Solve |-21/2|-(-2.5)+1-|1-21/2|

$$| - 2 \frac { 1 } { 2 } | - ( - 2.5 ) + 1 - | 1 - 2 \frac { 1 } { 2 } |$$

Evaluate

$$4.5$$

Solution Steps

Multiply 2 and 2 to get 4.

$$|-\frac{4+1}{2}|-\left(-2.5\right)+1-|1-\frac{2\times 2+1}{2}|$$

Add 4 and 1 to get 5.

$$|-\frac{5}{2}|-\left(-2.5\right)+1-|1-\frac{2\times 2+1}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{5}{2} is \frac{5}{2}.

$$\frac{5}{2}-\left(-2.5\right)+1-|1-\frac{2\times 2+1}{2}|$$

The opposite of -2.5 is 2.5.

$$\frac{5}{2}+2.5+1-|1-\frac{2\times 2+1}{2}|$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{5}{2}+\frac{5}{2}+1-|1-\frac{2\times 2+1}{2}|$$

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

$$\frac{5+5}{2}+1-|1-\frac{2\times 2+1}{2}|$$

Add 5 and 5 to get 10.

$$\frac{10}{2}+1-|1-\frac{2\times 2+1}{2}|$$

Divide 10 by 2 to get 5.

$$5+1-|1-\frac{2\times 2+1}{2}|$$

Add 5 and 1 to get 6.

$$6-|1-\frac{2\times 2+1}{2}|$$

Multiply 2 and 2 to get 4.

$$6-|1-\frac{4+1}{2}|$$

Add 4 and 1 to get 5.

$$6-|1-\frac{5}{2}|$$

Convert 1 to fraction \frac{2}{2}.

$$6-|\frac{2}{2}-\frac{5}{2}|$$

Since \frac{2}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$6-|\frac{2-5}{2}|$$

Subtract 5 from 2 to get -3.

$$6-|-\frac{3}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{3}{2} is \frac{3}{2}.

$$6-\frac{3}{2}$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{12}{2}-\frac{3}{2}$$

Since \frac{12}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-3}{2}$$

Subtract 3 from 12 to get 9.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$