Solve |1/4-2/4+6/4+|3-1/5-frac{11}{5}

$$| \frac { 1 } { 4 } - \frac { 2 } { 4 } + \frac { 6 } { 4 } + | \frac { 3 - 1 } { 5 } - \frac { 11 } { 5 }$$

Evaluate

$$\frac{61}{20}=3.05$$

Solution Steps

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

$$|\frac{1-2}{4}+\frac{6}{4}+|\frac{3-1}{5}-\frac{11}{5}||$$

Subtract 2 from 1 to get -1.

$$|-\frac{1}{4}+\frac{6}{4}+|\frac{3-1}{5}-\frac{11}{5}||$$

Since -\frac{1}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$|\frac{-1+6}{4}+|\frac{3-1}{5}-\frac{11}{5}||$$

Add -1 and 6 to get 5.

$$|\frac{5}{4}+|\frac{3-1}{5}-\frac{11}{5}||$$

Subtract 1 from 3 to get 2.

$$|\frac{5}{4}+|\frac{2}{5}-\frac{11}{5}||$$

Since \frac{2}{5} and \frac{11}{5} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{5}{4}+|\frac{2-11}{5}||$$

Subtract 11 from 2 to get -9.

$$|\frac{5}{4}+|-\frac{9}{5}||$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{9}{5} is \frac{9}{5}.

$$|\frac{5}{4}+\frac{9}{5}|$$

Least common multiple of 4 and 5 is 20. Convert \frac{5}{4} and \frac{9}{5} to fractions with denominator 20.

$$|\frac{25}{20}+\frac{36}{20}|$$

Since \frac{25}{20} and \frac{36}{20} have the same denominator, add them by adding their numerators.

$$|\frac{25+36}{20}|$$

Add 25 and 36 to get 61.

$$|\frac{61}{20}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{61}{20} is \frac{61}{20}.

$$\frac{61}{20}$$

Factor

$$\frac{61}{2 ^ {2} \cdot 5} = 3\frac{1}{20} = 3.05$$