Solve 3/5text{of}25quadtext{(b)}1/2text{of}24quadtext{(c)}1/3text{of}33

$$\frac { 3 } { 5 } \text { of } 25 \quad \text { (b) } \frac { 1 } { 2 } \text { of } 24 \quad \text { (c) } \frac { 1 } { 3 } \text { of } 33$$

Evaluate

$$1980bc\left(fo\right)^{3}$$

Solution Steps

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

$$\frac{3}{5}o^{2}f\times 25b\times \frac{1}{2}f\times 24c\times \frac{1}{3}of\times 33$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{3}{5}o^{3}f\times 25b\times \frac{1}{2}f\times 24c\times \frac{1}{3}f\times 33$$

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

$$\frac{3}{5}o^{3}f^{2}\times 25b\times \frac{1}{2}\times 24c\times \frac{1}{3}f\times 33$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{3}{5}o^{3}f^{3}\times 25b\times \frac{1}{2}\times 24c\times \frac{1}{3}\times 33$$

Express \frac{3}{5}\times 25 as a single fraction.

$$\frac{3\times 25}{5}o^{3}f^{3}b\times \frac{1}{2}\times 24c\times \frac{1}{3}\times 33$$

Multiply 3 and 25 to get 75.

$$\frac{75}{5}o^{3}f^{3}b\times \frac{1}{2}\times 24c\times \frac{1}{3}\times 33$$

Divide 75 by 5 to get 15.

$$15o^{3}f^{3}b\times \frac{1}{2}\times 24c\times \frac{1}{3}\times 33$$

Multiply 15 and \frac{1}{2} to get \frac{15}{2}.

$$\frac{15}{2}o^{3}f^{3}b\times 24c\times \frac{1}{3}\times 33$$

Express \frac{15}{2}\times 24 as a single fraction.

$$\frac{15\times 24}{2}o^{3}f^{3}bc\times \frac{1}{3}\times 33$$

Multiply 15 and 24 to get 360.

$$\frac{360}{2}o^{3}f^{3}bc\times \frac{1}{3}\times 33$$

Divide 360 by 2 to get 180.

$$180o^{3}f^{3}bc\times \frac{1}{3}\times 33$$

Multiply 180 and \frac{1}{3} to get \frac{180}{3}.

$$\frac{180}{3}o^{3}f^{3}bc\times 33$$

Divide 180 by 3 to get 60.

$$60o^{3}f^{3}bc\times 33$$

Multiply 60 and 33 to get 1980.

$$1980o^{3}f^{3}bc$$

Differentiate w.r.t. b

$$1980c\left(fo\right)^{3}$$