Solve -12-32/3-132/3+312/15--101/2-3frac{1}{2}

$$-12-3 \frac{ 2 }{ 3 } -13 \frac{ 2 }{ 3 } +31 \frac{ 2 }{ 15 } --10 \frac{ 1 }{ 2 } -3 \frac{ 1 }{ 2 }$$

Evaluate

$$\frac{44}{5}=8.8$$

Solution Steps

Multiply 3 and 3 to get 9.

$$-12-\frac{9+2}{3}-\frac{13\times 3+2}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add 9 and 2 to get 11.

$$-12-\frac{11}{3}-\frac{13\times 3+2}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Convert -12 to fraction -\frac{36}{3}.

$$-\frac{36}{3}-\frac{11}{3}-\frac{13\times 3+2}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Since -\frac{36}{3} and \frac{11}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-36-11}{3}-\frac{13\times 3+2}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Subtract 11 from -36 to get -47.

$$-\frac{47}{3}-\frac{13\times 3+2}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Multiply 13 and 3 to get 39.

$$-\frac{47}{3}-\frac{39+2}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add 39 and 2 to get 41.

$$-\frac{47}{3}-\frac{41}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Since -\frac{47}{3} and \frac{41}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-47-41}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Subtract 41 from -47 to get -88.

$$-\frac{88}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Multiply 31 and 15 to get 465.

$$-\frac{88}{3}+\frac{465+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add 465 and 2 to get 467.

$$-\frac{88}{3}+\frac{467}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Least common multiple of 3 and 15 is 15. Convert -\frac{88}{3} and \frac{467}{15} to fractions with denominator 15.

$$-\frac{440}{15}+\frac{467}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Since -\frac{440}{15} and \frac{467}{15} have the same denominator, add them by adding their numerators.

$$\frac{-440+467}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add -440 and 467 to get 27.

$$\frac{27}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Reduce the fraction \frac{27}{15} to lowest terms by extracting and canceling out 3.

$$\frac{9}{5}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Multiply 10 and 2 to get 20.

$$\frac{9}{5}-\left(-\frac{20+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add 20 and 1 to get 21.

$$\frac{9}{5}-\left(-\frac{21}{2}\right)-\frac{3\times 2+1}{2}$$

The opposite of -\frac{21}{2} is \frac{21}{2}.

$$\frac{9}{5}+\frac{21}{2}-\frac{3\times 2+1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{9}{5} and \frac{21}{2} to fractions with denominator 10.

$$\frac{18}{10}+\frac{105}{10}-\frac{3\times 2+1}{2}$$

Since \frac{18}{10} and \frac{105}{10} have the same denominator, add them by adding their numerators.

$$\frac{18+105}{10}-\frac{3\times 2+1}{2}$$

Add 18 and 105 to get 123.

$$\frac{123}{10}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{123}{10}-\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{123}{10}-\frac{7}{2}$$

Least common multiple of 10 and 2 is 10. Convert \frac{123}{10} and \frac{7}{2} to fractions with denominator 10.

$$\frac{123}{10}-\frac{35}{10}$$

Since \frac{123}{10} and \frac{35}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{123-35}{10}$$

Subtract 35 from 123 to get 88.

$$\frac{88}{10}$$

Reduce the fraction \frac{88}{10} to lowest terms by extracting and canceling out 2.

$$\frac{44}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 11}{5} = 8\frac{4}{5} = 8.8$$