Solve (4/3-7/9)-(-9/15--12/5)

$$( \frac { 4 } { 3 } - \frac { 7 } { 9 } ) - ( \frac { - 9 } { 15 } - \frac { - 12 } { 5 } )$$

Evaluate

$$-\frac{56}{45}\approx -1.244444444$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{7}{9} to fractions with denominator 9.

$$\frac{12}{9}-\frac{7}{9}-\left(\frac{-9}{15}-\frac{-12}{5}\right)$$

Since \frac{12}{9} and \frac{7}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-7}{9}-\left(\frac{-9}{15}-\frac{-12}{5}\right)$$

Subtract 7 from 12 to get 5.

$$\frac{5}{9}-\left(\frac{-9}{15}-\frac{-12}{5}\right)$$

Reduce the fraction \frac{-9}{15} to lowest terms by extracting and canceling out 3.

$$\frac{5}{9}-\left(-\frac{3}{5}-\frac{-12}{5}\right)$$

Fraction \frac{-12}{5} can be rewritten as -\frac{12}{5} by extracting the negative sign.

$$\frac{5}{9}-\left(-\frac{3}{5}-\left(-\frac{12}{5}\right)\right)$$

The opposite of -\frac{12}{5} is \frac{12}{5}.

$$\frac{5}{9}-\left(-\frac{3}{5}+\frac{12}{5}\right)$$

Since -\frac{3}{5} and \frac{12}{5} have the same denominator, add them by adding their numerators.

$$\frac{5}{9}-\frac{-3+12}{5}$$

Add -3 and 12 to get 9.

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

Least common multiple of 9 and 5 is 45. Convert \frac{5}{9} and \frac{9}{5} to fractions with denominator 45.

$$\frac{25}{45}-\frac{81}{45}$$

Since \frac{25}{45} and \frac{81}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-81}{45}$$

Subtract 81 from 25 to get -56.

$$-\frac{56}{45}$$

Factor

$$-\frac{56}{45} = -1\frac{11}{45} = -1.2444444444444445$$