Solve (2/3*2/7+5/3)*frac{1/2}{2}

$$\frac { ( \frac { 2 } { 3 } \times \frac { 2 } { 7 } + \frac { 5 } { 3 } ) \times \frac { 1 } { 2 } } { 2 }$$

Evaluate

$$\frac{13}{28}\approx 0.464285714$$

Solution Steps

Multiply \frac{2}{3} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{2\times 2}{3\times 7}+\frac{5}{3}\right)\times \frac{1}{2}}{2}$$

Do the multiplications in the fraction \frac{2\times 2}{3\times 7}.

$$\frac{\left(\frac{4}{21}+\frac{5}{3}\right)\times \frac{1}{2}}{2}$$

Least common multiple of 21 and 3 is 21. Convert \frac{4}{21} and \frac{5}{3} to fractions with denominator 21.

$$\frac{\left(\frac{4}{21}+\frac{35}{21}\right)\times \frac{1}{2}}{2}$$

Since \frac{4}{21} and \frac{35}{21} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+35}{21}\times \frac{1}{2}}{2}$$

Add 4 and 35 to get 39.

$$\frac{\frac{39}{21}\times \frac{1}{2}}{2}$$

Reduce the fraction \frac{39}{21} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{13}{7}\times \frac{1}{2}}{2}$$

Multiply \frac{13}{7} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 1}{7\times 2}}{2}$$

Do the multiplications in the fraction \frac{13\times 1}{7\times 2}.

$$\frac{\frac{13}{14}}{2}$$

Express \frac{\frac{13}{14}}{2} as a single fraction.

$$\frac{13}{14\times 2}$$

Multiply 14 and 2 to get 28.

$$\frac{13}{28}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 7} = 0.4642857142857143$$