Solve (-7/2-1)-(11/14-3/2)-3/14

$$( - \frac { 7 } { 2 } - 1 ) - ( \frac { 11 } { 14 } - \frac { 3 } { 2 } ) - \frac { 3 } { 14 }$$

Evaluate

$$-4$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$-\frac{7}{2}-\frac{2}{2}-\left(\frac{11}{14}-\frac{3}{2}\right)-\frac{3}{14}$$

Since -\frac{7}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-2}{2}-\left(\frac{11}{14}-\frac{3}{2}\right)-\frac{3}{14}$$

Subtract 2 from -7 to get -9.

$$-\frac{9}{2}-\left(\frac{11}{14}-\frac{3}{2}\right)-\frac{3}{14}$$

Least common multiple of 14 and 2 is 14. Convert \frac{11}{14} and \frac{3}{2} to fractions with denominator 14.

$$-\frac{9}{2}-\left(\frac{11}{14}-\frac{21}{14}\right)-\frac{3}{14}$$

Since \frac{11}{14} and \frac{21}{14} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{9}{2}-\frac{11-21}{14}-\frac{3}{14}$$

Subtract 21 from 11 to get -10.

$$-\frac{9}{2}-\frac{-10}{14}-\frac{3}{14}$$

Reduce the fraction \frac{-10}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{9}{2}-\left(-\frac{5}{7}\right)-\frac{3}{14}$$

The opposite of -\frac{5}{7} is \frac{5}{7}.

$$-\frac{9}{2}+\frac{5}{7}-\frac{3}{14}$$

Least common multiple of 2 and 7 is 14. Convert -\frac{9}{2} and \frac{5}{7} to fractions with denominator 14.

$$-\frac{63}{14}+\frac{10}{14}-\frac{3}{14}$$

Since -\frac{63}{14} and \frac{10}{14} have the same denominator, add them by adding their numerators.

$$\frac{-63+10}{14}-\frac{3}{14}$$

Add -63 and 10 to get -53.

$$-\frac{53}{14}-\frac{3}{14}$$

Since -\frac{53}{14} and \frac{3}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-53-3}{14}$$

Subtract 3 from -53 to get -56.

$$\frac{-56}{14}$$

Divide -56 by 14 to get -4.

$$-4$$

Factor

$$-4$$