Solve 5/8x2/3=

$$\frac { 5 } { 8 } x \frac { 2 } { 3 } =$$

Evaluate

$$\frac{5x}{12}$$

Solution Steps

Multiply \frac{5}{8} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 2}{8\times 3}x$$

Do the multiplications in the fraction \frac{5\times 2}{8\times 3}.

$$\frac{10}{24}x$$

Reduce the fraction \frac{10}{24} to lowest terms by extracting and canceling out 2.

$$\frac{5}{12}x$$

Differentiate w.r.t. x

$$\frac{5}{12} = 0.4166666666666667$$

Steps Using Definition of a Derivative

Multiply \frac{5}{8} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 2}{8\times 3}x)$$

Do the multiplications in the fraction \frac{5\times 2}{8\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{24}x)$$

Reduce the fraction \frac{10}{24} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{12}x)$$

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

$$\frac{5}{12}x^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{12}x^{0}$$

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

$$\frac{5}{12}\times 1$$

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

$$\frac{5}{12}$$