Solve 1/3+3/14+22/3+111/14

$$\frac { 1 } { 3 } + \frac { 3 } { 14 } + 2 \frac { 2 } { 3 } + 1 \frac { 11 } { 14 }$$

Evaluate

$$5$$

Solution Steps

Least common multiple of 3 and 14 is 42. Convert \frac{1}{3} and \frac{3}{14} to fractions with denominator 42.

$$\frac{14}{42}+\frac{9}{42}+\frac{2\times 3+2}{3}+\frac{1\times 14+11}{14}$$

Since \frac{14}{42} and \frac{9}{42} have the same denominator, add them by adding their numerators.

$$\frac{14+9}{42}+\frac{2\times 3+2}{3}+\frac{1\times 14+11}{14}$$

Add 14 and 9 to get 23.

$$\frac{23}{42}+\frac{2\times 3+2}{3}+\frac{1\times 14+11}{14}$$

Multiply 2 and 3 to get 6.

$$\frac{23}{42}+\frac{6+2}{3}+\frac{1\times 14+11}{14}$$

Add 6 and 2 to get 8.

$$\frac{23}{42}+\frac{8}{3}+\frac{1\times 14+11}{14}$$

Least common multiple of 42 and 3 is 42. Convert \frac{23}{42} and \frac{8}{3} to fractions with denominator 42.

$$\frac{23}{42}+\frac{112}{42}+\frac{1\times 14+11}{14}$$

Since \frac{23}{42} and \frac{112}{42} have the same denominator, add them by adding their numerators.

$$\frac{23+112}{42}+\frac{1\times 14+11}{14}$$

Add 23 and 112 to get 135.

$$\frac{135}{42}+\frac{1\times 14+11}{14}$$

Reduce the fraction \frac{135}{42} to lowest terms by extracting and canceling out 3.

$$\frac{45}{14}+\frac{1\times 14+11}{14}$$

Multiply 1 and 14 to get 14.

$$\frac{45}{14}+\frac{14+11}{14}$$

Add 14 and 11 to get 25.

$$\frac{45}{14}+\frac{25}{14}$$

Since \frac{45}{14} and \frac{25}{14} have the same denominator, add them by adding their numerators.

$$\frac{45+25}{14}$$

Add 45 and 25 to get 70.

$$\frac{70}{14}$$

Divide 70 by 14 to get 5.

$$5$$

Factor

$$5$$