Solve (32)2/5-(125)1/3-(9)3/2=

$$(32) \frac{ 2 }{ 5 } -(125) \frac{ 1 }{ 3 } -(9) \frac{ 3 }{ 2 } =$$

Evaluate

$$-\frac{1271}{30}\approx -42.366666667$$

Solution Steps

Express 32\times \frac{2}{5} as a single fraction.

$$\frac{32\times 2}{5}-125\times \frac{1}{3}-9\times \frac{3}{2}$$

Multiply 32 and 2 to get 64.

$$\frac{64}{5}-125\times \frac{1}{3}-9\times \frac{3}{2}$$

Multiply 125 and \frac{1}{3} to get \frac{125}{3}.

$$\frac{64}{5}-\frac{125}{3}-9\times \frac{3}{2}$$

Least common multiple of 5 and 3 is 15. Convert \frac{64}{5} and \frac{125}{3} to fractions with denominator 15.

$$\frac{192}{15}-\frac{625}{15}-9\times \frac{3}{2}$$

Since \frac{192}{15} and \frac{625}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{192-625}{15}-9\times \frac{3}{2}$$

Subtract 625 from 192 to get -433.

$$-\frac{433}{15}-9\times \frac{3}{2}$$

Express 9\times \frac{3}{2} as a single fraction.

$$-\frac{433}{15}-\frac{9\times 3}{2}$$

Multiply 9 and 3 to get 27.

$$-\frac{433}{15}-\frac{27}{2}$$

Least common multiple of 15 and 2 is 30. Convert -\frac{433}{15} and \frac{27}{2} to fractions with denominator 30.

$$-\frac{866}{30}-\frac{405}{30}$$

Since -\frac{866}{30} and \frac{405}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-866-405}{30}$$

Subtract 405 from -866 to get -1271.

$$-\frac{1271}{30}$$

Factor

$$-\frac{1271}{30} = -42\frac{11}{30} = -42.36666666666667$$