Solve (-11/2+21/3-13/14)*(-42)

$$( - 1 \frac { 1 } { 2 } + 2 \frac { 1 } { 3 } - \frac { 13 } { 14 } ) \times ( - 42 )$$

Evaluate

$$4$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\left(-\frac{2+1}{2}+\frac{2\times 3+1}{3}-\frac{13}{14}\right)\left(-42\right)$$

Add 2 and 1 to get 3.

$$\left(-\frac{3}{2}+\frac{2\times 3+1}{3}-\frac{13}{14}\right)\left(-42\right)$$

Multiply 2 and 3 to get 6.

$$\left(-\frac{3}{2}+\frac{6+1}{3}-\frac{13}{14}\right)\left(-42\right)$$

Add 6 and 1 to get 7.

$$\left(-\frac{3}{2}+\frac{7}{3}-\frac{13}{14}\right)\left(-42\right)$$

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{7}{3} to fractions with denominator 6.

$$\left(-\frac{9}{6}+\frac{14}{6}-\frac{13}{14}\right)\left(-42\right)$$

Since -\frac{9}{6} and \frac{14}{6} have the same denominator, add them by adding their numerators.

$$\left(\frac{-9+14}{6}-\frac{13}{14}\right)\left(-42\right)$$

Add -9 and 14 to get 5.

$$\left(\frac{5}{6}-\frac{13}{14}\right)\left(-42\right)$$

Least common multiple of 6 and 14 is 42. Convert \frac{5}{6} and \frac{13}{14} to fractions with denominator 42.

$$\left(\frac{35}{42}-\frac{39}{42}\right)\left(-42\right)$$

Since \frac{35}{42} and \frac{39}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-39}{42}\left(-42\right)$$

Subtract 39 from 35 to get -4.

$$\frac{-4}{42}\left(-42\right)$$

Reduce the fraction \frac{-4}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{21}\left(-42\right)$$

Express -\frac{2}{21}\left(-42\right) as a single fraction.

$$\frac{-2\left(-42\right)}{21}$$

Multiply -2 and -42 to get 84.

$$\frac{84}{21}$$

Divide 84 by 21 to get 4.

$$4$$

Factor

$$2^{2}$$