Solve 5^2/6*(8/2-4/12):7+[1+(4/3)^2]*frac{1}{2}=

$$\frac { 5 ^ { 2 } } { 6 } \cdot ( \frac { 8 } { 2 } - \frac { 4 } { 12 } ) : 7 + [ 1 + ( \frac { 4 } { 3 } ) ^ { 2 } ] \cdot \frac { 1 } { 2 } =$$

Evaluate

$$\frac{25}{7}\approx 3.571428571$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{25}{6}\left(\frac{8}{2}-\frac{4}{12}\right)}{7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Divide 8 by 2 to get 4.

$$\frac{\frac{25}{6}\left(4-\frac{4}{12}\right)}{7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

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

$$\frac{\frac{25}{6}\left(4-\frac{1}{3}\right)}{7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{\frac{25}{6}\left(\frac{12}{3}-\frac{1}{3}\right)}{7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Since \frac{12}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25}{6}\times \frac{12-1}{3}}{7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Subtract 1 from 12 to get 11.

$$\frac{\frac{25}{6}\times \frac{11}{3}}{7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Multiply \frac{25}{6} times \frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25\times 11}{6\times 3}}{7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{25\times 11}{6\times 3}.

$$\frac{\frac{275}{18}}{7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Express \frac{\frac{275}{18}}{7} as a single fraction.

$$\frac{275}{18\times 7}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Multiply 18 and 7 to get 126.

$$\frac{275}{126}+\left(1+\left(\frac{4}{3}\right)^{2}\right)\times \frac{1}{2}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{275}{126}+\left(1+\frac{16}{9}\right)\times \frac{1}{2}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{275}{126}+\left(\frac{9}{9}+\frac{16}{9}\right)\times \frac{1}{2}$$

Since \frac{9}{9} and \frac{16}{9} have the same denominator, add them by adding their numerators.

$$\frac{275}{126}+\frac{9+16}{9}\times \frac{1}{2}$$

Add 9 and 16 to get 25.

$$\frac{275}{126}+\frac{25}{9}\times \frac{1}{2}$$

Multiply \frac{25}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{275}{126}+\frac{25\times 1}{9\times 2}$$

Do the multiplications in the fraction \frac{25\times 1}{9\times 2}.

$$\frac{275}{126}+\frac{25}{18}$$

Least common multiple of 126 and 18 is 126. Convert \frac{275}{126} and \frac{25}{18} to fractions with denominator 126.

$$\frac{275}{126}+\frac{175}{126}$$

Since \frac{275}{126} and \frac{175}{126} have the same denominator, add them by adding their numerators.

$$\frac{275+175}{126}$$

Add 275 and 175 to get 450.

$$\frac{450}{126}$$

Reduce the fraction \frac{450}{126} to lowest terms by extracting and canceling out 18.

$$\frac{25}{7}$$

Factor

$$\frac{5 ^ {2}}{7} = 3\frac{4}{7} = 3.5714285714285716$$