Solve 14/27+5/18+7/9+5/6-frac{1}{3}-frac{71}{81}-frac{41}{54}=

$$\frac { 14 } { 27 } + \frac { 5 } { 18 } + \frac { 7 } { 9 } + \frac { 5 } { 6 } - \frac { 1 } { 3 } - \frac { 71 } { 81 } - \frac { 41 } { 54 } =$$

Evaluate

$$\frac{71}{162}\approx 0.438271605$$

Solution Steps

Least common multiple of 27 and 18 is 54. Convert \frac{14}{27} and \frac{5}{18} to fractions with denominator 54.

$$\frac{28}{54}+\frac{15}{54}+\frac{7}{9}+\frac{5}{6}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Since \frac{28}{54} and \frac{15}{54} have the same denominator, add them by adding their numerators.

$$\frac{28+15}{54}+\frac{7}{9}+\frac{5}{6}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Add 28 and 15 to get 43.

$$\frac{43}{54}+\frac{7}{9}+\frac{5}{6}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Least common multiple of 54 and 9 is 54. Convert \frac{43}{54} and \frac{7}{9} to fractions with denominator 54.

$$\frac{43}{54}+\frac{42}{54}+\frac{5}{6}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Since \frac{43}{54} and \frac{42}{54} have the same denominator, add them by adding their numerators.

$$\frac{43+42}{54}+\frac{5}{6}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Add 43 and 42 to get 85.

$$\frac{85}{54}+\frac{5}{6}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Least common multiple of 54 and 6 is 54. Convert \frac{85}{54} and \frac{5}{6} to fractions with denominator 54.

$$\frac{85}{54}+\frac{45}{54}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Since \frac{85}{54} and \frac{45}{54} have the same denominator, add them by adding their numerators.

$$\frac{85+45}{54}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Add 85 and 45 to get 130.

$$\frac{130}{54}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Reduce the fraction \frac{130}{54} to lowest terms by extracting and canceling out 2.

$$\frac{65}{27}-\frac{1}{3}-\frac{71}{81}-\frac{41}{54}$$

Least common multiple of 27 and 3 is 27. Convert \frac{65}{27} and \frac{1}{3} to fractions with denominator 27.

$$\frac{65}{27}-\frac{9}{27}-\frac{71}{81}-\frac{41}{54}$$

Since \frac{65}{27} and \frac{9}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-9}{27}-\frac{71}{81}-\frac{41}{54}$$

Subtract 9 from 65 to get 56.

$$\frac{56}{27}-\frac{71}{81}-\frac{41}{54}$$

Least common multiple of 27 and 81 is 81. Convert \frac{56}{27} and \frac{71}{81} to fractions with denominator 81.

$$\frac{168}{81}-\frac{71}{81}-\frac{41}{54}$$

Since \frac{168}{81} and \frac{71}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{168-71}{81}-\frac{41}{54}$$

Subtract 71 from 168 to get 97.

$$\frac{97}{81}-\frac{41}{54}$$

Least common multiple of 81 and 54 is 162. Convert \frac{97}{81} and \frac{41}{54} to fractions with denominator 162.

$$\frac{194}{162}-\frac{123}{162}$$

Since \frac{194}{162} and \frac{123}{162} have the same denominator, subtract them by subtracting their numerators.

$$\frac{194-123}{162}$$

Subtract 123 from 194 to get 71.

$$\frac{71}{162}$$

Factor

$$\frac{71}{2 \cdot 3 ^ {4}} = 0.4382716049382716$$