Solve (A)4/9quad(B)1/3quad(C)2/9quad(D)1/2

$$( A ) \frac { 4 } { 9 } \quad ( B ) \frac { 1 } { 3 } \quad ( C ) \frac { 2 } { 9 } \quad ( D ) \frac { 1 } { 2 }$$

Evaluate

$$\frac{4ABCD}{243}$$

Solution Steps

Multiply \frac{4}{9} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$A\times \frac{4\times 1}{9\times 3}BC\times \frac{2}{9}D\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{4\times 1}{9\times 3}.

$$A\times \frac{4}{27}BC\times \frac{2}{9}D\times \frac{1}{2}$$

Multiply \frac{4}{27} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$A\times \frac{4\times 2}{27\times 9}BCD\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{4\times 2}{27\times 9}.

$$A\times \frac{8}{243}BCD\times \frac{1}{2}$$

Multiply \frac{8}{243} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$A\times \frac{8\times 1}{243\times 2}BCD$$

Do the multiplications in the fraction \frac{8\times 1}{243\times 2}.

$$A\times \frac{8}{486}BCD$$

Reduce the fraction \frac{8}{486} to lowest terms by extracting and canceling out 2.

$$A\times \frac{4}{243}BCD$$

Differentiate w.r.t. A

$$\frac{4BCD}{243}$$