Solve 2a/3-5a/12=

$$\frac { 2 a } { 3 } - \frac { 5 a } { 12 } =$$

Evaluate

$$\frac{a}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 12 is 12. Multiply \frac{2a}{3} times \frac{4}{4}.

$$\frac{4\times 2a}{12}-\frac{5a}{12}$$

Since \frac{4\times 2a}{12} and \frac{5a}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 2a-5a}{12}$$

Do the multiplications in 4\times 2a-5a.

$$\frac{8a-5a}{12}$$

Combine like terms in 8a-5a.

$$\frac{3a}{12}$$

Divide 3a by 12 to get \frac{1}{4}a.

$$\frac{1}{4}a$$

Differentiate w.r.t. a

$$\frac{1}{4} = 0.25$$

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 12 is 12. Multiply \frac{2a}{3} times \frac{4}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4\times 2a}{12}-\frac{5a}{12})$$

Since \frac{4\times 2a}{12} and \frac{5a}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4\times 2a-5a}{12})$$

Do the multiplications in 4\times 2a-5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8a-5a}{12})$$

Combine like terms in 8a-5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3a}{12})$$

Divide 3a by 12 to get \frac{1}{4}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{4}a)$$

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

$$\frac{1}{4}a^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{4}a^{0}$$

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

$$\frac{1}{4}\times 1$$

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

$$\frac{1}{4}$$