Solve 1/6{2/5div(7/3*2/5)+frac{1}{4}}=

$$\frac { 1 } { 6 } \{ \frac { 2 } { 5 } \div ( \frac { 7 } { 3 } \cdot \frac { 2 } { 5 } ) + \frac { 1 } { 4 } \} =$$

Evaluate

$$\frac{19}{168}\approx 0.113095238$$

Solution Steps

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

$$\frac{1}{6}\left(\frac{\frac{2}{5}}{\frac{7\times 2}{3\times 5}}+\frac{1}{4}\right)$$

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

$$\frac{1}{6}\left(\frac{\frac{2}{5}}{\frac{14}{15}}+\frac{1}{4}\right)$$

Divide \frac{2}{5} by \frac{14}{15} by multiplying \frac{2}{5} by the reciprocal of \frac{14}{15}.

$$\frac{1}{6}\left(\frac{2}{5}\times \frac{15}{14}+\frac{1}{4}\right)$$

Multiply \frac{2}{5} times \frac{15}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6}\left(\frac{2\times 15}{5\times 14}+\frac{1}{4}\right)$$

Do the multiplications in the fraction \frac{2\times 15}{5\times 14}.

$$\frac{1}{6}\left(\frac{30}{70}+\frac{1}{4}\right)$$

Reduce the fraction \frac{30}{70} to lowest terms by extracting and canceling out 10.

$$\frac{1}{6}\left(\frac{3}{7}+\frac{1}{4}\right)$$

Least common multiple of 7 and 4 is 28. Convert \frac{3}{7} and \frac{1}{4} to fractions with denominator 28.

$$\frac{1}{6}\left(\frac{12}{28}+\frac{7}{28}\right)$$

Since \frac{12}{28} and \frac{7}{28} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}\times \frac{12+7}{28}$$

Add 12 and 7 to get 19.

$$\frac{1}{6}\times \frac{19}{28}$$

Multiply \frac{1}{6} times \frac{19}{28} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 19}{6\times 28}$$

Do the multiplications in the fraction \frac{1\times 19}{6\times 28}.

$$\frac{19}{168}$$

Factor

$$\frac{19}{2 ^ {3} \cdot 3 \cdot 7} = 0.1130952380952381$$