Solve 1/4(100/3.1^3+3*3.1)

$$\frac{ 1 }{ 4 } ( \frac{ 100 }{ { 3.1 }^{ 3 } } +3 \times 3.1)$$

Evaluate

$$\frac{3770563}{1191640}\approx 3.164179618$$

Solution Steps

Calculate 3.1 to the power of 3 and get 29.791.

$$\frac{1}{4}\left(\frac{100}{29.791}+3\times 3.1\right)$$

Expand \frac{100}{29.791} by multiplying both numerator and the denominator by 1000.

$$\frac{1}{4}\left(\frac{100000}{29791}+3\times 3.1\right)$$

Multiply 3 and 3.1 to get 9.3.

$$\frac{1}{4}\left(\frac{100000}{29791}+9.3\right)$$

Convert decimal number 9.3 to fraction \frac{93}{10}.

$$\frac{1}{4}\left(\frac{100000}{29791}+\frac{93}{10}\right)$$

Least common multiple of 29791 and 10 is 297910. Convert \frac{100000}{29791} and \frac{93}{10} to fractions with denominator 297910.

$$\frac{1}{4}\left(\frac{1000000}{297910}+\frac{2770563}{297910}\right)$$

Since \frac{1000000}{297910} and \frac{2770563}{297910} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}\times \frac{1000000+2770563}{297910}$$

Add 1000000 and 2770563 to get 3770563.

$$\frac{1}{4}\times \frac{3770563}{297910}$$

Multiply \frac{1}{4} times \frac{3770563}{297910} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3770563}{4\times 297910}$$

Do the multiplications in the fraction \frac{1\times 3770563}{4\times 297910}.

$$\frac{3770563}{1191640}$$

Factor

$$\frac{613 \cdot 6151}{5 \cdot 2 ^ {3} \cdot 31 ^ {3}} = 3\frac{195643}{1191640} = 3.164179618005438$$