Solve -9(1/8-5/4)-5/9

$$- 9 ( \frac { 1 } { 8 } - \frac { 5 } { 4 } ) - \frac { 5 } { 9 }$$

Evaluate

$$\frac{689}{72}\approx 9.569444444$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{1}{8} and \frac{5}{4} to fractions with denominator 8.

$$-9\left(\frac{1}{8}-\frac{10}{8}\right)-\frac{5}{9}$$

Since \frac{1}{8} and \frac{10}{8} have the same denominator, subtract them by subtracting their numerators.

$$-9\times \frac{1-10}{8}-\frac{5}{9}$$

Subtract 10 from 1 to get -9.

$$-9\left(-\frac{9}{8}\right)-\frac{5}{9}$$

Express -9\left(-\frac{9}{8}\right) as a single fraction.

$$\frac{-9\left(-9\right)}{8}-\frac{5}{9}$$

Multiply -9 and -9 to get 81.

$$\frac{81}{8}-\frac{5}{9}$$

Least common multiple of 8 and 9 is 72. Convert \frac{81}{8} and \frac{5}{9} to fractions with denominator 72.

$$\frac{729}{72}-\frac{40}{72}$$

Since \frac{729}{72} and \frac{40}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{729-40}{72}$$

Subtract 40 from 729 to get 689.

$$\frac{689}{72}$$

Factor

$$\frac{13 \cdot 53}{2 ^ {3} \cdot 3 ^ {2}} = 9\frac{41}{72} = 9.569444444444445$$