Solve 1/4left(1/3+1/4right)+1/6*frac{1}{3}

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

Evaluate

$$\frac{29}{144}\approx 0.201388889$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{1}{4}\left(\frac{4}{12}+\frac{3}{12}\right)+\frac{1}{6}\times \frac{1}{3}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}\times \frac{4+3}{12}+\frac{1}{6}\times \frac{1}{3}$$

Add 4 and 3 to get 7.

$$\frac{1}{4}\times \frac{7}{12}+\frac{1}{6}\times \frac{1}{3}$$

Multiply \frac{1}{4} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{4\times 12}+\frac{1}{6}\times \frac{1}{3}$$

Do the multiplications in the fraction \frac{1\times 7}{4\times 12}.

$$\frac{7}{48}+\frac{1}{6}\times \frac{1}{3}$$

Multiply \frac{1}{6} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{48}+\frac{1\times 1}{6\times 3}$$

Do the multiplications in the fraction \frac{1\times 1}{6\times 3}.

$$\frac{7}{48}+\frac{1}{18}$$

Least common multiple of 48 and 18 is 144. Convert \frac{7}{48} and \frac{1}{18} to fractions with denominator 144.

$$\frac{21}{144}+\frac{8}{144}$$

Since \frac{21}{144} and \frac{8}{144} have the same denominator, add them by adding their numerators.

$$\frac{21+8}{144}$$

Add 21 and 8 to get 29.

$$\frac{29}{144}$$

Factor

$$\frac{29}{2 ^ {4} \cdot 3 ^ {2}} = 0.2013888888888889$$