Solve 29/24-(5/24-4/9)

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

Evaluate

$$\frac{13}{9}\approx 1.444444444$$

Solution Steps

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

$$\frac{29}{24}-\left(\frac{15}{72}-\frac{32}{72}\right)$$

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

$$\frac{29}{24}-\frac{15-32}{72}$$

Subtract 32 from 15 to get -17.

$$\frac{29}{24}-\left(-\frac{17}{72}\right)$$

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

$$\frac{29}{24}+\frac{17}{72}$$

Least common multiple of 24 and 72 is 72. Convert \frac{29}{24} and \frac{17}{72} to fractions with denominator 72.

$$\frac{87}{72}+\frac{17}{72}$$

Since \frac{87}{72} and \frac{17}{72} have the same denominator, add them by adding their numerators.

$$\frac{87+17}{72}$$

Add 87 and 17 to get 104.

$$\frac{104}{72}$$

Reduce the fraction \frac{104}{72} to lowest terms by extracting and canceling out 8.

$$\frac{13}{9}$$

Factor

$$\frac{13}{3 ^ {2}} = 1\frac{4}{9} = 1.4444444444444444$$