Solve 2/3-(-3/5)-3/5-1/2-(-0.4)+3.2

$$\frac { 2 } { 3 } - ( - \frac { 3 } { 5 } ) - \frac { 3 } { 5 } - \frac { 1 } { 2 } - ( - 0.4 ) + 3.2$$

Evaluate

$$\frac{113}{30}\approx 3.766666667$$

Solution Steps

The opposite of -\frac{3}{5} is \frac{3}{5}.

$$\frac{2}{3}+\frac{3}{5}-\frac{3}{5}-\frac{1}{2}-\left(-0.4\right)+3.2$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{10}{15}+\frac{9}{15}-\frac{3}{5}-\frac{1}{2}-\left(-0.4\right)+3.2$$

Since \frac{10}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+9}{15}-\frac{3}{5}-\frac{1}{2}-\left(-0.4\right)+3.2$$

Add 10 and 9 to get 19.

$$\frac{19}{15}-\frac{3}{5}-\frac{1}{2}-\left(-0.4\right)+3.2$$

Least common multiple of 15 and 5 is 15. Convert \frac{19}{15} and \frac{3}{5} to fractions with denominator 15.

$$\frac{19}{15}-\frac{9}{15}-\frac{1}{2}-\left(-0.4\right)+3.2$$

Since \frac{19}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-9}{15}-\frac{1}{2}-\left(-0.4\right)+3.2$$

Subtract 9 from 19 to get 10.

$$\frac{10}{15}-\frac{1}{2}-\left(-0.4\right)+3.2$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}-\frac{1}{2}-\left(-0.4\right)+3.2$$

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

$$\frac{4}{6}-\frac{3}{6}-\left(-0.4\right)+3.2$$

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

$$\frac{4-3}{6}-\left(-0.4\right)+3.2$$

Subtract 3 from 4 to get 1.

$$\frac{1}{6}-\left(-0.4\right)+3.2$$

The opposite of -0.4 is 0.4.

$$\frac{1}{6}+0.4+3.2$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}+\frac{2}{5}+3.2$$

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{2}{5} to fractions with denominator 30.

$$\frac{5}{30}+\frac{12}{30}+3.2$$

Since \frac{5}{30} and \frac{12}{30} have the same denominator, add them by adding their numerators.

$$\frac{5+12}{30}+3.2$$

Add 5 and 12 to get 17.

$$\frac{17}{30}+3.2$$

Convert decimal number 3.2 to fraction \frac{32}{10}. Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{17}{30}+\frac{16}{5}$$

Least common multiple of 30 and 5 is 30. Convert \frac{17}{30} and \frac{16}{5} to fractions with denominator 30.

$$\frac{17}{30}+\frac{96}{30}$$

Since \frac{17}{30} and \frac{96}{30} have the same denominator, add them by adding their numerators.

$$\frac{17+96}{30}$$

Add 17 and 96 to get 113.

$$\frac{113}{30}$$

Factor

$$\frac{113}{2 \cdot 3 \cdot 5} = 3\frac{23}{30} = 3.7666666666666666$$