Solve (1/2-11/6)*(-11/2)=

$$( \frac { 1 } { 2 } - 1 \frac { 1 } { 6 } ) \times ( - 1 \frac { 1 } { 2 } ) =$$

Evaluate

$$1$$

Solution Steps

Multiply 1 and 6 to get 6.

$$\left(\frac{1}{2}-\frac{6+1}{6}\right)\left(-\frac{1\times 2+1}{2}\right)$$

Add 6 and 1 to get 7.

$$\left(\frac{1}{2}-\frac{7}{6}\right)\left(-\frac{1\times 2+1}{2}\right)$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{7}{6} to fractions with denominator 6.

$$\left(\frac{3}{6}-\frac{7}{6}\right)\left(-\frac{1\times 2+1}{2}\right)$$

Since \frac{3}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-7}{6}\left(-\frac{1\times 2+1}{2}\right)$$

Subtract 7 from 3 to get -4.

$$\frac{-4}{6}\left(-\frac{1\times 2+1}{2}\right)$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{3}\left(-\frac{2+1}{2}\right)$$

Add 2 and 1 to get 3.

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

Multiply -\frac{2}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{-2\left(-3\right)}{3\times 2}.

$$\frac{6}{6}$$

Divide 6 by 6 to get 1.

$$1$$

Factor

$$1$$