Solve 51/2div11/3quad(t)2/5div2

$$5 \frac { 1 } { 2 } \div \frac { 11 } { 3 } \quad ( t ) \frac { 2 } { 5 } \div 2$$

Evaluate

$$\frac{3t}{10}$$

Solution Steps

Divide \frac{5\times 2+1}{2} by \frac{11}{3} by multiplying \frac{5\times 2+1}{2} by the reciprocal of \frac{11}{3}.

$$\frac{\frac{\left(5\times 2+1\right)\times 3}{2\times 11}t\times \frac{2}{5}}{2}$$

Multiply 5 and 2 to get 10.

$$\frac{\frac{\left(10+1\right)\times 3}{2\times 11}t\times \frac{2}{5}}{2}$$

Add 10 and 1 to get 11.

$$\frac{\frac{11\times 3}{2\times 11}t\times \frac{2}{5}}{2}$$

Multiply 11 and 3 to get 33.

$$\frac{\frac{33}{2\times 11}t\times \frac{2}{5}}{2}$$

Multiply 2 and 11 to get 22.

$$\frac{\frac{33}{22}t\times \frac{2}{5}}{2}$$

Reduce the fraction \frac{33}{22} to lowest terms by extracting and canceling out 11.

$$\frac{\frac{3}{2}t\times \frac{2}{5}}{2}$$

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

$$\frac{\frac{3\times 2}{2\times 5}t}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{3}{5}t}{2}$$

Divide \frac{3}{5}t by 2 to get \frac{3}{10}t.

$$\frac{3}{10}t$$

Expand

$$\frac{3t}{10}$$

Solution Steps

Divide \frac{5\times 2+1}{2} by \frac{11}{3} by multiplying \frac{5\times 2+1}{2} by the reciprocal of \frac{11}{3}.

$$\frac{\frac{\left(5\times 2+1\right)\times 3}{2\times 11}t\times \frac{2}{5}}{2}$$

Multiply 5 and 2 to get 10.

$$\frac{\frac{\left(10+1\right)\times 3}{2\times 11}t\times \frac{2}{5}}{2}$$

Add 10 and 1 to get 11.

$$\frac{\frac{11\times 3}{2\times 11}t\times \frac{2}{5}}{2}$$

Multiply 11 and 3 to get 33.

$$\frac{\frac{33}{2\times 11}t\times \frac{2}{5}}{2}$$

Multiply 2 and 11 to get 22.

$$\frac{\frac{33}{22}t\times \frac{2}{5}}{2}$$

Reduce the fraction \frac{33}{22} to lowest terms by extracting and canceling out 11.

$$\frac{\frac{3}{2}t\times \frac{2}{5}}{2}$$

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

$$\frac{\frac{3\times 2}{2\times 5}t}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{3}{5}t}{2}$$

Divide \frac{3}{5}t by 2 to get \frac{3}{10}t.

$$\frac{3}{10}t$$