Solve 3/14-5/-7+1/2

$$\frac { 3 } { 14 } - \frac { 5 } { - 7 } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{10}{7}\approx 1.428571429$$

Solution Steps

Fraction \frac{5}{-7} can be rewritten as -\frac{5}{7} by extracting the negative sign.

$$\frac{3}{14}-\left(-\frac{5}{7}\right)+\frac{1}{2}$$

The opposite of -\frac{5}{7} is \frac{5}{7}.

$$\frac{3}{14}+\frac{5}{7}+\frac{1}{2}$$

Least common multiple of 14 and 7 is 14. Convert \frac{3}{14} and \frac{5}{7} to fractions with denominator 14.

$$\frac{3}{14}+\frac{10}{14}+\frac{1}{2}$$

Since \frac{3}{14} and \frac{10}{14} have the same denominator, add them by adding their numerators.

$$\frac{3+10}{14}+\frac{1}{2}$$

Add 3 and 10 to get 13.

$$\frac{13}{14}+\frac{1}{2}$$

Least common multiple of 14 and 2 is 14. Convert \frac{13}{14} and \frac{1}{2} to fractions with denominator 14.

$$\frac{13}{14}+\frac{7}{14}$$

Since \frac{13}{14} and \frac{7}{14} have the same denominator, add them by adding their numerators.

$$\frac{13+7}{14}$$

Add 13 and 7 to get 20.

$$\frac{20}{14}$$

Reduce the fraction \frac{20}{14} to lowest terms by extracting and canceling out 2.

$$\frac{10}{7}$$

Factor

$$\frac{2 \cdot 5}{7} = 1\frac{3}{7} = 1.4285714285714286$$