Solve (41/x)(-2/3)(a/12)(-21/3)

$$( 4 \frac { 1 } { x } ) ( - \frac { 2 } { 3 } ) ( \frac { a } { 12 } ) ( - 2 \frac { 1 } { 3 } )$$

Evaluate

$$\frac{14a}{27x}$$

Solution Steps

Express 4\left(-\frac{2}{3}\right) as a single fraction.

$$\frac{4\left(-2\right)}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{2\times 3+1}{3}\right)$$

Multiply 4 and -2 to get -8.

$$\frac{-8}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{2\times 3+1}{3}\right)$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$-\frac{8}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{2\times 3+1}{3}\right)$$

Multiply 2 and 3 to get 6.

$$-\frac{8}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{6+1}{3}\right)$$

Add 6 and 1 to get 7.

$$-\frac{8}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{7}{3}\right)$$

Multiply -\frac{8}{3} times -\frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8\left(-7\right)}{3\times 3}\times \frac{1}{x}\times \frac{a}{12}$$

Do the multiplications in the fraction \frac{-8\left(-7\right)}{3\times 3}.

$$\frac{56}{9}\times \frac{1}{x}\times \frac{a}{12}$$

Multiply \frac{56}{9} times \frac{1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56}{9x}\times \frac{a}{12}$$

Multiply \frac{56}{9x} times \frac{a}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56a}{9x\times 12}$$

Cancel out 4 in both numerator and denominator.

$$\frac{14a}{3\times 9x}$$

Multiply 3 and 9 to get 27.

$$\frac{14a}{27x}$$

Expand

$$\frac{14a}{27x}$$

Solution Steps

Express 4\left(-\frac{2}{3}\right) as a single fraction.

$$\frac{4\left(-2\right)}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{2\times 3+1}{3}\right)$$

Multiply 4 and -2 to get -8.

$$\frac{-8}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{2\times 3+1}{3}\right)$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$-\frac{8}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{2\times 3+1}{3}\right)$$

Multiply 2 and 3 to get 6.

$$-\frac{8}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{6+1}{3}\right)$$

Add 6 and 1 to get 7.

$$-\frac{8}{3}\times \frac{1}{x}\times \frac{a}{12}\left(-\frac{7}{3}\right)$$

Multiply -\frac{8}{3} times -\frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8\left(-7\right)}{3\times 3}\times \frac{1}{x}\times \frac{a}{12}$$

Do the multiplications in the fraction \frac{-8\left(-7\right)}{3\times 3}.

$$\frac{56}{9}\times \frac{1}{x}\times \frac{a}{12}$$

Multiply \frac{56}{9} times \frac{1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56}{9x}\times \frac{a}{12}$$

Multiply \frac{56}{9x} times \frac{a}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56a}{9x\times 12}$$

Cancel out 4 in both numerator and denominator.

$$\frac{14a}{3\times 9x}$$

Multiply 3 and 9 to get 27.

$$\frac{14a}{27x}$$