Solve -1/2-51/5-1+31/5-4.5+21/3

$$- \frac { 1 } { 2 } - 5 \frac { 1 } { 5 } - 1 + 3 \frac { 1 } { 5 } - 4.5 + 2 \frac { 1 } { 3 }$$

Evaluate

$$-\frac{17}{3}\approx -5.666666667$$

Solution Steps

Multiply 5 and 5 to get 25.

$$-\frac{1}{2}-\frac{25+1}{5}-1+\frac{3\times 5+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Add 25 and 1 to get 26.

$$-\frac{1}{2}-\frac{26}{5}-1+\frac{3\times 5+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{26}{5} to fractions with denominator 10.

$$-\frac{5}{10}-\frac{52}{10}-1+\frac{3\times 5+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Since -\frac{5}{10} and \frac{52}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-52}{10}-1+\frac{3\times 5+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Subtract 52 from -5 to get -57.

$$-\frac{57}{10}-1+\frac{3\times 5+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Convert 1 to fraction \frac{10}{10}.

$$-\frac{57}{10}-\frac{10}{10}+\frac{3\times 5+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Since -\frac{57}{10} and \frac{10}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-57-10}{10}+\frac{3\times 5+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Subtract 10 from -57 to get -67.

$$-\frac{67}{10}+\frac{3\times 5+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Multiply 3 and 5 to get 15.

$$-\frac{67}{10}+\frac{15+1}{5}-4.5+\frac{2\times 3+1}{3}$$

Add 15 and 1 to get 16.

$$-\frac{67}{10}+\frac{16}{5}-4.5+\frac{2\times 3+1}{3}$$

Least common multiple of 10 and 5 is 10. Convert -\frac{67}{10} and \frac{16}{5} to fractions with denominator 10.

$$-\frac{67}{10}+\frac{32}{10}-4.5+\frac{2\times 3+1}{3}$$

Since -\frac{67}{10} and \frac{32}{10} have the same denominator, add them by adding their numerators.

$$\frac{-67+32}{10}-4.5+\frac{2\times 3+1}{3}$$

Add -67 and 32 to get -35.

$$\frac{-35}{10}-4.5+\frac{2\times 3+1}{3}$$

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

$$-\frac{7}{2}-4.5+\frac{2\times 3+1}{3}$$

Convert decimal number 4.5 to fraction \frac{45}{10}. Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{7}{2}-\frac{9}{2}+\frac{2\times 3+1}{3}$$

Since -\frac{7}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-9}{2}+\frac{2\times 3+1}{3}$$

Subtract 9 from -7 to get -16.

$$\frac{-16}{2}+\frac{2\times 3+1}{3}$$

Divide -16 by 2 to get -8.

$$-8+\frac{2\times 3+1}{3}$$

Multiply 2 and 3 to get 6.

$$-8+\frac{6+1}{3}$$

Add 6 and 1 to get 7.

$$-8+\frac{7}{3}$$

Convert -8 to fraction -\frac{24}{3}.

$$-\frac{24}{3}+\frac{7}{3}$$

Since -\frac{24}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{-24+7}{3}$$

Add -24 and 7 to get -17.

$$-\frac{17}{3}$$

Factor

$$-\frac{17}{3} = -5\frac{2}{3} = -5.666666666666667$$