Solve 150/60quadtext{(c)}84/98

$$\frac { 150 } { 60 } \quad \text { (c) } \frac { 84 } { 98 }$$

Evaluate

$$\frac{15c}{7}$$

Solution Steps

Reduce the fraction \frac{150}{60} to lowest terms by extracting and canceling out 30.

$$\frac{5}{2}c\times \frac{84}{98}$$

Reduce the fraction \frac{84}{98} to lowest terms by extracting and canceling out 14.

$$\frac{5}{2}c\times \frac{6}{7}$$

Multiply \frac{5}{2} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 6}{2\times 7}c$$

Do the multiplications in the fraction \frac{5\times 6}{2\times 7}.

$$\frac{30}{14}c$$

Reduce the fraction \frac{30}{14} to lowest terms by extracting and canceling out 2.

$$\frac{15}{7}c$$

Differentiate w.r.t. c

$$\frac{15}{7} = 2\frac{1}{7} = 2.142857142857143$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{150}{60} to lowest terms by extracting and canceling out 30.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{5}{2}c\times \frac{84}{98})$$

Reduce the fraction \frac{84}{98} to lowest terms by extracting and canceling out 14.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{5}{2}c\times \frac{6}{7})$$

Multiply \frac{5}{2} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{5\times 6}{2\times 7}c)$$

Do the multiplications in the fraction \frac{5\times 6}{2\times 7}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{30}{14}c)$$

Reduce the fraction \frac{30}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{15}{7}c)$$

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

$$\frac{15}{7}c^{1-1}$$

Subtract 1 from 1.

$$\frac{15}{7}c^{0}$$

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

$$\frac{15}{7}\times 1$$

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

$$\frac{15}{7}$$