Solve [(-1/2)+3/7]+(-4/3)

$$[ ( \frac { - 1 } { 2 } ) + \frac { 3 } { 7 } ] + ( \frac { - 4 } { 3 } )$$

Evaluate

$$-\frac{59}{42}\approx -1.404761905$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

Least common multiple of 2 and 7 is 14. Convert -\frac{1}{2} and \frac{3}{7} to fractions with denominator 14.

$$-\frac{7}{14}+\frac{6}{14}+\frac{-4}{3}$$

Since -\frac{7}{14} and \frac{6}{14} have the same denominator, add them by adding their numerators.

$$\frac{-7+6}{14}+\frac{-4}{3}$$

Add -7 and 6 to get -1.

$$-\frac{1}{14}+\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$-\frac{1}{14}-\frac{4}{3}$$

Least common multiple of 14 and 3 is 42. Convert -\frac{1}{14} and \frac{4}{3} to fractions with denominator 42.

$$-\frac{3}{42}-\frac{56}{42}$$

Since -\frac{3}{42} and \frac{56}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-56}{42}$$

Subtract 56 from -3 to get -59.

$$-\frac{59}{42}$$

Factor

$$-\frac{59}{42} = -1\frac{17}{42} = -1.4047619047619047$$