Solve -1/7+5/2-3/14+4/21-frac{10}{3}

$$- \frac { 1 } { 7 } + \frac { 5 } { 2 } - \frac { 3 } { 14 } + \frac { 4 } { 21 } - \frac { 10 } { 3 }$$

Evaluate

$$-1$$

Solution Steps

Least common multiple of 7 and 2 is 14. Convert -\frac{1}{7} and \frac{5}{2} to fractions with denominator 14.

$$-\frac{2}{14}+\frac{35}{14}-\frac{3}{14}+\frac{4}{21}-\frac{10}{3}$$

Since -\frac{2}{14} and \frac{35}{14} have the same denominator, add them by adding their numerators.

$$\frac{-2+35}{14}-\frac{3}{14}+\frac{4}{21}-\frac{10}{3}$$

Add -2 and 35 to get 33.

$$\frac{33}{14}-\frac{3}{14}+\frac{4}{21}-\frac{10}{3}$$

Since \frac{33}{14} and \frac{3}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-3}{14}+\frac{4}{21}-\frac{10}{3}$$

Subtract 3 from 33 to get 30.

$$\frac{30}{14}+\frac{4}{21}-\frac{10}{3}$$

Reduce the fraction \frac{30}{14} to lowest terms by extracting and canceling out 2.

$$\frac{15}{7}+\frac{4}{21}-\frac{10}{3}$$

Least common multiple of 7 and 21 is 21. Convert \frac{15}{7} and \frac{4}{21} to fractions with denominator 21.

$$\frac{45}{21}+\frac{4}{21}-\frac{10}{3}$$

Since \frac{45}{21} and \frac{4}{21} have the same denominator, add them by adding their numerators.

$$\frac{45+4}{21}-\frac{10}{3}$$

Add 45 and 4 to get 49.

$$\frac{49}{21}-\frac{10}{3}$$

Reduce the fraction \frac{49}{21} to lowest terms by extracting and canceling out 7.

$$\frac{7}{3}-\frac{10}{3}$$

Since \frac{7}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-10}{3}$$

Subtract 10 from 7 to get -3.

$$\frac{-3}{3}$$

Divide -3 by 3 to get -1.

$$-1$$

Factor

$$-1$$