Solve 2/3(9/4d(-21/3)+7/4d)+frac{3}{5}*(-2frac{2}{3}d+frac{5}{12}d)

$$\frac { 2 } { 3 } ( \frac { 9 } { 4 } d ( - 2 \frac { 1 } { 3 } ) + \frac { 7 } { 4 } d ) + \frac { 3 } { 5 } \cdot ( - 2 \frac { 2 } { 3 } d + \frac { 5 } { 12 } d )$$

Evaluate

$$-\frac{221d}{60}$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{2}{3}\left(\frac{9}{4}d\left(-\frac{6+1}{3}\right)+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Add 6 and 1 to get 7.

$$\frac{2}{3}\left(\frac{9}{4}d\left(-\frac{7}{3}\right)+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Multiply \frac{9}{4} times -\frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}\left(\frac{9\left(-7\right)}{4\times 3}d+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Do the multiplications in the fraction \frac{9\left(-7\right)}{4\times 3}.

$$\frac{2}{3}\left(\frac{-63}{12}d+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Reduce the fraction \frac{-63}{12} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}\left(-\frac{21}{4}d+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Combine -\frac{21}{4}d and \frac{7}{4}d to get -\frac{7}{2}d.

$$\frac{2}{3}\left(-\frac{7}{2}\right)d+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Multiply \frac{2}{3} times -\frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-7\right)}{3\times 2}d+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{-7}{3}d+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$-\frac{7}{3}d+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Multiply 2 and 3 to get 6.

$$-\frac{7}{3}d+\frac{3}{5}\left(\left(-\frac{6+2}{3}\right)d+\frac{5}{12}d\right)$$

Add 6 and 2 to get 8.

$$-\frac{7}{3}d+\frac{3}{5}\left(-\frac{8}{3}d+\frac{5}{12}d\right)$$

Combine -\frac{8}{3}d and \frac{5}{12}d to get -\frac{9}{4}d.

$$-\frac{7}{3}d+\frac{3}{5}\left(-\frac{9}{4}\right)d$$

Multiply \frac{3}{5} times -\frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{7}{3}d+\frac{3\left(-9\right)}{5\times 4}d$$

Do the multiplications in the fraction \frac{3\left(-9\right)}{5\times 4}.

$$-\frac{7}{3}d+\frac{-27}{20}d$$

Fraction \frac{-27}{20} can be rewritten as -\frac{27}{20} by extracting the negative sign.

$$-\frac{7}{3}d-\frac{27}{20}d$$

Combine -\frac{7}{3}d and -\frac{27}{20}d to get -\frac{221}{60}d.

$$-\frac{221}{60}d$$

Expand

$$-\frac{221d}{60}$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{2}{3}\left(\frac{9}{4}d\left(-\frac{6+1}{3}\right)+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Add 6 and 1 to get 7.

$$\frac{2}{3}\left(\frac{9}{4}d\left(-\frac{7}{3}\right)+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Multiply \frac{9}{4} times -\frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}\left(\frac{9\left(-7\right)}{4\times 3}d+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Do the multiplications in the fraction \frac{9\left(-7\right)}{4\times 3}.

$$\frac{2}{3}\left(\frac{-63}{12}d+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Reduce the fraction \frac{-63}{12} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}\left(-\frac{21}{4}d+\frac{7}{4}d\right)+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Combine -\frac{21}{4}d and \frac{7}{4}d to get -\frac{7}{2}d.

$$\frac{2}{3}\left(-\frac{7}{2}\right)d+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Multiply \frac{2}{3} times -\frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-7\right)}{3\times 2}d+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{-7}{3}d+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$-\frac{7}{3}d+\frac{3}{5}\left(\left(-\frac{2\times 3+2}{3}\right)d+\frac{5}{12}d\right)$$

Multiply 2 and 3 to get 6.

$$-\frac{7}{3}d+\frac{3}{5}\left(\left(-\frac{6+2}{3}\right)d+\frac{5}{12}d\right)$$

Add 6 and 2 to get 8.

$$-\frac{7}{3}d+\frac{3}{5}\left(-\frac{8}{3}d+\frac{5}{12}d\right)$$

Combine -\frac{8}{3}d and \frac{5}{12}d to get -\frac{9}{4}d.

$$-\frac{7}{3}d+\frac{3}{5}\left(-\frac{9}{4}\right)d$$

Multiply \frac{3}{5} times -\frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{7}{3}d+\frac{3\left(-9\right)}{5\times 4}d$$

Do the multiplications in the fraction \frac{3\left(-9\right)}{5\times 4}.

$$-\frac{7}{3}d+\frac{-27}{20}d$$

Fraction \frac{-27}{20} can be rewritten as -\frac{27}{20} by extracting the negative sign.

$$-\frac{7}{3}d-\frac{27}{20}d$$

Combine -\frac{7}{3}d and -\frac{27}{20}d to get -\frac{221}{60}d.

$$-\frac{221}{60}d$$