Solve tan1/2|1/2+1/3-1/4|+|frac{1}{3}+frac{1}{2}-1|

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

Evaluate

$$\frac{128817940717701551}{750000000000000000}\approx 0.171757254$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.005090587623602068 + | \frac{1}{3} + \frac{1}{2} - 1 |$$

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

$$0.005090587623602068+|\frac{2}{6}+\frac{3}{6}-1|$$

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

$$0.005090587623602068+|\frac{2+3}{6}-1|$$

Add 2 and 3 to get 5.

$$0.005090587623602068+|\frac{5}{6}-1|$$

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

$$0.005090587623602068+|\frac{5}{6}-\frac{6}{6}|$$

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

$$0.005090587623602068+|\frac{5-6}{6}|$$

Subtract 6 from 5 to get -1.

$$0.005090587623602068+|-\frac{1}{6}|$$

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}.

$$0.005090587623602068+\frac{1}{6}$$

Convert decimal number 0.005090587623602068 to fraction \frac{1272646905900517}{10000000000}. Reduce the fraction \frac{1272646905900517}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1272646905900517}{250000000000000000}+\frac{1}{6}$$

Least common multiple of 250000000000000000 and 6 is 750000000000000000. Convert \frac{1272646905900517}{250000000000000000} and \frac{1}{6} to fractions with denominator 750000000000000000.

$$\frac{3817940717701551}{750000000000000000}+\frac{125000000000000000}{750000000000000000}$$

Since \frac{3817940717701551}{750000000000000000} and \frac{125000000000000000}{750000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{3817940717701551+125000000000000000}{750000000000000000}$$

Add 3817940717701551 and 125000000000000000 to get 128817940717701551.

$$\frac{128817940717701551}{750000000000000000}$$

Factor

$$\frac{27697 \cdot 4650970889183}{3 \cdot 2 ^ {16} \cdot 5 ^ {18}} = 0.17175725429026872$$