Solve 13/20+11/14+-5/7+7/10

$$\frac { 13 } { 20 } + \frac { 11 } { 14 } + \frac { - 5 } { 7 } + \frac { 7 } { 10 }$$

Evaluate

$$\frac{199}{140}\approx 1.421428571$$

Solution Steps

Least common multiple of 20 and 14 is 140. Convert \frac{13}{20} and \frac{11}{14} to fractions with denominator 140.

$$\frac{91}{140}+\frac{110}{140}+\frac{-5}{7}+\frac{7}{10}$$

Since \frac{91}{140} and \frac{110}{140} have the same denominator, add them by adding their numerators.

$$\frac{91+110}{140}+\frac{-5}{7}+\frac{7}{10}$$

Add 91 and 110 to get 201.

$$\frac{201}{140}+\frac{-5}{7}+\frac{7}{10}$$

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

$$\frac{201}{140}-\frac{5}{7}+\frac{7}{10}$$

Least common multiple of 140 and 7 is 140. Convert \frac{201}{140} and \frac{5}{7} to fractions with denominator 140.

$$\frac{201}{140}-\frac{100}{140}+\frac{7}{10}$$

Since \frac{201}{140} and \frac{100}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{201-100}{140}+\frac{7}{10}$$

Subtract 100 from 201 to get 101.

$$\frac{101}{140}+\frac{7}{10}$$

Least common multiple of 140 and 10 is 140. Convert \frac{101}{140} and \frac{7}{10} to fractions with denominator 140.

$$\frac{101}{140}+\frac{98}{140}$$

Since \frac{101}{140} and \frac{98}{140} have the same denominator, add them by adding their numerators.

$$\frac{101+98}{140}$$

Add 101 and 98 to get 199.

$$\frac{199}{140}$$

Factor

$$\frac{199}{2 ^ {2} \cdot 5 \cdot 7} = 1\frac{59}{140} = 1.4214285714285715$$