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

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

Evaluate

$$\frac{94}{5}=18.8$$

Solution Steps

Multiply 3 and 3 to get 9.

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

Add 9 and 2 to get 11.

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

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

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

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

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

Subtract 11 from -36 to get -47.

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

Multiply 3 and 3 to get 9.

$$-\frac{47}{3}-1\times \frac{9+2}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add 9 and 2 to get 11.

$$-\frac{47}{3}-1\times \frac{11}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Multiply 1 and \frac{11}{3} to get \frac{11}{3}.

$$-\frac{47}{3}-\frac{11}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Since -\frac{47}{3} and \frac{11}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-47-11}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Subtract 11 from -47 to get -58.

$$-\frac{58}{3}+\frac{31\times 15+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Multiply 31 and 15 to get 465.

$$-\frac{58}{3}+\frac{465+2}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add 465 and 2 to get 467.

$$-\frac{58}{3}+\frac{467}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Least common multiple of 3 and 15 is 15. Convert -\frac{58}{3} and \frac{467}{15} to fractions with denominator 15.

$$-\frac{290}{15}+\frac{467}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Since -\frac{290}{15} and \frac{467}{15} have the same denominator, add them by adding their numerators.

$$\frac{-290+467}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add -290 and 467 to get 177.

$$\frac{177}{15}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Reduce the fraction \frac{177}{15} to lowest terms by extracting and canceling out 3.

$$\frac{59}{5}-\left(-\frac{10\times 2+1}{2}\right)-\frac{3\times 2+1}{2}$$

Multiply 10 and 2 to get 20.

$$\frac{59}{5}-\left(-\frac{20+1}{2}\right)-\frac{3\times 2+1}{2}$$

Add 20 and 1 to get 21.

$$\frac{59}{5}-\left(-\frac{21}{2}\right)-\frac{3\times 2+1}{2}$$

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

$$\frac{59}{5}+\frac{21}{2}-\frac{3\times 2+1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{59}{5} and \frac{21}{2} to fractions with denominator 10.

$$\frac{118}{10}+\frac{105}{10}-\frac{3\times 2+1}{2}$$

Since \frac{118}{10} and \frac{105}{10} have the same denominator, add them by adding their numerators.

$$\frac{118+105}{10}-\frac{3\times 2+1}{2}$$

Add 118 and 105 to get 223.

$$\frac{223}{10}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{223}{10}-\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{223}{10}-\frac{7}{2}$$

Least common multiple of 10 and 2 is 10. Convert \frac{223}{10} and \frac{7}{2} to fractions with denominator 10.

$$\frac{223}{10}-\frac{35}{10}$$

Since \frac{223}{10} and \frac{35}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{223-35}{10}$$

Subtract 35 from 223 to get 188.

$$\frac{188}{10}$$

Reduce the fraction \frac{188}{10} to lowest terms by extracting and canceling out 2.

$$\frac{94}{5}$$

Factor

$$\frac{2 \cdot 47}{5} = 18\frac{4}{5} = 18.8$$