Solve 3/2(3/2-1)(3/2-2)(3/2-3)

$$\frac{ 3 }{ 2 } ( \frac{ 3 }{ 2 } -1)( \frac{ 3 }{ 2 } -2)( \frac{ 3 }{ 2 } -3)$$

Evaluate

$$\frac{9}{16}=0.5625$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{3}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

Multiply \frac{3}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 1}{2\times 2}.

$$\frac{3}{4}\left(\frac{3}{2}-2\right)\left(\frac{3}{2}-3\right)$$

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

$$\frac{3}{4}\left(\frac{3}{2}-\frac{4}{2}\right)\left(\frac{3}{2}-3\right)$$

Since \frac{3}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}\times \frac{3-4}{2}\left(\frac{3}{2}-3\right)$$

Subtract 4 from 3 to get -1.

$$\frac{3}{4}\left(-\frac{1}{2}\right)\left(\frac{3}{2}-3\right)$$

Multiply \frac{3}{4} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-1\right)}{4\times 2}\left(\frac{3}{2}-3\right)$$

Do the multiplications in the fraction \frac{3\left(-1\right)}{4\times 2}.

$$\frac{-3}{8}\left(\frac{3}{2}-3\right)$$

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

$$-\frac{3}{8}\left(\frac{3}{2}-3\right)$$

Convert 3 to fraction \frac{6}{2}.

$$-\frac{3}{8}\left(\frac{3}{2}-\frac{6}{2}\right)$$

Since \frac{3}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{8}\times \frac{3-6}{2}$$

Subtract 6 from 3 to get -3.

$$-\frac{3}{8}\left(-\frac{3}{2}\right)$$

Multiply -\frac{3}{8} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-3\right)}{8\times 2}$$

Do the multiplications in the fraction \frac{-3\left(-3\right)}{8\times 2}.

$$\frac{9}{16}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {4}} = 0.5625$$