Solve 2/5div21/2quad(u)21/5

$$\frac { 2 } { 5 } \div 2 \frac { 1 } { 2 } \quad ( u ) 2 \frac { 1 } { 5 }$$

Evaluate

$$\frac{44u}{125}$$

Solution Steps

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

$$\frac{2\times 2}{5\left(2\times 2+1\right)}u\times \frac{2\times 5+1}{5}$$

Multiply 2 and 2 to get 4.

$$\frac{4}{5\left(2\times 2+1\right)}u\times \frac{2\times 5+1}{5}$$

Multiply 2 and 2 to get 4.

$$\frac{4}{5\left(4+1\right)}u\times \frac{2\times 5+1}{5}$$

Add 4 and 1 to get 5.

$$\frac{4}{5\times 5}u\times \frac{2\times 5+1}{5}$$

Multiply 5 and 5 to get 25.

$$\frac{4}{25}u\times \frac{2\times 5+1}{5}$$

Multiply 2 and 5 to get 10.

$$\frac{4}{25}u\times \frac{10+1}{5}$$

Add 10 and 1 to get 11.

$$\frac{4}{25}u\times \frac{11}{5}$$

Multiply \frac{4}{25} times \frac{11}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 11}{25\times 5}u$$

Do the multiplications in the fraction \frac{4\times 11}{25\times 5}.

$$\frac{44}{125}u$$

Expand

$$\frac{44u}{125}$$

Solution Steps

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

$$\frac{2\times 2}{5\left(2\times 2+1\right)}u\times \frac{2\times 5+1}{5}$$

Multiply 2 and 2 to get 4.

$$\frac{4}{5\left(2\times 2+1\right)}u\times \frac{2\times 5+1}{5}$$

Multiply 2 and 2 to get 4.

$$\frac{4}{5\left(4+1\right)}u\times \frac{2\times 5+1}{5}$$

Add 4 and 1 to get 5.

$$\frac{4}{5\times 5}u\times \frac{2\times 5+1}{5}$$

Multiply 5 and 5 to get 25.

$$\frac{4}{25}u\times \frac{2\times 5+1}{5}$$

Multiply 2 and 5 to get 10.

$$\frac{4}{25}u\times \frac{10+1}{5}$$

Add 10 and 1 to get 11.

$$\frac{4}{25}u\times \frac{11}{5}$$

Multiply \frac{4}{25} times \frac{11}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 11}{25\times 5}u$$

Do the multiplications in the fraction \frac{4\times 11}{25\times 5}.

$$\frac{44}{125}u$$