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

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

Evaluate

$$\frac{161}{30}\approx 5.366666667$$

Solution Steps

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}-\frac{1}{3}+\frac{3}{2}-\frac{4}{5}+3$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{3}+\frac{3}{2}-\frac{4}{5}+3$$

Subtract 1 from 6 to get 5.

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

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{10}{6}+\frac{9}{6}-\frac{4}{5}+3$$

Since \frac{10}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{10+9}{6}-\frac{4}{5}+3$$

Add 10 and 9 to get 19.

$$\frac{19}{6}-\frac{4}{5}+3$$

Least common multiple of 6 and 5 is 30. Convert \frac{19}{6} and \frac{4}{5} to fractions with denominator 30.

$$\frac{95}{30}-\frac{24}{30}+3$$

Since \frac{95}{30} and \frac{24}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{95-24}{30}+3$$

Subtract 24 from 95 to get 71.

$$\frac{71}{30}+3$$

Convert 3 to fraction \frac{90}{30}.

$$\frac{71}{30}+\frac{90}{30}$$

Since \frac{71}{30} and \frac{90}{30} have the same denominator, add them by adding their numerators.

$$\frac{71+90}{30}$$

Add 71 and 90 to get 161.

$$\frac{161}{30}$$

Factor

$$\frac{7 \cdot 23}{2 \cdot 3 \cdot 5} = 5\frac{11}{30} = 5.366666666666666$$