Solve (-122/3)div14-(-81/3)div(-14)+101/3div14

$$( - 12 \frac { 2 } { 3 } ) \div 14 - ( - 8 \frac { 1 } { 3 } ) \div ( - 14 ) + 10 \frac { 1 } { 3 } \div 14$$

Evaluate

$$-\frac{16}{21}\approx -0.761904762$$

Solution Steps

Multiply 12 and 3 to get 36.

$$\frac{-\frac{36+2}{3}}{14}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Add 36 and 2 to get 38.

$$\frac{-\frac{38}{3}}{14}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Express \frac{-\frac{38}{3}}{14} as a single fraction.

$$\frac{-38}{3\times 14}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Multiply 3 and 14 to get 42.

$$\frac{-38}{42}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Reduce the fraction \frac{-38}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{19}{21}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Multiply 8 and 3 to get 24.

$$-\frac{19}{21}-\frac{-\frac{24+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Add 24 and 1 to get 25.

$$-\frac{19}{21}-\frac{-\frac{25}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Express \frac{-\frac{25}{3}}{-14} as a single fraction.

$$-\frac{19}{21}-\frac{-25}{3\left(-14\right)}+\frac{\frac{10\times 3+1}{3}}{14}$$

Multiply 3 and -14 to get -42.

$$-\frac{19}{21}-\frac{-25}{-42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Fraction \frac{-25}{-42} can be simplified to \frac{25}{42} by removing the negative sign from both the numerator and the denominator.

$$-\frac{19}{21}-\frac{25}{42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Least common multiple of 21 and 42 is 42. Convert -\frac{19}{21} and \frac{25}{42} to fractions with denominator 42.

$$-\frac{38}{42}-\frac{25}{42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Since -\frac{38}{42} and \frac{25}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-38-25}{42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Subtract 25 from -38 to get -63.

$$\frac{-63}{42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Reduce the fraction \frac{-63}{42} to lowest terms by extracting and canceling out 21.

$$-\frac{3}{2}+\frac{\frac{10\times 3+1}{3}}{14}$$

Express \frac{\frac{10\times 3+1}{3}}{14} as a single fraction.

$$-\frac{3}{2}+\frac{10\times 3+1}{3\times 14}$$

Multiply 10 and 3 to get 30.

$$-\frac{3}{2}+\frac{30+1}{3\times 14}$$

Add 30 and 1 to get 31.

$$-\frac{3}{2}+\frac{31}{3\times 14}$$

Multiply 3 and 14 to get 42.

$$-\frac{3}{2}+\frac{31}{42}$$

Least common multiple of 2 and 42 is 42. Convert -\frac{3}{2} and \frac{31}{42} to fractions with denominator 42.

$$-\frac{63}{42}+\frac{31}{42}$$

Since -\frac{63}{42} and \frac{31}{42} have the same denominator, add them by adding their numerators.

$$\frac{-63+31}{42}$$

Add -63 and 31 to get -32.

$$\frac{-32}{42}$$

Reduce the fraction \frac{-32}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{16}{21}$$

Factor

$$-\frac{16}{21} = -0.7619047619047619$$