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

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

Evaluate

$$\frac{19}{24}\approx 0.791666667$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

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

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

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

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

$$\frac{5}{6}-\frac{1}{4}||\frac{5}{6}-1||$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{5}{6}-\frac{1}{4}||\frac{5}{6}-\frac{6}{6}||$$

Since \frac{5}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-\frac{1}{4}||\frac{5-6}{6}||$$

Subtract 6 from 5 to get -1.

$$\frac{5}{6}-\frac{1}{4}||-\frac{1}{6}||$$

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}{6} is \frac{1}{6}.

$$\frac{5}{6}-\frac{1}{4}|\frac{1}{6}|$$

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}{6} is \frac{1}{6}.

$$\frac{5}{6}-\frac{1}{4}\times \frac{1}{6}$$

Multiply \frac{1}{4} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}-\frac{1\times 1}{4\times 6}$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 6}.

$$\frac{5}{6}-\frac{1}{24}$$

Least common multiple of 6 and 24 is 24. Convert \frac{5}{6} and \frac{1}{24} to fractions with denominator 24.

$$\frac{20}{24}-\frac{1}{24}$$

Since \frac{20}{24} and \frac{1}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-1}{24}$$

Subtract 1 from 20 to get 19.

$$\frac{19}{24}$$

Factor

$$\frac{19}{2 ^ {3} \cdot 3} = 0.7916666666666666$$