Solve 1/3+8/5-(-3-4/2)+2-4/8=

$$\frac { 1 } { 3 } + \frac { 8 } { 5 } - ( - \frac { 3 - 4 } { 2 } ) + 2 - \frac { 4 } { 8 } =$$

Evaluate

$$\frac{44}{15}\approx 2.933333333$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{8}{5} to fractions with denominator 15.

$$\frac{5}{15}+\frac{24}{15}-\left(-\frac{3-4}{2}\right)+2-\frac{4}{8}$$

Since \frac{5}{15} and \frac{24}{15} have the same denominator, add them by adding their numerators.

$$\frac{5+24}{15}-\left(-\frac{3-4}{2}\right)+2-\frac{4}{8}$$

Add 5 and 24 to get 29.

$$\frac{29}{15}-\left(-\frac{3-4}{2}\right)+2-\frac{4}{8}$$

Subtract 4 from 3 to get -1.

$$\frac{29}{15}-\left(-\frac{-1}{2}\right)+2-\frac{4}{8}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{29}{15}-\left(-\left(-\frac{1}{2}\right)\right)+2-\frac{4}{8}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{29}{15}-\frac{1}{2}+2-\frac{4}{8}$$

Least common multiple of 15 and 2 is 30. Convert \frac{29}{15} and \frac{1}{2} to fractions with denominator 30.

$$\frac{58}{30}-\frac{15}{30}+2-\frac{4}{8}$$

Since \frac{58}{30} and \frac{15}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{58-15}{30}+2-\frac{4}{8}$$

Subtract 15 from 58 to get 43.

$$\frac{43}{30}+2-\frac{4}{8}$$

Convert 2 to fraction \frac{60}{30}.

$$\frac{43}{30}+\frac{60}{30}-\frac{4}{8}$$

Since \frac{43}{30} and \frac{60}{30} have the same denominator, add them by adding their numerators.

$$\frac{43+60}{30}-\frac{4}{8}$$

Add 43 and 60 to get 103.

$$\frac{103}{30}-\frac{4}{8}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{103}{30}-\frac{1}{2}$$

Least common multiple of 30 and 2 is 30. Convert \frac{103}{30} and \frac{1}{2} to fractions with denominator 30.

$$\frac{103}{30}-\frac{15}{30}$$

Since \frac{103}{30} and \frac{15}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{103-15}{30}$$

Subtract 15 from 103 to get 88.

$$\frac{88}{30}$$

Reduce the fraction \frac{88}{30} to lowest terms by extracting and canceling out 2.

$$\frac{44}{15}$$

Factor

$$\frac{2 ^ {2} \cdot 11}{3 \cdot 5} = 2\frac{14}{15} = 2.933333333333333$$