Solve 1/5-1/4+1/3-3/2+3

$$\frac { 1 } { 5 } - \frac { 1 } { 4 } + \frac { 1 } { 3 } - \frac { 3 } { 2 } + 3$$

Evaluate

$$\frac{107}{60}\approx 1.783333333$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{1}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{4}{20}-\frac{5}{20}+\frac{1}{3}-\frac{3}{2}+3$$

Since \frac{4}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-5}{20}+\frac{1}{3}-\frac{3}{2}+3$$

Subtract 5 from 4 to get -1.

$$-\frac{1}{20}+\frac{1}{3}-\frac{3}{2}+3$$

Least common multiple of 20 and 3 is 60. Convert -\frac{1}{20} and \frac{1}{3} to fractions with denominator 60.

$$-\frac{3}{60}+\frac{20}{60}-\frac{3}{2}+3$$

Since -\frac{3}{60} and \frac{20}{60} have the same denominator, add them by adding their numerators.

$$\frac{-3+20}{60}-\frac{3}{2}+3$$

Add -3 and 20 to get 17.

$$\frac{17}{60}-\frac{3}{2}+3$$

Least common multiple of 60 and 2 is 60. Convert \frac{17}{60} and \frac{3}{2} to fractions with denominator 60.

$$\frac{17}{60}-\frac{90}{60}+3$$

Since \frac{17}{60} and \frac{90}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-90}{60}+3$$

Subtract 90 from 17 to get -73.

$$-\frac{73}{60}+3$$

Convert 3 to fraction \frac{180}{60}.

$$-\frac{73}{60}+\frac{180}{60}$$

Since -\frac{73}{60} and \frac{180}{60} have the same denominator, add them by adding their numerators.

$$\frac{-73+180}{60}$$

Add -73 and 180 to get 107.

$$\frac{107}{60}$$

Factor

$$\frac{107}{2 ^ {2} \cdot 3 \cdot 5} = 1\frac{47}{60} = 1.7833333333333334$$