Solve 133/4+(-0.25)-(-41/4)+|-3-1/4|

$$13 \frac { 3 } { 4 } + ( - 0.25 ) - ( - 4 \frac { 1 } { 4 } ) + | - 3 - \frac { 1 } { 4 } |$$

Evaluate

$$21$$

Solution Steps

Multiply 13 and 4 to get 52.

$$\frac{52+3}{4}-0.25-\left(-\frac{4\times 4+1}{4}\right)+|-3-\frac{1}{4}|$$

Add 52 and 3 to get 55.

$$\frac{55}{4}-0.25-\left(-\frac{4\times 4+1}{4}\right)+|-3-\frac{1}{4}|$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{55}{4}-\frac{1}{4}-\left(-\frac{4\times 4+1}{4}\right)+|-3-\frac{1}{4}|$$

Since \frac{55}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-1}{4}-\left(-\frac{4\times 4+1}{4}\right)+|-3-\frac{1}{4}|$$

Subtract 1 from 55 to get 54.

$$\frac{54}{4}-\left(-\frac{4\times 4+1}{4}\right)+|-3-\frac{1}{4}|$$

Reduce the fraction \frac{54}{4} to lowest terms by extracting and canceling out 2.

$$\frac{27}{2}-\left(-\frac{4\times 4+1}{4}\right)+|-3-\frac{1}{4}|$$

Multiply 4 and 4 to get 16.

$$\frac{27}{2}-\left(-\frac{16+1}{4}\right)+|-3-\frac{1}{4}|$$

Add 16 and 1 to get 17.

$$\frac{27}{2}-\left(-\frac{17}{4}\right)+|-3-\frac{1}{4}|$$

The opposite of -\frac{17}{4} is \frac{17}{4}.

$$\frac{27}{2}+\frac{17}{4}+|-3-\frac{1}{4}|$$

Least common multiple of 2 and 4 is 4. Convert \frac{27}{2} and \frac{17}{4} to fractions with denominator 4.

$$\frac{54}{4}+\frac{17}{4}+|-3-\frac{1}{4}|$$

Since \frac{54}{4} and \frac{17}{4} have the same denominator, add them by adding their numerators.

$$\frac{54+17}{4}+|-3-\frac{1}{4}|$$

Add 54 and 17 to get 71.

$$\frac{71}{4}+|-3-\frac{1}{4}|$$

Convert -3 to fraction -\frac{12}{4}.

$$\frac{71}{4}+|-\frac{12}{4}-\frac{1}{4}|$$

Since -\frac{12}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{71}{4}+|\frac{-12-1}{4}|$$

Subtract 1 from -12 to get -13.

$$\frac{71}{4}+|-\frac{13}{4}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{13}{4} is \frac{13}{4}.

$$\frac{71}{4}+\frac{13}{4}$$

Since \frac{71}{4} and \frac{13}{4} have the same denominator, add them by adding their numerators.

$$\frac{71+13}{4}$$

Add 71 and 13 to get 84.

$$\frac{84}{4}$$

Divide 84 by 4 to get 21.

$$21$$

Factor

$$3\times 7$$