Solve -27/5-(-29/4-51/8

$$- \frac{ 27 }{ 5 } -(- \frac{ 29 }{ 4 } - \frac{ 51 }{ 8 }$$

Evaluate

$$\frac{329}{40}=8.225$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert -\frac{29}{4} and \frac{51}{8} to fractions with denominator 8.

$$-\frac{27}{5}-\left(-\frac{58}{8}-\frac{51}{8}\right)$$

Since -\frac{58}{8} and \frac{51}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{27}{5}-\frac{-58-51}{8}$$

Subtract 51 from -58 to get -109.

$$-\frac{27}{5}-\left(-\frac{109}{8}\right)$$

The opposite of -\frac{109}{8} is \frac{109}{8}.

$$-\frac{27}{5}+\frac{109}{8}$$

Least common multiple of 5 and 8 is 40. Convert -\frac{27}{5} and \frac{109}{8} to fractions with denominator 40.

$$-\frac{216}{40}+\frac{545}{40}$$

Since -\frac{216}{40} and \frac{545}{40} have the same denominator, add them by adding their numerators.

$$\frac{-216+545}{40}$$

Add -216 and 545 to get 329.

$$\frac{329}{40}$$

Factor

$$\frac{7 \cdot 47}{2 ^ {3} \cdot 5} = 8\frac{9}{40} = 8.225$$