Solve -6/21+13/18+40/3

$$- \frac{ 6 }{ 21 } + \frac{ 13 }{ 18 } + \frac{ 40 }{ 3 }$$

Evaluate

$$\frac{1735}{126}\approx 13.76984127$$

Solution Steps

Reduce the fraction \frac{6}{21} to lowest terms by extracting and canceling out 3.

$$-\frac{2}{7}+\frac{13}{18}+\frac{40}{3}$$

Least common multiple of 7 and 18 is 126. Convert -\frac{2}{7} and \frac{13}{18} to fractions with denominator 126.

$$-\frac{36}{126}+\frac{91}{126}+\frac{40}{3}$$

Since -\frac{36}{126} and \frac{91}{126} have the same denominator, add them by adding their numerators.

$$\frac{-36+91}{126}+\frac{40}{3}$$

Add -36 and 91 to get 55.

$$\frac{55}{126}+\frac{40}{3}$$

Least common multiple of 126 and 3 is 126. Convert \frac{55}{126} and \frac{40}{3} to fractions with denominator 126.

$$\frac{55}{126}+\frac{1680}{126}$$

Since \frac{55}{126} and \frac{1680}{126} have the same denominator, add them by adding their numerators.

$$\frac{55+1680}{126}$$

Add 55 and 1680 to get 1735.

$$\frac{1735}{126}$$

Factor

$$\frac{5 \cdot 347}{2 \cdot 3 ^ {2} \cdot 7} = 13\frac{97}{126} = 13.76984126984127$$