Solve 1/2+(4/5+4/7)-8/3

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

Evaluate

$$-\frac{167}{210}\approx -0.795238095$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{4}{5} to fractions with denominator 10.

$$\frac{5}{10}+\frac{8}{10}+\frac{4}{7}-\frac{8}{3}$$

Since \frac{5}{10} and \frac{8}{10} have the same denominator, add them by adding their numerators.

$$\frac{5+8}{10}+\frac{4}{7}-\frac{8}{3}$$

Add 5 and 8 to get 13.

$$\frac{13}{10}+\frac{4}{7}-\frac{8}{3}$$

Least common multiple of 10 and 7 is 70. Convert \frac{13}{10} and \frac{4}{7} to fractions with denominator 70.

$$\frac{91}{70}+\frac{40}{70}-\frac{8}{3}$$

Since \frac{91}{70} and \frac{40}{70} have the same denominator, add them by adding their numerators.

$$\frac{91+40}{70}-\frac{8}{3}$$

Add 91 and 40 to get 131.

$$\frac{131}{70}-\frac{8}{3}$$

Least common multiple of 70 and 3 is 210. Convert \frac{131}{70} and \frac{8}{3} to fractions with denominator 210.

$$\frac{393}{210}-\frac{560}{210}$$

Since \frac{393}{210} and \frac{560}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{393-560}{210}$$

Subtract 560 from 393 to get -167.

$$-\frac{167}{210}$$

Factor

$$-\frac{167}{210} = -0.7952380952380952$$