Solve 8/20+7/19+3/18+6/20+frac{3}{19}+frac{7}{18}+frac{3}{20}+frac{8}{19}+frac{7}{18}=

$$\frac { 8 } { 20 } + \frac { 7 } { 19 } + \frac { 3 } { 18 } + \frac { 6 } { 20 } + \frac { 3 } { 19 } + \frac { 7 } { 18 } + \frac { 3 } { 20 } + \frac { 8 } { 19 } + \frac { 7 } { 18 } =$$

Evaluate

$$\frac{9377}{3420}\approx 2.741812865$$

Solution Steps

Reduce the fraction \frac{8}{20} to lowest terms by extracting and canceling out 4.

$$\frac{2}{5}+\frac{7}{19}+\frac{3}{18}+\frac{6}{20}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Least common multiple of 5 and 19 is 95. Convert \frac{2}{5} and \frac{7}{19} to fractions with denominator 95.

$$\frac{38}{95}+\frac{35}{95}+\frac{3}{18}+\frac{6}{20}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Since \frac{38}{95} and \frac{35}{95} have the same denominator, add them by adding their numerators.

$$\frac{38+35}{95}+\frac{3}{18}+\frac{6}{20}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Add 38 and 35 to get 73.

$$\frac{73}{95}+\frac{3}{18}+\frac{6}{20}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{73}{95}+\frac{1}{6}+\frac{6}{20}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Least common multiple of 95 and 6 is 570. Convert \frac{73}{95} and \frac{1}{6} to fractions with denominator 570.

$$\frac{438}{570}+\frac{95}{570}+\frac{6}{20}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Since \frac{438}{570} and \frac{95}{570} have the same denominator, add them by adding their numerators.

$$\frac{438+95}{570}+\frac{6}{20}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Add 438 and 95 to get 533.

$$\frac{533}{570}+\frac{6}{20}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{533}{570}+\frac{3}{10}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Least common multiple of 570 and 10 is 570. Convert \frac{533}{570} and \frac{3}{10} to fractions with denominator 570.

$$\frac{533}{570}+\frac{171}{570}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Since \frac{533}{570} and \frac{171}{570} have the same denominator, add them by adding their numerators.

$$\frac{533+171}{570}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Add 533 and 171 to get 704.

$$\frac{704}{570}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Reduce the fraction \frac{704}{570} to lowest terms by extracting and canceling out 2.

$$\frac{352}{285}+\frac{3}{19}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Least common multiple of 285 and 19 is 285. Convert \frac{352}{285} and \frac{3}{19} to fractions with denominator 285.

$$\frac{352}{285}+\frac{45}{285}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Since \frac{352}{285} and \frac{45}{285} have the same denominator, add them by adding their numerators.

$$\frac{352+45}{285}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Add 352 and 45 to get 397.

$$\frac{397}{285}+\frac{7}{18}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Least common multiple of 285 and 18 is 1710. Convert \frac{397}{285} and \frac{7}{18} to fractions with denominator 1710.

$$\frac{2382}{1710}+\frac{665}{1710}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Since \frac{2382}{1710} and \frac{665}{1710} have the same denominator, add them by adding their numerators.

$$\frac{2382+665}{1710}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Add 2382 and 665 to get 3047.

$$\frac{3047}{1710}+\frac{3}{20}+\frac{8}{19}+\frac{7}{18}$$

Least common multiple of 1710 and 20 is 3420. Convert \frac{3047}{1710} and \frac{3}{20} to fractions with denominator 3420.

$$\frac{6094}{3420}+\frac{513}{3420}+\frac{8}{19}+\frac{7}{18}$$

Since \frac{6094}{3420} and \frac{513}{3420} have the same denominator, add them by adding their numerators.

$$\frac{6094+513}{3420}+\frac{8}{19}+\frac{7}{18}$$

Add 6094 and 513 to get 6607.

$$\frac{6607}{3420}+\frac{8}{19}+\frac{7}{18}$$

Least common multiple of 3420 and 19 is 3420. Convert \frac{6607}{3420} and \frac{8}{19} to fractions with denominator 3420.

$$\frac{6607}{3420}+\frac{1440}{3420}+\frac{7}{18}$$

Since \frac{6607}{3420} and \frac{1440}{3420} have the same denominator, add them by adding their numerators.

$$\frac{6607+1440}{3420}+\frac{7}{18}$$

Add 6607 and 1440 to get 8047.

$$\frac{8047}{3420}+\frac{7}{18}$$

Least common multiple of 3420 and 18 is 3420. Convert \frac{8047}{3420} and \frac{7}{18} to fractions with denominator 3420.

$$\frac{8047}{3420}+\frac{1330}{3420}$$

Since \frac{8047}{3420} and \frac{1330}{3420} have the same denominator, add them by adding their numerators.

$$\frac{8047+1330}{3420}$$

Add 8047 and 1330 to get 9377.

$$\frac{9377}{3420}$$

Factor

$$\frac{9377}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 \cdot 19} = 2\frac{2537}{3420} = 2.741812865497076$$