Solve 3/8+7/2+-3/5+9/8+frac{-3}{2}+frac{6}{5}

$$\frac { 3 } { 8 } + \frac { 7 } { 2 } + \frac { - 3 } { 5 } + \frac { 9 } { 8 } + \frac { - 3 } { 2 } + \frac { 6 } { 5 }$$

Evaluate

$$\frac{41}{10}=4.1$$

Solution Steps

Least common multiple of 8 and 2 is 8. Convert \frac{3}{8} and \frac{7}{2} to fractions with denominator 8.

$$\frac{3}{8}+\frac{28}{8}+\frac{-3}{5}+\frac{9}{8}+\frac{-3}{2}+\frac{6}{5}$$

Since \frac{3}{8} and \frac{28}{8} have the same denominator, add them by adding their numerators.

$$\frac{3+28}{8}+\frac{-3}{5}+\frac{9}{8}+\frac{-3}{2}+\frac{6}{5}$$

Add 3 and 28 to get 31.

$$\frac{31}{8}+\frac{-3}{5}+\frac{9}{8}+\frac{-3}{2}+\frac{6}{5}$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$\frac{31}{8}-\frac{3}{5}+\frac{9}{8}+\frac{-3}{2}+\frac{6}{5}$$

Least common multiple of 8 and 5 is 40. Convert \frac{31}{8} and \frac{3}{5} to fractions with denominator 40.

$$\frac{155}{40}-\frac{24}{40}+\frac{9}{8}+\frac{-3}{2}+\frac{6}{5}$$

Since \frac{155}{40} and \frac{24}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{155-24}{40}+\frac{9}{8}+\frac{-3}{2}+\frac{6}{5}$$

Subtract 24 from 155 to get 131.

$$\frac{131}{40}+\frac{9}{8}+\frac{-3}{2}+\frac{6}{5}$$

Least common multiple of 40 and 8 is 40. Convert \frac{131}{40} and \frac{9}{8} to fractions with denominator 40.

$$\frac{131}{40}+\frac{45}{40}+\frac{-3}{2}+\frac{6}{5}$$

Since \frac{131}{40} and \frac{45}{40} have the same denominator, add them by adding their numerators.

$$\frac{131+45}{40}+\frac{-3}{2}+\frac{6}{5}$$

Add 131 and 45 to get 176.

$$\frac{176}{40}+\frac{-3}{2}+\frac{6}{5}$$

Reduce the fraction \frac{176}{40} to lowest terms by extracting and canceling out 8.

$$\frac{22}{5}+\frac{-3}{2}+\frac{6}{5}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{22}{5}-\frac{3}{2}+\frac{6}{5}$$

Least common multiple of 5 and 2 is 10. Convert \frac{22}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{44}{10}-\frac{15}{10}+\frac{6}{5}$$

Since \frac{44}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-15}{10}+\frac{6}{5}$$

Subtract 15 from 44 to get 29.

$$\frac{29}{10}+\frac{6}{5}$$

Least common multiple of 10 and 5 is 10. Convert \frac{29}{10} and \frac{6}{5} to fractions with denominator 10.

$$\frac{29}{10}+\frac{12}{10}$$

Since \frac{29}{10} and \frac{12}{10} have the same denominator, add them by adding their numerators.

$$\frac{29+12}{10}$$

Add 29 and 12 to get 41.

$$\frac{41}{10}$$

Factor

$$\frac{41}{2 \cdot 5} = 4\frac{1}{10} = 4.1$$