Solve (+173/4)-(+6.25)-(-81/2)+(-0.75)-(-221/4)

$$( + 17 \frac { 3 } { 4 } ) - ( + 6.25 ) - ( - 8 \frac { 1 } { 2 } ) + ( - 0.75 ) - ( - 22 \frac { 1 } { 4 } )$$

Evaluate

$$41.5$$

Solution Steps

Multiply 17 and 4 to get 68.

$$\frac{68+3}{4}-6.25-\left(-\frac{8\times 2+1}{2}\right)-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Add 68 and 3 to get 71.

$$\frac{71}{4}-6.25-\left(-\frac{8\times 2+1}{2}\right)-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Convert decimal number 6.25 to fraction \frac{625}{100}. Reduce the fraction \frac{625}{100} to lowest terms by extracting and canceling out 25.

$$\frac{71}{4}-\frac{25}{4}-\left(-\frac{8\times 2+1}{2}\right)-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Since \frac{71}{4} and \frac{25}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{71-25}{4}-\left(-\frac{8\times 2+1}{2}\right)-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Subtract 25 from 71 to get 46.

$$\frac{46}{4}-\left(-\frac{8\times 2+1}{2}\right)-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Reduce the fraction \frac{46}{4} to lowest terms by extracting and canceling out 2.

$$\frac{23}{2}-\left(-\frac{8\times 2+1}{2}\right)-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Multiply 8 and 2 to get 16.

$$\frac{23}{2}-\left(-\frac{16+1}{2}\right)-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Add 16 and 1 to get 17.

$$\frac{23}{2}-\left(-\frac{17}{2}\right)-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

The opposite of -\frac{17}{2} is \frac{17}{2}.

$$\frac{23}{2}+\frac{17}{2}-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Since \frac{23}{2} and \frac{17}{2} have the same denominator, add them by adding their numerators.

$$\frac{23+17}{2}-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Add 23 and 17 to get 40.

$$\frac{40}{2}-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Divide 40 by 2 to get 20.

$$20-0.75-\left(-\frac{22\times 4+1}{4}\right)$$

Subtract 0.75 from 20 to get 19.25.

$$19.25-\left(-\frac{22\times 4+1}{4}\right)$$

Multiply 22 and 4 to get 88.

$$19.25-\left(-\frac{88+1}{4}\right)$$

Add 88 and 1 to get 89.

$$19.25-\left(-\frac{89}{4}\right)$$

The opposite of -\frac{89}{4} is \frac{89}{4}.

$$19.25+\frac{89}{4}$$

Convert decimal number 19.25 to fraction \frac{1925}{100}. Reduce the fraction \frac{1925}{100} to lowest terms by extracting and canceling out 25.

$$\frac{77}{4}+\frac{89}{4}$$

Since \frac{77}{4} and \frac{89}{4} have the same denominator, add them by adding their numerators.

$$\frac{77+89}{4}$$

Add 77 and 89 to get 166.

$$\frac{166}{4}$$

Reduce the fraction \frac{166}{4} to lowest terms by extracting and canceling out 2.

$$\frac{83}{2}$$

Factor

$$\frac{83}{2} = 41\frac{1}{2} = 41.5$$