Solve 2/a*3a/6quadtext{f}5w/7*2w/9

$$\frac { 2 } { a } \times \frac { 3 a } { 6 } \quad \text { f } \frac { 5 w } { 7 } \times \frac { 2 w } { 9 }$$

Evaluate

$$\frac{10fw^{2}}{63}$$

Solution Steps

Divide 3a by 6 to get \frac{1}{2}a.

$$\frac{2}{a}\times \frac{1}{2}af\times \frac{5w}{7}\times \frac{2w}{9}$$

Multiply \frac{2}{a} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{a\times 2}af\times \frac{5w}{7}\times \frac{2w}{9}$$

Express \frac{2}{a\times 2}a as a single fraction.

$$\frac{2a}{a\times 2}f\times \frac{5w}{7}\times \frac{2w}{9}$$

Cancel out 2a in both numerator and denominator.

$$1f\times \frac{5w}{7}\times \frac{2w}{9}$$

Express 1\times \frac{5w}{7} as a single fraction.

$$\frac{5w}{7}f\times \frac{2w}{9}$$

Multiply \frac{5w}{7} times \frac{2w}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5w\times 2w}{7\times 9}f$$

Multiply w and w to get w^{2}.

$$\frac{5w^{2}\times 2}{7\times 9}f$$

Multiply 5 and 2 to get 10.

$$\frac{10w^{2}}{7\times 9}f$$

Multiply 7 and 9 to get 63.

$$\frac{10w^{2}}{63}f$$

Express \frac{10w^{2}}{63}f as a single fraction.

$$\frac{10w^{2}f}{63}$$

Differentiate w.r.t. f

$$\frac{10w^{2}}{63}$$