Solve 4:8/9-7/2:(-2)=

$$4 : \frac { 8 } { 9 } - \frac { 7 } { 2 } : ( - 2 ) =$$

Evaluate

$$\frac{25}{4}=6.25$$

Solution Steps

Divide 4 by \frac{8}{9} by multiplying 4 by the reciprocal of \frac{8}{9}.

$$4\times \frac{9}{8}-\frac{\frac{7}{2}}{-2}$$

Express 4\times \frac{9}{8} as a single fraction.

$$\frac{4\times 9}{8}-\frac{\frac{7}{2}}{-2}$$

Multiply 4 and 9 to get 36.

$$\frac{36}{8}-\frac{\frac{7}{2}}{-2}$$

Reduce the fraction \frac{36}{8} to lowest terms by extracting and canceling out 4.

$$\frac{9}{2}-\frac{\frac{7}{2}}{-2}$$

Express \frac{\frac{7}{2}}{-2} as a single fraction.

$$\frac{9}{2}-\frac{7}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

$$\frac{9}{2}-\frac{7}{-4}$$

Fraction \frac{7}{-4} can be rewritten as -\frac{7}{4} by extracting the negative sign.

$$\frac{9}{2}-\left(-\frac{7}{4}\right)$$

The opposite of -\frac{7}{4} is \frac{7}{4}.

$$\frac{9}{2}+\frac{7}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{9}{2} and \frac{7}{4} to fractions with denominator 4.

$$\frac{18}{4}+\frac{7}{4}$$

Since \frac{18}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{18+7}{4}$$

Add 18 and 7 to get 25.

$$\frac{25}{4}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2}} = 6\frac{1}{4} = 6.25$$