Solve 0.1a/5*135/2/0.05

$$\frac { \frac { 0.1 a } { 5 } \times \frac { 135 } { 2 } } { 0.05 }$$

Evaluate

$$27a$$

Solution Steps

Divide 0.1a by 5 to get 0.02a.

$$\frac{0.02a\times \frac{135}{2}}{0.05}$$

Convert decimal number 0.02 to fraction \frac{2}{100}. Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{50}a\times \frac{135}{2}}{0.05}$$

Multiply \frac{1}{50} times \frac{135}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 135}{50\times 2}a}{0.05}$$

Do the multiplications in the fraction \frac{1\times 135}{50\times 2}.

$$\frac{\frac{135}{100}a}{0.05}$$

Reduce the fraction \frac{135}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{27}{20}a}{0.05}$$

Divide \frac{27}{20}a by 0.05 to get 27a.

$$27a$$

Differentiate w.r.t. a

$$27$$

Steps Using Definition of a Derivative

Divide 0.1a by 5 to get 0.02a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{0.02a\times \frac{135}{2}}{0.05})$$

Convert decimal number 0.02 to fraction \frac{2}{100}. Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{50}a\times \frac{135}{2}}{0.05})$$

Multiply \frac{1}{50} times \frac{135}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1\times 135}{50\times 2}a}{0.05})$$

Do the multiplications in the fraction \frac{1\times 135}{50\times 2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{135}{100}a}{0.05})$$

Reduce the fraction \frac{135}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{27}{20}a}{0.05})$$

Divide \frac{27}{20}a by 0.05 to get 27a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(27a)$$

The derivative of ax^{n} is nax^{n-1}.

$$27a^{1-1}$$

Subtract 1 from 1.

$$27a^{0}$$

For any term t except 0, t^{0}=1.

$$27\times 1$$

For any term t, t\times 1=t and 1t=t.

$$27$$