Solve 1/4left(2/11+6/19+10/17+frac{3}{7}right)

$$\frac{ 1 }{ 4 } \left( \frac{ 2 }{ 11 } + \frac{ 6 }{ 19 } + \frac{ 10 }{ 17 } + \frac{ 3 }{ 7 } \right)$$

Evaluate

$$\frac{37665}{99484}\approx 0.378603595$$

Solution Steps

Least common multiple of 11 and 19 is 209. Convert \frac{2}{11} and \frac{6}{19} to fractions with denominator 209.

$$\frac{1}{4}\left(\frac{38}{209}+\frac{66}{209}+\frac{10}{17}+\frac{3}{7}\right)$$

Since \frac{38}{209} and \frac{66}{209} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}\left(\frac{38+66}{209}+\frac{10}{17}+\frac{3}{7}\right)$$

Add 38 and 66 to get 104.

$$\frac{1}{4}\left(\frac{104}{209}+\frac{10}{17}+\frac{3}{7}\right)$$

Least common multiple of 209 and 17 is 3553. Convert \frac{104}{209} and \frac{10}{17} to fractions with denominator 3553.

$$\frac{1}{4}\left(\frac{1768}{3553}+\frac{2090}{3553}+\frac{3}{7}\right)$$

Since \frac{1768}{3553} and \frac{2090}{3553} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}\left(\frac{1768+2090}{3553}+\frac{3}{7}\right)$$

Add 1768 and 2090 to get 3858.

$$\frac{1}{4}\left(\frac{3858}{3553}+\frac{3}{7}\right)$$

Least common multiple of 3553 and 7 is 24871. Convert \frac{3858}{3553} and \frac{3}{7} to fractions with denominator 24871.

$$\frac{1}{4}\left(\frac{27006}{24871}+\frac{10659}{24871}\right)$$

Since \frac{27006}{24871} and \frac{10659}{24871} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}\times \frac{27006+10659}{24871}$$

Add 27006 and 10659 to get 37665.

$$\frac{1}{4}\times \frac{37665}{24871}$$

Multiply \frac{1}{4} times \frac{37665}{24871} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 37665}{4\times 24871}$$

Do the multiplications in the fraction \frac{1\times 37665}{4\times 24871}.

$$\frac{37665}{99484}$$

Factor

$$\frac{3 ^ {5} \cdot 5 \cdot 31}{2 ^ {2} \cdot 7 \cdot 11 \cdot 17 \cdot 19} = 0.378603594547867$$