Solve |1/2-1/4|-5|1/4-1/2|

$$| \frac { 1 } { 2 } - \frac { 1 } { 4 } | - 5 | \frac { 1 } { 4 } - \frac { 1 } { 2 } |$$

Evaluate

$$-1$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$|\frac{2}{4}-\frac{1}{4}|-5|\frac{1}{4}-\frac{1}{2}|$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{2-1}{4}|-5|\frac{1}{4}-\frac{1}{2}|$$

Subtract 1 from 2 to get 1.

$$|\frac{1}{4}|-5|\frac{1}{4}-\frac{1}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{1}{4} is \frac{1}{4}.

$$\frac{1}{4}-5|\frac{1}{4}-\frac{1}{2}|$$

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{1}{4}-5|\frac{1}{4}-\frac{2}{4}|$$

Since \frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}-5|\frac{1-2}{4}|$$

Subtract 2 from 1 to get -1.

$$\frac{1}{4}-5|-\frac{1}{4}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{4} is \frac{1}{4}.

$$\frac{1}{4}-5\times \frac{1}{4}$$

Multiply 5 and \frac{1}{4} to get \frac{5}{4}.

$$\frac{1}{4}-\frac{5}{4}$$

Since \frac{1}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-5}{4}$$

Subtract 5 from 1 to get -4.

$$\frac{-4}{4}$$

Divide -4 by 4 to get -1.

$$-1$$

Factor

$$-1$$