Solve (-2/5+3/10+1/15)-2/7

$$( \frac { - 2 } { 5 } + \frac { 3 } { 10 } + \frac { 1 } { 15 } ) - \frac { 2 } { 7 }$$

Evaluate

$$-\frac{67}{210}\approx -0.319047619$$

Solution Steps

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$-\frac{2}{5}+\frac{3}{10}+\frac{1}{15}-\frac{2}{7}$$

Least common multiple of 5 and 10 is 10. Convert -\frac{2}{5} and \frac{3}{10} to fractions with denominator 10.

$$-\frac{4}{10}+\frac{3}{10}+\frac{1}{15}-\frac{2}{7}$$

Since -\frac{4}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{-4+3}{10}+\frac{1}{15}-\frac{2}{7}$$

Add -4 and 3 to get -1.

$$-\frac{1}{10}+\frac{1}{15}-\frac{2}{7}$$

Least common multiple of 10 and 15 is 30. Convert -\frac{1}{10} and \frac{1}{15} to fractions with denominator 30.

$$-\frac{3}{30}+\frac{2}{30}-\frac{2}{7}$$

Since -\frac{3}{30} and \frac{2}{30} have the same denominator, add them by adding their numerators.

$$\frac{-3+2}{30}-\frac{2}{7}$$

Add -3 and 2 to get -1.

$$-\frac{1}{30}-\frac{2}{7}$$

Least common multiple of 30 and 7 is 210. Convert -\frac{1}{30} and \frac{2}{7} to fractions with denominator 210.

$$-\frac{7}{210}-\frac{60}{210}$$

Since -\frac{7}{210} and \frac{60}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-60}{210}$$

Subtract 60 from -7 to get -67.

$$-\frac{67}{210}$$

Factor

$$-\frac{67}{210} = -0.319047619047619$$