numerators.

$$\frac{3+14}{18}\times \frac{36}{17}+\frac{4}{3}\left(\frac{1}{7}-\frac{1}{21}\right)$$

Add 3 and 14 to get 17.

$$\frac{17}{18}\times \frac{36}{17}+\frac{4}{3}\left(\frac{1}{7}-\frac{1}{21}\right)$$

Multiply \frac{17}{18} times \frac{36}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 36}{18\times 17}+\frac{4}{3}\left(\frac{1}{7}-\frac{1}{21}\right)$$

Cancel out 17 in both numerator and denominator.

$$\frac{36}{18}+\frac{4}{3}\left(\frac{1}{7}-\frac{1}{21}\right)$$

Divide 36 by 18 to get 2.

$$2+\frac{4}{3}\left(\frac{1}{7}-\frac{1}{21}\right)$$

Least common multiple of 7 and 21 is 21. Convert \frac{1}{7} and \frac{1}{21} to fractions with denominator 21.

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

Since \frac{3}{21} and \frac{1}{21} have the same denominator, subtract them by subtracting their numerators.

$$2+\frac{4}{3}\times \frac{3-1}{21}$$

Subtract 1 from 3 to get 2.

$$2+\frac{4}{3}\times \frac{2}{21}$$

Multiply \frac{4}{3} times \frac{2}{21} by multiplying numerator times numerator and denominator times denominator.

$$2+\frac{4\times 2}{3\times 21}$$

Do the multiplications in the fraction \frac{4\times 2}{3\times 21}.

$$2+\frac{8}{63}$$

Convert 2 to fraction \frac{126}{63}.

$$\frac{126}{63}+\frac{8}{63}$$

Since \frac{126}{63} and \frac{8}{63} have the same denominator, add them by adding their numerators.

$$\frac{126+8}{63}$$

Add 126 and 8 to get 134.

$$\frac{134}{63}$$

Factor

$$\frac{2 \cdot 67}{3 ^ {2} \cdot 7} = 2\frac{8}{63} = 2.126984126984127$$