Solve 2a/3-a/2

$$\frac { 2 a } { 3 } - \frac { a } { 2 }$$

Evaluate

$$\frac{a}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{2a}{3} times \frac{2}{2}. Multiply \frac{a}{2} times \frac{3}{3}.

$$\frac{2\times 2a}{6}-\frac{3a}{6}$$

Since \frac{2\times 2a}{6} and \frac{3a}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2a-3a}{6}$$

Do the multiplications in 2\times 2a-3a.

$$\frac{4a-3a}{6}$$

Combine like terms in 4a-3a.

$$\frac{a}{6}$$

Differentiate w.r.t. a

$$\frac{1}{6} = 0.16666666666666666$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{2a}{3} times \frac{2}{2}. Multiply \frac{a}{2} times \frac{3}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2\times 2a}{6}-\frac{3a}{6})$$

Since \frac{2\times 2a}{6} and \frac{3a}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2\times 2a-3a}{6})$$

Do the multiplications in 2\times 2a-3a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4a-3a}{6})$$

Combine like terms in 4a-3a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{6})$$

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

$$\frac{1}{6}a^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{6}a^{0}$$

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

$$\frac{1}{6}\times 1$$

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

$$\frac{1}{6}$$