Solve 80%text{of}4.5m

$$80 \% \text { of } 4.5 m$$

Evaluate

$$\frac{18m}{5}$$

Solution Steps

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$\frac{4}{5}\times 4.5m$$

Convert decimal number 4.5 to fraction \frac{45}{10}. Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}\times \frac{9}{2}m$$

Multiply \frac{4}{5} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 9}{5\times 2}m$$

Do the multiplications in the fraction \frac{4\times 9}{5\times 2}.

$$\frac{36}{10}m$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{18}{5}m$$

Differentiate w.r.t. m

$$3.6$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{4}{5}\times 4.5m)$$

Convert decimal number 4.5 to fraction \frac{45}{10}. Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{4}{5}\times \frac{9}{2}m)$$

Multiply \frac{4}{5} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{4\times 9}{5\times 2}m)$$

Do the multiplications in the fraction \frac{4\times 9}{5\times 2}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{36}{10}m)$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{18}{5}m)$$

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

$$\frac{18}{5}m^{1-1}$$

Subtract 1 from 1.

$$\frac{18}{5}m^{0}$$

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

$$\frac{18}{5}\times 1$$

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

$$\frac{18}{5}$$