Solve 929/24-(5/24-4/9)

$$9 \frac { 29 } { 24 } - ( \frac { 5 } { 24 } - \frac { 4 } { 9 } )$$

Evaluate

$$\frac{94}{9}\approx 10.444444444$$

Solution Steps

Multiply 9 and 24 to get 216.

$$\frac{216+29}{24}-\left(\frac{5}{24}-\frac{4}{9}\right)$$

Add 216 and 29 to get 245.

$$\frac{245}{24}-\left(\frac{5}{24}-\frac{4}{9}\right)$$

Least common multiple of 24 and 9 is 72. Convert \frac{5}{24} and \frac{4}{9} to fractions with denominator 72.

$$\frac{245}{24}-\left(\frac{15}{72}-\frac{32}{72}\right)$$

Since \frac{15}{72} and \frac{32}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{245}{24}-\frac{15-32}{72}$$

Subtract 32 from 15 to get -17.

$$\frac{245}{24}-\left(-\frac{17}{72}\right)$$

The opposite of -\frac{17}{72} is \frac{17}{72}.

$$\frac{245}{24}+\frac{17}{72}$$

Least common multiple of 24 and 72 is 72. Convert \frac{245}{24} and \frac{17}{72} to fractions with denominator 72.

$$\frac{735}{72}+\frac{17}{72}$$

Since \frac{735}{72} and \frac{17}{72} have the same denominator, add them by adding their numerators.

$$\frac{735+17}{72}$$

Add 735 and 17 to get 752.

$$\frac{752}{72}$$

Reduce the fraction \frac{752}{72} to lowest terms by extracting and canceling out 8.

$$\frac{94}{9}$$

Factor

$$\frac{2 \cdot 47}{3 ^ {2}} = 10\frac{4}{9} = 10.444444444444445$$