Solve 2+5/7+4/21-3/2-1+5/6

$$2 + \frac { 5 } { 7 } + \frac { 4 } { 21 } - \frac { 3 } { 2 } - 1 + \frac { 5 } { 6 }$$

Evaluate

$$\frac{26}{21}\approx 1.238095238$$

Solution Steps

Convert 2 to fraction \frac{14}{7}.

$$\frac{14}{7}+\frac{5}{7}+\frac{4}{21}-\frac{3}{2}-1+\frac{5}{6}$$

Since \frac{14}{7} and \frac{5}{7} have the same denominator, add them by adding their numerators.

$$\frac{14+5}{7}+\frac{4}{21}-\frac{3}{2}-1+\frac{5}{6}$$

Add 14 and 5 to get 19.

$$\frac{19}{7}+\frac{4}{21}-\frac{3}{2}-1+\frac{5}{6}$$

Least common multiple of 7 and 21 is 21. Convert \frac{19}{7} and \frac{4}{21} to fractions with denominator 21.

$$\frac{57}{21}+\frac{4}{21}-\frac{3}{2}-1+\frac{5}{6}$$

Since \frac{57}{21} and \frac{4}{21} have the same denominator, add them by adding their numerators.

$$\frac{57+4}{21}-\frac{3}{2}-1+\frac{5}{6}$$

Add 57 and 4 to get 61.

$$\frac{61}{21}-\frac{3}{2}-1+\frac{5}{6}$$

Least common multiple of 21 and 2 is 42. Convert \frac{61}{21} and \frac{3}{2} to fractions with denominator 42.

$$\frac{122}{42}-\frac{63}{42}-1+\frac{5}{6}$$

Since \frac{122}{42} and \frac{63}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{122-63}{42}-1+\frac{5}{6}$$

Subtract 63 from 122 to get 59.

$$\frac{59}{42}-1+\frac{5}{6}$$

Convert 1 to fraction \frac{42}{42}.

$$\frac{59}{42}-\frac{42}{42}+\frac{5}{6}$$

Since \frac{59}{42} and \frac{42}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59-42}{42}+\frac{5}{6}$$

Subtract 42 from 59 to get 17.

$$\frac{17}{42}+\frac{5}{6}$$

Least common multiple of 42 and 6 is 42. Convert \frac{17}{42} and \frac{5}{6} to fractions with denominator 42.

$$\frac{17}{42}+\frac{35}{42}$$

Since \frac{17}{42} and \frac{35}{42} have the same denominator, add them by adding their numerators.

$$\frac{17+35}{42}$$

Add 17 and 35 to get 52.

$$\frac{52}{42}$$

Reduce the fraction \frac{52}{42} to lowest terms by extracting and canceling out 2.

$$\frac{26}{21}$$

Factor

$$\frac{2 \cdot 13}{3 \cdot 7} = 1\frac{5}{21} = 1.2380952380952381$$