Solve (-163/4)-(-101/4)-(+11/2)

$$( - 16 \frac { 3 } { 4 } ) - ( - 10 \frac { 1 } { 4 } ) - ( + 1 \frac { 1 } { 2 } )$$

Evaluate

$$-8$$

Solution Steps

Multiply 16 and 4 to get 64.

$$-\frac{64+3}{4}-\left(-\frac{10\times 4+1}{4}\right)-\frac{1\times 2+1}{2}$$

Add 64 and 3 to get 67.

$$-\frac{67}{4}-\left(-\frac{10\times 4+1}{4}\right)-\frac{1\times 2+1}{2}$$

Multiply 10 and 4 to get 40.

$$-\frac{67}{4}-\left(-\frac{40+1}{4}\right)-\frac{1\times 2+1}{2}$$

Add 40 and 1 to get 41.

$$-\frac{67}{4}-\left(-\frac{41}{4}\right)-\frac{1\times 2+1}{2}$$

The opposite of -\frac{41}{4} is \frac{41}{4}.

$$-\frac{67}{4}+\frac{41}{4}-\frac{1\times 2+1}{2}$$

Since -\frac{67}{4} and \frac{41}{4} have the same denominator, add them by adding their numerators.

$$\frac{-67+41}{4}-\frac{1\times 2+1}{2}$$

Add -67 and 41 to get -26.

$$\frac{-26}{4}-\frac{1\times 2+1}{2}$$

Reduce the fraction \frac{-26}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{13}{2}-\frac{1\times 2+1}{2}$$

Multiply 1 and 2 to get 2.

$$-\frac{13}{2}-\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$-\frac{13}{2}-\frac{3}{2}$$

Since -\frac{13}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-13-3}{2}$$

Subtract 3 from -13 to get -16.

$$\frac{-16}{2}$$

Divide -16 by 2 to get -8.

$$-8$$

Factor

$$-8$$