Solve 4/5y7/8=

$$\frac { 4 } { 5 } y \frac { 7 } { 8 } =$$

Evaluate

$$\frac{7y}{10}$$

Solution Steps

Multiply \frac{4}{5} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 7}{5\times 8}y$$

Do the multiplications in the fraction \frac{4\times 7}{5\times 8}.

$$\frac{28}{40}y$$

Reduce the fraction \frac{28}{40} to lowest terms by extracting and canceling out 4.

$$\frac{7}{10}y$$

Differentiate w.r.t. y

$$\frac{7}{10} = 0.7$$

Steps Using Definition of a Derivative

Multiply \frac{4}{5} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4\times 7}{5\times 8}y)$$

Do the multiplications in the fraction \frac{4\times 7}{5\times 8}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{28}{40}y)$$

Reduce the fraction \frac{28}{40} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{7}{10}y)$$

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

$$\frac{7}{10}y^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{10}y^{0}$$

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

$$\frac{7}{10}\times 1$$

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

$$\frac{7}{10}$$