Solve 1/2*(10-x)(3/2x)

$$\frac{ 1 }{ 2 } \times (10-x)( \frac{ 3 }{ 2 } x)$$

Evaluate

$$\frac{3x\left(10-x\right)}{4}$$

Solution Steps

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

$$\frac{1\times 3}{2\times 2}\left(10-x\right)x$$

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

$$\frac{3}{4}\left(10-x\right)x$$

Use the distributive property to multiply \frac{3}{4} by 10-x.

$$\left(\frac{3}{4}\times 10+\frac{3}{4}\left(-1\right)x\right)x$$

Express \frac{3}{4}\times 10 as a single fraction.

$$\left(\frac{3\times 10}{4}+\frac{3}{4}\left(-1\right)x\right)x$$

Multiply 3 and 10 to get 30.

$$\left(\frac{30}{4}+\frac{3}{4}\left(-1\right)x\right)x$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\left(\frac{15}{2}+\frac{3}{4}\left(-1\right)x\right)x$$

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

$$\left(\frac{15}{2}-\frac{3}{4}x\right)x$$

Use the distributive property to multiply \frac{15}{2}-\frac{3}{4}x by x.

$$\frac{15}{2}x-\frac{3}{4}xx$$

Multiply x and x to get x^{2}.

$$\frac{15}{2}x-\frac{3}{4}x^{2}$$

Expand

$$-\frac{3x^{2}}{4}+\frac{15x}{2}$$

Solution Steps

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

$$\frac{1\times 3}{2\times 2}\left(10-x\right)x$$

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

$$\frac{3}{4}\left(10-x\right)x$$

Use the distributive property to multiply \frac{3}{4} by 10-x.

$$\left(\frac{3}{4}\times 10+\frac{3}{4}\left(-1\right)x\right)x$$

Express \frac{3}{4}\times 10 as a single fraction.

$$\left(\frac{3\times 10}{4}+\frac{3}{4}\left(-1\right)x\right)x$$

Multiply 3 and 10 to get 30.

$$\left(\frac{30}{4}+\frac{3}{4}\left(-1\right)x\right)x$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\left(\frac{15}{2}+\frac{3}{4}\left(-1\right)x\right)x$$

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

$$\left(\frac{15}{2}-\frac{3}{4}x\right)x$$

Use the distributive property to multiply \frac{15}{2}-\frac{3}{4}x by x.

$$\frac{15}{2}x-\frac{3}{4}xx$$

Multiply x and x to get x^{2}.

$$\frac{15}{2}x-\frac{3}{4}x^{2}$$