Solve (-3.5)+(-4/3)+(-3/4)+(+7/2)+0.75+(-1/3)

$$( - 3.5 ) + ( - \frac { 4 } { 3 } ) + ( - \frac { 3 } { 4 } ) + ( + \frac { 7 } { 2 } ) + 0.75 + ( - \frac { 1 } { 3 } )$$

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

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.

$$-\frac{7}{2}-\frac{4}{3}-\frac{3}{4}+\frac{7}{2}+0.75-\frac{1}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{7}{2} and \frac{4}{3} to fractions with denominator 6.

$$-\frac{21}{6}-\frac{8}{6}-\frac{3}{4}+\frac{7}{2}+0.75-\frac{1}{3}$$

Since -\frac{21}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-21-8}{6}-\frac{3}{4}+\frac{7}{2}+0.75-\frac{1}{3}$$

Subtract 8 from -21 to get -29.

$$-\frac{29}{6}-\frac{3}{4}+\frac{7}{2}+0.75-\frac{1}{3}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{29}{6} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{58}{12}-\frac{9}{12}+\frac{7}{2}+0.75-\frac{1}{3}$$

Since -\frac{58}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-58-9}{12}+\frac{7}{2}+0.75-\frac{1}{3}$$

Subtract 9 from -58 to get -67.

$$-\frac{67}{12}+\frac{7}{2}+0.75-\frac{1}{3}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{67}{12} and \frac{7}{2} to fractions with denominator 12.

$$-\frac{67}{12}+\frac{42}{12}+0.75-\frac{1}{3}$$

Since -\frac{67}{12} and \frac{42}{12} have the same denominator, add them by adding their numerators.

$$\frac{-67+42}{12}+0.75-\frac{1}{3}$$

Add -67 and 42 to get -25.

$$-\frac{25}{12}+0.75-\frac{1}{3}$$

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.

$$-\frac{25}{12}+\frac{3}{4}-\frac{1}{3}$$

Least common multiple of 12 and 4 is 12. Convert -\frac{25}{12} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{25}{12}+\frac{9}{12}-\frac{1}{3}$$

Since -\frac{25}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{-25+9}{12}-\frac{1}{3}$$

Add -25 and 9 to get -16.

$$\frac{-16}{12}-\frac{1}{3}$$

Reduce the fraction \frac{-16}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{4}{3}-\frac{1}{3}$$

Since -\frac{4}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4-1}{3}$$

Subtract 1 from -4 to get -5.

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

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$