Solve 15/2nquad5/9quad-4/48

$$\frac { 15 } { 2 n } \quad \frac { 5 } { 9 } \quad \frac { - 4 } { 48 }$$

Evaluate

$$-\frac{25}{72n}$$

Solution Steps

Reduce the fraction \frac{-4}{48} to lowest terms by extracting and canceling out 4.

$$\frac{15}{2n}\times \frac{5}{9}\left(-\frac{1}{12}\right)$$

Multiply \frac{5}{9} times -\frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{2n}\times \frac{5\left(-1\right)}{9\times 12}$$

Do the multiplications in the fraction \frac{5\left(-1\right)}{9\times 12}.

$$\frac{15}{2n}\times \frac{-5}{108}$$

Fraction \frac{-5}{108} can be rewritten as -\frac{5}{108} by extracting the negative sign.

$$\frac{15}{2n}\left(-\frac{5}{108}\right)$$

Multiply \frac{15}{2n} times -\frac{5}{108} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-15\times 5}{2n\times 108}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-5\times 5}{2\times 36n}$$

Multiply -5 and 5 to get -25.

$$\frac{-25}{2\times 36n}$$

Multiply 2 and 36 to get 72.

$$\frac{-25}{72n}$$

Differentiate w.r.t. n

$$\frac{25}{72n^{2}}$$