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

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

Evaluate

$$\frac{29}{10}=2.9$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{5}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{25}{20}+\frac{12}{20}-\frac{1}{2}+\frac{2}{3}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Since \frac{25}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$\frac{25+12}{20}-\frac{1}{2}+\frac{2}{3}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Add 25 and 12 to get 37.

$$\frac{37}{20}-\frac{1}{2}+\frac{2}{3}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Least common multiple of 20 and 2 is 20. Convert \frac{37}{20} and \frac{1}{2} to fractions with denominator 20.

$$\frac{37}{20}-\frac{10}{20}+\frac{2}{3}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Since \frac{37}{20} and \frac{10}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{37-10}{20}+\frac{2}{3}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Subtract 10 from 37 to get 27.

$$\frac{27}{20}+\frac{2}{3}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Least common multiple of 20 and 3 is 60. Convert \frac{27}{20} and \frac{2}{3} to fractions with denominator 60.

$$\frac{81}{60}+\frac{40}{60}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Since \frac{81}{60} and \frac{40}{60} have the same denominator, add them by adding their numerators.

$$\frac{81+40}{60}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Add 81 and 40 to get 121.

$$\frac{121}{60}-\frac{1}{4}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Least common multiple of 60 and 4 is 60. Convert \frac{121}{60} and \frac{1}{4} to fractions with denominator 60.

$$\frac{121}{60}-\frac{15}{60}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Since \frac{121}{60} and \frac{15}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121-15}{60}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Subtract 15 from 121 to get 106.

$$\frac{106}{60}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Reduce the fraction \frac{106}{60} to lowest terms by extracting and canceling out 2.

$$\frac{53}{30}+\frac{4}{5}-\frac{1}{3}+\frac{2}{3}$$

Least common multiple of 30 and 5 is 30. Convert \frac{53}{30} and \frac{4}{5} to fractions with denominator 30.

$$\frac{53}{30}+\frac{24}{30}-\frac{1}{3}+\frac{2}{3}$$

Since \frac{53}{30} and \frac{24}{30} have the same denominator, add them by adding their numerators.

$$\frac{53+24}{30}-\frac{1}{3}+\frac{2}{3}$$

Add 53 and 24 to get 77.

$$\frac{77}{30}-\frac{1}{3}+\frac{2}{3}$$

Least common multiple of 30 and 3 is 30. Convert \frac{77}{30} and \frac{1}{3} to fractions with denominator 30.

$$\frac{77}{30}-\frac{10}{30}+\frac{2}{3}$$

Since \frac{77}{30} and \frac{10}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{77-10}{30}+\frac{2}{3}$$

Subtract 10 from 77 to get 67.

$$\frac{67}{30}+\frac{2}{3}$$

Least common multiple of 30 and 3 is 30. Convert \frac{67}{30} and \frac{2}{3} to fractions with denominator 30.

$$\frac{67}{30}+\frac{20}{30}$$

Since \frac{67}{30} and \frac{20}{30} have the same denominator, add them by adding their numerators.

$$\frac{67+20}{30}$$

Add 67 and 20 to get 87.

$$\frac{87}{30}$$

Reduce the fraction \frac{87}{30} to lowest terms by extracting and canceling out 3.

$$\frac{29}{10}$$

Factor

$$\frac{29}{2 \cdot 5} = 2\frac{9}{10} = 2.9$$