Solve 1/2+2/3-3/5+1/7-frac{2}{5}-frac{8}{9}-frac{7}{4}

$$\frac { 1 } { 2 } + \frac { 2 } { 3 } - \frac { 3 } { 5 } + \frac { 1 } { 7 } - \frac { 2 } { 5 } - \frac { 8 } { 9 } - \frac { 7 } { 4 }$$

Evaluate

$$-\frac{587}{252}\approx -2.329365079$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{4}{6}-\frac{3}{5}+\frac{1}{7}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{6}-\frac{3}{5}+\frac{1}{7}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Add 3 and 4 to get 7.

$$\frac{7}{6}-\frac{3}{5}+\frac{1}{7}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Least common multiple of 6 and 5 is 30. Convert \frac{7}{6} and \frac{3}{5} to fractions with denominator 30.

$$\frac{35}{30}-\frac{18}{30}+\frac{1}{7}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Since \frac{35}{30} and \frac{18}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-18}{30}+\frac{1}{7}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Subtract 18 from 35 to get 17.

$$\frac{17}{30}+\frac{1}{7}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Least common multiple of 30 and 7 is 210. Convert \frac{17}{30} and \frac{1}{7} to fractions with denominator 210.

$$\frac{119}{210}+\frac{30}{210}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Since \frac{119}{210} and \frac{30}{210} have the same denominator, add them by adding their numerators.

$$\frac{119+30}{210}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Add 119 and 30 to get 149.

$$\frac{149}{210}-\frac{2}{5}-\frac{8}{9}-\frac{7}{4}$$

Least common multiple of 210 and 5 is 210. Convert \frac{149}{210} and \frac{2}{5} to fractions with denominator 210.

$$\frac{149}{210}-\frac{84}{210}-\frac{8}{9}-\frac{7}{4}$$

Since \frac{149}{210} and \frac{84}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{149-84}{210}-\frac{8}{9}-\frac{7}{4}$$

Subtract 84 from 149 to get 65.

$$\frac{65}{210}-\frac{8}{9}-\frac{7}{4}$$

Reduce the fraction \frac{65}{210} to lowest terms by extracting and canceling out 5.

$$\frac{13}{42}-\frac{8}{9}-\frac{7}{4}$$

Least common multiple of 42 and 9 is 126. Convert \frac{13}{42} and \frac{8}{9} to fractions with denominator 126.

$$\frac{39}{126}-\frac{112}{126}-\frac{7}{4}$$

Since \frac{39}{126} and \frac{112}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39-112}{126}-\frac{7}{4}$$

Subtract 112 from 39 to get -73.

$$-\frac{73}{126}-\frac{7}{4}$$

Least common multiple of 126 and 4 is 252. Convert -\frac{73}{126} and \frac{7}{4} to fractions with denominator 252.

$$-\frac{146}{252}-\frac{441}{252}$$

Since -\frac{146}{252} and \frac{441}{252} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-146-441}{252}$$

Subtract 441 from -146 to get -587.

$$-\frac{587}{252}$$

Factor

$$-\frac{587}{252} = -2\frac{83}{252} = -2.3293650793650795$$