Solve 5/14-3/5+17/10-1/2

$$\frac{ 5 }{ 14 } - \frac{ 3 }{ 5 } + \frac{ 17 }{ 10 } - \frac{ 1 }{ 2 }$$

Evaluate

$$\frac{67}{70}\approx 0.957142857$$

Solution Steps

Least common multiple of 14 and 5 is 70. Convert \frac{5}{14} and \frac{3}{5} to fractions with denominator 70.

$$\frac{25}{70}-\frac{42}{70}+\frac{17}{10}-\frac{1}{2}$$

Since \frac{25}{70} and \frac{42}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-42}{70}+\frac{17}{10}-\frac{1}{2}$$

Subtract 42 from 25 to get -17.

$$-\frac{17}{70}+\frac{17}{10}-\frac{1}{2}$$

Least common multiple of 70 and 10 is 70. Convert -\frac{17}{70} and \frac{17}{10} to fractions with denominator 70.

$$-\frac{17}{70}+\frac{119}{70}-\frac{1}{2}$$

Since -\frac{17}{70} and \frac{119}{70} have the same denominator, add them by adding their numerators.

$$\frac{-17+119}{70}-\frac{1}{2}$$

Add -17 and 119 to get 102.

$$\frac{102}{70}-\frac{1}{2}$$

Reduce the fraction \frac{102}{70} to lowest terms by extracting and canceling out 2.

$$\frac{51}{35}-\frac{1}{2}$$

Least common multiple of 35 and 2 is 70. Convert \frac{51}{35} and \frac{1}{2} to fractions with denominator 70.

$$\frac{102}{70}-\frac{35}{70}$$

Since \frac{102}{70} and \frac{35}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{102-35}{70}$$

Subtract 35 from 102 to get 67.

$$\frac{67}{70}$$

Factor

$$\frac{67}{2 \cdot 5 \cdot 7} = 0.9571428571428572$$