Solve |5/6|-1/2+17/24

$$| \frac { 5 } { 6 } | - \frac { 1 } { 2 } + \frac { 17 } { 24 }$$

Evaluate

$$\frac{25}{24}\approx 1.041666667$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{5}{6} is \frac{5}{6}.

$$\frac{5}{6}-\frac{1}{2}+\frac{17}{24}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{5}{6}-\frac{3}{6}+\frac{17}{24}$$

Since \frac{5}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-3}{6}+\frac{17}{24}$$

Subtract 3 from 5 to get 2.

$$\frac{2}{6}+\frac{17}{24}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}+\frac{17}{24}$$

Least common multiple of 3 and 24 is 24. Convert \frac{1}{3} and \frac{17}{24} to fractions with denominator 24.

$$\frac{8}{24}+\frac{17}{24}$$

Since \frac{8}{24} and \frac{17}{24} have the same denominator, add them by adding their numerators.

$$\frac{8+17}{24}$$

Add 8 and 17 to get 25.

$$\frac{25}{24}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {3} \cdot 3} = 1\frac{1}{24} = 1.0416666666666667$$