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

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

Evaluate

$$\frac{251}{60}\approx 4.183333333$$

Solution Steps

Convert 5 to fraction \frac{25}{5}.

$$\frac{3}{5}+\frac{25}{5}-\frac{4}{3}-\frac{3}{4}+\frac{2}{3}$$

Since \frac{3}{5} and \frac{25}{5} have the same denominator, add them by adding their numerators.

$$\frac{3+25}{5}-\frac{4}{3}-\frac{3}{4}+\frac{2}{3}$$

Add 3 and 25 to get 28.

$$\frac{28}{5}-\frac{4}{3}-\frac{3}{4}+\frac{2}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{28}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{84}{15}-\frac{20}{15}-\frac{3}{4}+\frac{2}{3}$$

Since \frac{84}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{84-20}{15}-\frac{3}{4}+\frac{2}{3}$$

Subtract 20 from 84 to get 64.

$$\frac{64}{15}-\frac{3}{4}+\frac{2}{3}$$

Least common multiple of 15 and 4 is 60. Convert \frac{64}{15} and \frac{3}{4} to fractions with denominator 60.

$$\frac{256}{60}-\frac{45}{60}+\frac{2}{3}$$

Since \frac{256}{60} and \frac{45}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{256-45}{60}+\frac{2}{3}$$

Subtract 45 from 256 to get 211.

$$\frac{211}{60}+\frac{2}{3}$$

Least common multiple of 60 and 3 is 60. Convert \frac{211}{60} and \frac{2}{3} to fractions with denominator 60.

$$\frac{211}{60}+\frac{40}{60}$$

Since \frac{211}{60} and \frac{40}{60} have the same denominator, add them by adding their numerators.

$$\frac{211+40}{60}$$

Add 211 and 40 to get 251.

$$\frac{251}{60}$$

Factor

$$\frac{251}{2 ^ {2} \cdot 3 \cdot 5} = 4\frac{11}{60} = 4.183333333333334$$