Solve (2)(-8/9)*(21/4-41/2-11/8)

$$( 2 ) ( - \frac { 8 } { 9 } ) \times ( 2 \frac { 1 } { 4 } - 4 \frac { 1 } { 2 } - 1 \frac { 1 } { 8 } )$$

Evaluate

$$6$$

Solution Steps

Express 2\left(-\frac{8}{9}\right) as a single fraction.

$$\frac{2\left(-8\right)}{9}\left(\frac{2\times 4+1}{4}-\frac{4\times 2+1}{2}-\frac{1\times 8+1}{8}\right)$$

Multiply 2 and -8 to get -16.

$$\frac{-16}{9}\left(\frac{2\times 4+1}{4}-\frac{4\times 2+1}{2}-\frac{1\times 8+1}{8}\right)$$

Fraction \frac{-16}{9} can be rewritten as -\frac{16}{9} by extracting the negative sign.

$$-\frac{16}{9}\left(\frac{2\times 4+1}{4}-\frac{4\times 2+1}{2}-\frac{8+1}{8}\right)$$

Multiply 2 and 4 to get 8.

$$-\frac{16}{9}\left(\frac{8+1}{4}-\frac{4\times 2+1}{2}-\frac{8+1}{8}\right)$$

Add 8 and 1 to get 9.

$$-\frac{16}{9}\left(\frac{9}{4}-\frac{4\times 2+1}{2}-\frac{8+1}{8}\right)$$

Multiply 4 and 2 to get 8.

$$-\frac{16}{9}\left(\frac{9}{4}-\frac{8+1}{2}-\frac{8+1}{8}\right)$$

Add 8 and 1 to get 9.

$$-\frac{16}{9}\left(\frac{9}{4}-\frac{9}{2}-\frac{8+1}{8}\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{9}{2} to fractions with denominator 4.

$$-\frac{16}{9}\left(\frac{9}{4}-\frac{18}{4}-\frac{8+1}{8}\right)$$

Since \frac{9}{4} and \frac{18}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{16}{9}\left(\frac{9-18}{4}-\frac{8+1}{8}\right)$$

Subtract 18 from 9 to get -9.

$$-\frac{16}{9}\left(-\frac{9}{4}-\frac{8+1}{8}\right)$$

Add 8 and 1 to get 9.

$$-\frac{16}{9}\left(-\frac{9}{4}-\frac{9}{8}\right)$$

Least common multiple of 4 and 8 is 8. Convert -\frac{9}{4} and \frac{9}{8} to fractions with denominator 8.

$$-\frac{16}{9}\left(-\frac{18}{8}-\frac{9}{8}\right)$$

Since -\frac{18}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{16}{9}\times \frac{-18-9}{8}$$

Subtract 9 from -18 to get -27.

$$-\frac{16}{9}\left(-\frac{27}{8}\right)$$

Multiply -\frac{16}{9} times -\frac{27}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16\left(-27\right)}{9\times 8}$$

Do the multiplications in the fraction \frac{-16\left(-27\right)}{9\times 8}.

$$\frac{432}{72}$$

Divide 432 by 72 to get 6.

$$6$$

Factor

$$2\times 3$$