Solve 10/4-3/2div[6-8/3]4-9/2

$$\frac { 10 } { 4 } - \frac { 3 } { 2 } \div [ \frac { 6 - 8 } { 3 } ] 4 - \frac { 9 } { 2 }$$

Evaluate

$$7$$

Solution Steps

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}-\frac{\frac{3}{2}}{\frac{6-8}{3}}\times 4-\frac{9}{2}$$

Divide \frac{3}{2} by \frac{6-8}{3} by multiplying \frac{3}{2} by the reciprocal of \frac{6-8}{3}.

$$\frac{5}{2}-\frac{3\times 3}{2\left(6-8\right)}\times 4-\frac{9}{2}$$

Multiply 3 and 3 to get 9.

$$\frac{5}{2}-\frac{9}{2\left(6-8\right)}\times 4-\frac{9}{2}$$

Subtract 8 from 6 to get -2.

$$\frac{5}{2}-\frac{9}{2\left(-2\right)}\times 4-\frac{9}{2}$$

Multiply 2 and -2 to get -4.

$$\frac{5}{2}-\frac{9}{-4}\times 4-\frac{9}{2}$$

Fraction \frac{9}{-4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{5}{2}-\left(-\frac{9}{4}\times 4\right)-\frac{9}{2}$$

Cancel out 4 and 4.

$$\frac{5}{2}-\left(-9\right)-\frac{9}{2}$$

The opposite of -9 is 9.

$$\frac{5}{2}+9-\frac{9}{2}$$

Convert 9 to fraction \frac{18}{2}.

$$\frac{5}{2}+\frac{18}{2}-\frac{9}{2}$$

Since \frac{5}{2} and \frac{18}{2} have the same denominator, add them by adding their numerators.

$$\frac{5+18}{2}-\frac{9}{2}$$

Add 5 and 18 to get 23.

$$\frac{23}{2}-\frac{9}{2}$$

Since \frac{23}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-9}{2}$$

Subtract 9 from 23 to get 14.

$$\frac{14}{2}$$

Divide 14 by 2 to get 7.

$$7$$

Factor

$$7$$