Solve (3/7-1/21-11/3)*(4+1/2)

$$( \frac { 3 } { 7 } - \frac { 1 } { 21 } - \frac { 11 } { 3 } ) \cdot ( 4 + \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{207}{14}\approx -14.785714286$$

Solution Steps

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

$$\left(\frac{9}{21}-\frac{1}{21}-\frac{11}{3}\right)\left(4+\frac{1}{2}\right)$$

Since \frac{9}{21} and \frac{1}{21} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{9-1}{21}-\frac{11}{3}\right)\left(4+\frac{1}{2}\right)$$

Subtract 1 from 9 to get 8.

$$\left(\frac{8}{21}-\frac{11}{3}\right)\left(4+\frac{1}{2}\right)$$

Least common multiple of 21 and 3 is 21. Convert \frac{8}{21} and \frac{11}{3} to fractions with denominator 21.

$$\left(\frac{8}{21}-\frac{77}{21}\right)\left(4+\frac{1}{2}\right)$$

Since \frac{8}{21} and \frac{77}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-77}{21}\left(4+\frac{1}{2}\right)$$

Subtract 77 from 8 to get -69.

$$\frac{-69}{21}\left(4+\frac{1}{2}\right)$$

Reduce the fraction \frac{-69}{21} to lowest terms by extracting and canceling out 3.

$$-\frac{23}{7}\left(4+\frac{1}{2}\right)$$

Convert 4 to fraction \frac{8}{2}.

$$-\frac{23}{7}\left(\frac{8}{2}+\frac{1}{2}\right)$$

Since \frac{8}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$-\frac{23}{7}\times \frac{8+1}{2}$$

Add 8 and 1 to get 9.

$$-\frac{23}{7}\times \frac{9}{2}$$

Multiply -\frac{23}{7} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-23\times 9}{7\times 2}$$

Do the multiplications in the fraction \frac{-23\times 9}{7\times 2}.

$$\frac{-207}{14}$$

Fraction \frac{-207}{14} can be rewritten as -\frac{207}{14} by extracting the negative sign.

$$-\frac{207}{14}$$

Factor

$$-\frac{207}{14} = -14\frac{11}{14} = -14.785714285714286$$