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

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

Evaluate

$$\frac{149}{30}\approx 4.966666667$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{4}{6}+\frac{3}{6}+4-\frac{1}{5}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{6}+4-\frac{1}{5}$$

Add 4 and 3 to get 7.

$$\frac{7}{6}+4-\frac{1}{5}$$

Convert 4 to fraction \frac{24}{6}.

$$\frac{7}{6}+\frac{24}{6}-\frac{1}{5}$$

Since \frac{7}{6} and \frac{24}{6} have the same denominator, add them by adding their numerators.

$$\frac{7+24}{6}-\frac{1}{5}$$

Add 7 and 24 to get 31.

$$\frac{31}{6}-\frac{1}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{31}{6} and \frac{1}{5} to fractions with denominator 30.

$$\frac{155}{30}-\frac{6}{30}$$

Since \frac{155}{30} and \frac{6}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{155-6}{30}$$

Subtract 6 from 155 to get 149.

$$\frac{149}{30}$$

Factor

$$\frac{149}{2 \cdot 3 \cdot 5} = 4\frac{29}{30} = 4.966666666666667$$