Solve (31/2-93/4):(-2,5)

$$( 3 \frac { 1 } { 2 } - 9 \frac { 3 } { 4 } ) : ( - 2,5 )$$

Evaluate

$$2,5$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{\frac{6+1}{2}-\frac{9\times 4+3}{4}}{-2,5}$$

Add 6 and 1 to get 7.

$$\frac{\frac{7}{2}-\frac{9\times 4+3}{4}}{-2,5}$$

Multiply 9 and 4 to get 36.

$$\frac{\frac{7}{2}-\frac{36+3}{4}}{-2,5}$$

Add 36 and 3 to get 39.

$$\frac{\frac{7}{2}-\frac{39}{4}}{-2,5}$$

Least common multiple of 2 and 4 is 4. Convert \frac{7}{2} and \frac{39}{4} to fractions with denominator 4.

$$\frac{\frac{14}{4}-\frac{39}{4}}{-2,5}$$

Since \frac{14}{4} and \frac{39}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-39}{4}}{-2,5}$$

Subtract 39 from 14 to get -25.

$$\frac{-\frac{25}{4}}{-2,5}$$

Express \frac{-\frac{25}{4}}{-2,5} as a single fraction.

$$\frac{-25}{4\left(-2,5\right)}$$

Multiply 4 and -2,5 to get -10.

$$\frac{-25}{-10}$$

Reduce the fraction \frac{-25}{-10} to lowest terms by extracting and canceling out -5.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$