Solve (2/5e-1/10e)(2/9e)

$$( \frac { 2 } { 5 e } - \frac { 1 } { 10 e } ) ( \frac { 2 } { 9 e } )$$

Evaluate

$$\frac{1}{15e^{2}}\approx 0.009022352$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5e and 10e is 10e. Multiply \frac{2}{5e} times \frac{2}{2}.

$$\left(\frac{2\times 2}{10e}-\frac{1}{10e}\right)\times \frac{2}{9e}$$

Since \frac{2\times 2}{10e} and \frac{1}{10e} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2-1}{10e}\times \frac{2}{9e}$$

Do the multiplications in 2\times 2-1.

$$\frac{4-1}{10e}\times \frac{2}{9e}$$

Do the calculations in 4-1.

$$\frac{3}{10e}\times \frac{2}{9e}$$

Multiply \frac{3}{10e} times \frac{2}{9e} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{10e\times 9e}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{1}{3\times 5ee}$$

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

$$\frac{1}{3\times 5e^{2}}$$

Multiply 3 and 5 to get 15.

$$\frac{1}{15e^{2}}$$

Expand

$$\frac{1}{15e^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5e and 10e is 10e. Multiply \frac{2}{5e} times \frac{2}{2}.

$$\left(\frac{2\times 2}{10e}-\frac{1}{10e}\right)\times \frac{2}{9e}$$

Since \frac{2\times 2}{10e} and \frac{1}{10e} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2-1}{10e}\times \frac{2}{9e}$$

Do the multiplications in 2\times 2-1.

$$\frac{4-1}{10e}\times \frac{2}{9e}$$

Do the calculations in 4-1.

$$\frac{3}{10e}\times \frac{2}{9e}$$

Multiply \frac{3}{10e} times \frac{2}{9e} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{10e\times 9e}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{1}{3\times 5ee}$$

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

$$\frac{1}{3\times 5e^{2}}$$

Multiply 3 and 5 to get 15.

$$\frac{1}{15e^{2}}$$