Solve 28/5left(5/7/frac{3{2}}+1/14right)

$$\frac{ 28 }{ 5 } \left( \frac{ \frac{ 5 }{ 7 } }{ \frac{ 3 }{ 2 } } + \frac{ 1 }{ 14 } \right)$$

Evaluate

$$\frac{46}{15}\approx 3.066666667$$

Solution Steps

Divide \frac{5}{7} by \frac{3}{2} by multiplying \frac{5}{7} by the reciprocal of \frac{3}{2}.

$$\frac{28}{5}\left(\frac{5}{7}\times \frac{2}{3}+\frac{1}{14}\right)$$

Multiply \frac{5}{7} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28}{5}\left(\frac{5\times 2}{7\times 3}+\frac{1}{14}\right)$$

Do the multiplications in the fraction \frac{5\times 2}{7\times 3}.

$$\frac{28}{5}\left(\frac{10}{21}+\frac{1}{14}\right)$$

Least common multiple of 21 and 14 is 42. Convert \frac{10}{21} and \frac{1}{14} to fractions with denominator 42.

$$\frac{28}{5}\left(\frac{20}{42}+\frac{3}{42}\right)$$

Since \frac{20}{42} and \frac{3}{42} have the same denominator, add them by adding their numerators.

$$\frac{28}{5}\times \frac{20+3}{42}$$

Add 20 and 3 to get 23.

$$\frac{28}{5}\times \frac{23}{42}$$

Multiply \frac{28}{5} times \frac{23}{42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28\times 23}{5\times 42}$$

Do the multiplications in the fraction \frac{28\times 23}{5\times 42}.

$$\frac{644}{210}$$

Reduce the fraction \frac{644}{210} to lowest terms by extracting and canceling out 14.

$$\frac{46}{15}$$

Factor

$$\frac{2 \cdot 23}{3 \cdot 5} = 3\frac{1}{15} = 3.066666666666667$$