Solve (-3/7-2/3)-(-4/3+3/21)

$$( - \frac { 3 } { 7 } - \frac { 2 } { 3 } ) - ( - \frac { 4 } { 3 } + \frac { 3 } { 21 } )$$

Evaluate

$$\frac{2}{21}\approx 0.095238095$$

Solution Steps

Least common multiple of 7 and 3 is 21. Convert -\frac{3}{7} and \frac{2}{3} to fractions with denominator 21.

$$-\frac{9}{21}-\frac{14}{21}-\left(-\frac{4}{3}+\frac{3}{21}\right)$$

Since -\frac{9}{21} and \frac{14}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-14}{21}-\left(-\frac{4}{3}+\frac{3}{21}\right)$$

Subtract 14 from -9 to get -23.

$$-\frac{23}{21}-\left(-\frac{4}{3}+\frac{3}{21}\right)$$

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

$$-\frac{23}{21}-\left(-\frac{4}{3}+\frac{1}{7}\right)$$

Least common multiple of 3 and 7 is 21. Convert -\frac{4}{3} and \frac{1}{7} to fractions with denominator 21.

$$-\frac{23}{21}-\left(-\frac{28}{21}+\frac{3}{21}\right)$$

Since -\frac{28}{21} and \frac{3}{21} have the same denominator, add them by adding their numerators.

$$-\frac{23}{21}-\frac{-28+3}{21}$$

Add -28 and 3 to get -25.

$$-\frac{23}{21}-\left(-\frac{25}{21}\right)$$

The opposite of -\frac{25}{21} is \frac{25}{21}.

$$-\frac{23}{21}+\frac{25}{21}$$

Since -\frac{23}{21} and \frac{25}{21} have the same denominator, add them by adding their numerators.

$$\frac{-23+25}{21}$$

Add -23 and 25 to get 2.

$$\frac{2}{21}$$

Factor

$$\frac{2}{3 \cdot 7} = 0.09523809523809523$$