Solve (-3,5)+(-4/5)+(-7/4)+(+7/2)+0,75+(-7/3)

$$( - 3,5 ) + ( - \frac { 4 } { 5 } ) + ( - \frac { 7 } { 4 } ) + ( + \frac { 7 } { 2 } ) + 0,75 + ( - \frac { 7 } { 3 } )$$

Evaluate

$$-\frac{62}{15}\approx -4,133333333$$

Solution Steps

Convert decimal number -3,5 to fraction -\frac{35}{10}. Reduce the fraction -\frac{35}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{7}{2}-\frac{4}{5}-\frac{7}{4}+\frac{7}{2}+0,75-\frac{7}{3}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{7}{2} and \frac{4}{5} to fractions with denominator 10.

$$-\frac{35}{10}-\frac{8}{10}-\frac{7}{4}+\frac{7}{2}+0,75-\frac{7}{3}$$

Since -\frac{35}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-35-8}{10}-\frac{7}{4}+\frac{7}{2}+0,75-\frac{7}{3}$$

Subtract 8 from -35 to get -43.

$$-\frac{43}{10}-\frac{7}{4}+\frac{7}{2}+0,75-\frac{7}{3}$$

Least common multiple of 10 and 4 is 20. Convert -\frac{43}{10} and \frac{7}{4} to fractions with denominator 20.

$$-\frac{86}{20}-\frac{35}{20}+\frac{7}{2}+0,75-\frac{7}{3}$$

Since -\frac{86}{20} and \frac{35}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-86-35}{20}+\frac{7}{2}+0,75-\frac{7}{3}$$

Subtract 35 from -86 to get -121.

$$-\frac{121}{20}+\frac{7}{2}+0,75-\frac{7}{3}$$

Least common multiple of 20 and 2 is 20. Convert -\frac{121}{20} and \frac{7}{2} to fractions with denominator 20.

$$-\frac{121}{20}+\frac{70}{20}+0,75-\frac{7}{3}$$

Since -\frac{121}{20} and \frac{70}{20} have the same denominator, add them by adding their numerators.

$$\frac{-121+70}{20}+0,75-\frac{7}{3}$$

Add -121 and 70 to get -51.

$$-\frac{51}{20}+0,75-\frac{7}{3}$$

Convert decimal number 0,75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{51}{20}+\frac{3}{4}-\frac{7}{3}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{51}{20} and \frac{3}{4} to fractions with denominator 20.

$$-\frac{51}{20}+\frac{15}{20}-\frac{7}{3}$$

Since -\frac{51}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{-51+15}{20}-\frac{7}{3}$$

Add -51 and 15 to get -36.

$$\frac{-36}{20}-\frac{7}{3}$$

Reduce the fraction \frac{-36}{20} to lowest terms by extracting and canceling out 4.

$$-\frac{9}{5}-\frac{7}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{9}{5} and \frac{7}{3} to fractions with denominator 15.

$$-\frac{27}{15}-\frac{35}{15}$$

Since -\frac{27}{15} and \frac{35}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-27-35}{15}$$

Subtract 35 from -27 to get -62.

$$-\frac{62}{15}$$

Factor

$$-\frac{62}{15} = -4\frac{2}{15} = -4.133333333333334$$