Solve 13/3-3/4+4/5+2/3+frac{5}{6}-frac{1}{3}+frac{1}{4}+frac{4}{5}-frac{3}{6}

$$\frac{ 13 }{ 3 } - \frac{ 3 }{ 4 } + \frac{ 4 }{ 5 } + \frac{ 2 }{ 3 } + \frac{ 5 }{ 6 } - \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 } + \frac{ 4 }{ 5 } - \frac{ 3 }{ 6 }$$

Evaluate

$$\frac{61}{10}=6.1$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{13}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{52}{12}-\frac{9}{12}+\frac{4}{5}+\frac{2}{3}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Since \frac{52}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-9}{12}+\frac{4}{5}+\frac{2}{3}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Subtract 9 from 52 to get 43.

$$\frac{43}{12}+\frac{4}{5}+\frac{2}{3}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Least common multiple of 12 and 5 is 60. Convert \frac{43}{12} and \frac{4}{5} to fractions with denominator 60.

$$\frac{215}{60}+\frac{48}{60}+\frac{2}{3}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Since \frac{215}{60} and \frac{48}{60} have the same denominator, add them by adding their numerators.

$$\frac{215+48}{60}+\frac{2}{3}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Add 215 and 48 to get 263.

$$\frac{263}{60}+\frac{2}{3}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Least common multiple of 60 and 3 is 60. Convert \frac{263}{60} and \frac{2}{3} to fractions with denominator 60.

$$\frac{263}{60}+\frac{40}{60}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Since \frac{263}{60} and \frac{40}{60} have the same denominator, add them by adding their numerators.

$$\frac{263+40}{60}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Add 263 and 40 to get 303.

$$\frac{303}{60}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Reduce the fraction \frac{303}{60} to lowest terms by extracting and canceling out 3.

$$\frac{101}{20}+\frac{5}{6}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Least common multiple of 20 and 6 is 60. Convert \frac{101}{20} and \frac{5}{6} to fractions with denominator 60.

$$\frac{303}{60}+\frac{50}{60}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Since \frac{303}{60} and \frac{50}{60} have the same denominator, add them by adding their numerators.

$$\frac{303+50}{60}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Add 303 and 50 to get 353.

$$\frac{353}{60}-\frac{1}{3}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Least common multiple of 60 and 3 is 60. Convert \frac{353}{60} and \frac{1}{3} to fractions with denominator 60.

$$\frac{353}{60}-\frac{20}{60}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Since \frac{353}{60} and \frac{20}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{353-20}{60}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Subtract 20 from 353 to get 333.

$$\frac{333}{60}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Reduce the fraction \frac{333}{60} to lowest terms by extracting and canceling out 3.

$$\frac{111}{20}+\frac{1}{4}+\frac{4}{5}-\frac{3}{6}$$

Least common multiple of 20 and 4 is 20. Convert \frac{111}{20} and \frac{1}{4} to fractions with denominator 20.

$$\frac{111}{20}+\frac{5}{20}+\frac{4}{5}-\frac{3}{6}$$

Since \frac{111}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{111+5}{20}+\frac{4}{5}-\frac{3}{6}$$

Add 111 and 5 to get 116.

$$\frac{116}{20}+\frac{4}{5}-\frac{3}{6}$$

Reduce the fraction \frac{116}{20} to lowest terms by extracting and canceling out 4.

$$\frac{29}{5}+\frac{4}{5}-\frac{3}{6}$$

Since \frac{29}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$\frac{29+4}{5}-\frac{3}{6}$$

Add 29 and 4 to get 33.

$$\frac{33}{5}-\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{33}{5}-\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{33}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{66}{10}-\frac{5}{10}$$

Since \frac{66}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{66-5}{10}$$

Subtract 5 from 66 to get 61.

$$\frac{61}{10}$$

Factor

$$\frac{61}{2 \cdot 5} = 6\frac{1}{10} = 6.1$$