Solve 3(5/13)-4(5/13)^3

$$3 ( \frac { 5 } { 13 } ) - 4 ( \frac { 5 } { 13 } ) ^ { 3 }$$

Evaluate

$$\frac{2035}{2197}\approx 0.926263086$$

Solution Steps

Express 3\times \frac{5}{13} as a single fraction.

$$\frac{3\times 5}{13}-4\times \left(\frac{5}{13}\right)^{3}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{13}-4\times \left(\frac{5}{13}\right)^{3}$$

Calculate \frac{5}{13} to the power of 3 and get \frac{125}{2197}.

$$\frac{15}{13}-4\times \frac{125}{2197}$$

Express 4\times \frac{125}{2197} as a single fraction.

$$\frac{15}{13}-\frac{4\times 125}{2197}$$

Multiply 4 and 125 to get 500.

$$\frac{15}{13}-\frac{500}{2197}$$

Least common multiple of 13 and 2197 is 2197. Convert \frac{15}{13} and \frac{500}{2197} to fractions with denominator 2197.

$$\frac{2535}{2197}-\frac{500}{2197}$$

Since \frac{2535}{2197} and \frac{500}{2197} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2535-500}{2197}$$

Subtract 500 from 2535 to get 2035.

$$\frac{2035}{2197}$$

Factor

$$\frac{5 \cdot 11 \cdot 37}{13 ^ {3}} = 0.9262630860263996$$