Solve 1/2(3-t)5/3t*5/4

$$\frac { 1 } { 2 } ( 3 - t ) \frac { 5 } { 3 } t \times \frac { 5 } { 4 }$$

Evaluate

$$\frac{25t\left(3-t\right)}{24}$$

Solution Steps

Multiply \frac{1}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{2\times 3}\left(3-t\right)t\times \frac{5}{4}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 3}.

$$\frac{5}{6}\left(3-t\right)t\times \frac{5}{4}$$

Multiply \frac{5}{6} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 5}{6\times 4}\left(3-t\right)t$$

Do the multiplications in the fraction \frac{5\times 5}{6\times 4}.

$$\frac{25}{24}\left(3-t\right)t$$

Use the distributive property to multiply \frac{25}{24} by 3-t.

$$\left(\frac{25}{24}\times 3+\frac{25}{24}\left(-1\right)t\right)t$$

Express \frac{25}{24}\times 3 as a single fraction.

$$\left(\frac{25\times 3}{24}+\frac{25}{24}\left(-1\right)t\right)t$$

Multiply 25 and 3 to get 75.

$$\left(\frac{75}{24}+\frac{25}{24}\left(-1\right)t\right)t$$

Reduce the fraction \frac{75}{24} to lowest terms by extracting and canceling out 3.

$$\left(\frac{25}{8}+\frac{25}{24}\left(-1\right)t\right)t$$

Multiply \frac{25}{24} and -1 to get -\frac{25}{24}.

$$\left(\frac{25}{8}-\frac{25}{24}t\right)t$$

Use the distributive property to multiply \frac{25}{8}-\frac{25}{24}t by t.

$$\frac{25}{8}t-\frac{25}{24}tt$$

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

$$\frac{25}{8}t-\frac{25}{24}t^{2}$$

Expand

$$-\frac{25t^{2}}{24}+\frac{25t}{8}$$

Solution Steps

Multiply \frac{1}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{2\times 3}\left(3-t\right)t\times \frac{5}{4}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 3}.

$$\frac{5}{6}\left(3-t\right)t\times \frac{5}{4}$$

Multiply \frac{5}{6} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 5}{6\times 4}\left(3-t\right)t$$

Do the multiplications in the fraction \frac{5\times 5}{6\times 4}.

$$\frac{25}{24}\left(3-t\right)t$$

Use the distributive property to multiply \frac{25}{24} by 3-t.

$$\left(\frac{25}{24}\times 3+\frac{25}{24}\left(-1\right)t\right)t$$

Express \frac{25}{24}\times 3 as a single fraction.

$$\left(\frac{25\times 3}{24}+\frac{25}{24}\left(-1\right)t\right)t$$

Multiply 25 and 3 to get 75.

$$\left(\frac{75}{24}+\frac{25}{24}\left(-1\right)t\right)t$$

Reduce the fraction \frac{75}{24} to lowest terms by extracting and canceling out 3.

$$\left(\frac{25}{8}+\frac{25}{24}\left(-1\right)t\right)t$$

Multiply \frac{25}{24} and -1 to get -\frac{25}{24}.

$$\left(\frac{25}{8}-\frac{25}{24}t\right)t$$

Use the distributive property to multiply \frac{25}{8}-\frac{25}{24}t by t.

$$\frac{25}{8}t-\frac{25}{24}tt$$

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

$$\frac{25}{8}t-\frac{25}{24}t^{2}$$