Solve 3*(2/7)^2/2*(frac{2{7})^2+8*2/7+4}

$$\frac { 3 \times ( \frac { 2 } { 7 } ) ^ { 2 } } { 2 \times ( \frac { 2 } { 7 } ) ^ { 2 } + 8 \times \frac { 2 } { 7 } + 4 }$$

Evaluate

$$\frac{3}{79}\approx 0.037974684$$

Solution Steps

Calculate \frac{2}{7} to the power of 2 and get \frac{4}{49}.

$$\frac{3\times \frac{4}{49}}{2\times \left(\frac{2}{7}\right)^{2}+8\times \frac{2}{7}+4}$$

Express 3\times \frac{4}{49} as a single fraction.

$$\frac{\frac{3\times 4}{49}}{2\times \left(\frac{2}{7}\right)^{2}+8\times \frac{2}{7}+4}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{12}{49}}{2\times \left(\frac{2}{7}\right)^{2}+8\times \frac{2}{7}+4}$$

Calculate \frac{2}{7} to the power of 2 and get \frac{4}{49}.

$$\frac{\frac{12}{49}}{2\times \frac{4}{49}+8\times \frac{2}{7}+4}$$

Express 2\times \frac{4}{49} as a single fraction.

$$\frac{\frac{12}{49}}{\frac{2\times 4}{49}+8\times \frac{2}{7}+4}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{12}{49}}{\frac{8}{49}+8\times \frac{2}{7}+4}$$

Express 8\times \frac{2}{7} as a single fraction.

$$\frac{\frac{12}{49}}{\frac{8}{49}+\frac{8\times 2}{7}+4}$$

Multiply 8 and 2 to get 16.

$$\frac{\frac{12}{49}}{\frac{8}{49}+\frac{16}{7}+4}$$

Least common multiple of 49 and 7 is 49. Convert \frac{8}{49} and \frac{16}{7} to fractions with denominator 49.

$$\frac{\frac{12}{49}}{\frac{8}{49}+\frac{112}{49}+4}$$

Since \frac{8}{49} and \frac{112}{49} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12}{49}}{\frac{8+112}{49}+4}$$

Add 8 and 112 to get 120.

$$\frac{\frac{12}{49}}{\frac{120}{49}+4}$$

Convert 4 to fraction \frac{196}{49}.

$$\frac{\frac{12}{49}}{\frac{120}{49}+\frac{196}{49}}$$

Since \frac{120}{49} and \frac{196}{49} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12}{49}}{\frac{120+196}{49}}$$

Add 120 and 196 to get 316.

$$\frac{\frac{12}{49}}{\frac{316}{49}}$$

Divide \frac{12}{49} by \frac{316}{49} by multiplying \frac{12}{49} by the reciprocal of \frac{316}{49}.

$$\frac{12}{49}\times \frac{49}{316}$$

Multiply \frac{12}{49} times \frac{49}{316} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 49}{49\times 316}$$

Cancel out 49 in both numerator and denominator.

$$\frac{12}{316}$$

Reduce the fraction \frac{12}{316} to lowest terms by extracting and canceling out 4.

$$\frac{3}{79}$$

Factor

$$\frac{3}{79} = 0.0379746835443038$$