Solve -4/8+-30/28-30/21--42/-21

$$- \frac { 4 } { 8 } + \frac { - 30 } { 28 } - \frac { 30 } { 21 } - \frac { - 42 } { - 21 }$$

Evaluate

$$-5$$

Solution Steps

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{2}+\frac{-30}{28}-\frac{30}{21}-\frac{-42}{-21}$$

Reduce the fraction \frac{-30}{28} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}-\frac{15}{14}-\frac{30}{21}-\frac{-42}{-21}$$

Least common multiple of 2 and 14 is 14. Convert -\frac{1}{2} and \frac{15}{14} to fractions with denominator 14.

$$-\frac{7}{14}-\frac{15}{14}-\frac{30}{21}-\frac{-42}{-21}$$

Since -\frac{7}{14} and \frac{15}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-15}{14}-\frac{30}{21}-\frac{-42}{-21}$$

Subtract 15 from -7 to get -22.

$$\frac{-22}{14}-\frac{30}{21}-\frac{-42}{-21}$$

Reduce the fraction \frac{-22}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{7}-\frac{30}{21}-\frac{-42}{-21}$$

Reduce the fraction \frac{30}{21} to lowest terms by extracting and canceling out 3.

$$-\frac{11}{7}-\frac{10}{7}-\frac{-42}{-21}$$

Since -\frac{11}{7} and \frac{10}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-10}{7}-\frac{-42}{-21}$$

Subtract 10 from -11 to get -21.

$$\frac{-21}{7}-\frac{-42}{-21}$$

Divide -21 by 7 to get -3.

$$-3-\frac{-42}{-21}$$

Divide -42 by -21 to get 2.

$$-3-2$$

Subtract 2 from -3 to get -5.

$$-5$$

Factor

$$-5$$