Solve |-7/2|+6+(-5/7)

$$| - \frac { 7 } { 2 } | + 6 + ( - \frac { 5 } { 7 } )$$

Evaluate

$$\frac{123}{14}\approx 8.785714286$$

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{7}{2} is \frac{7}{2}.

$$\frac{7}{2}+6-\frac{5}{7}$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{7}{2}+\frac{12}{2}-\frac{5}{7}$$

Since \frac{7}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$\frac{7+12}{2}-\frac{5}{7}$$

Add 7 and 12 to get 19.

$$\frac{19}{2}-\frac{5}{7}$$

Least common multiple of 2 and 7 is 14. Convert \frac{19}{2} and \frac{5}{7} to fractions with denominator 14.

$$\frac{133}{14}-\frac{10}{14}$$

Since \frac{133}{14} and \frac{10}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{133-10}{14}$$

Subtract 10 from 133 to get 123.

$$\frac{123}{14}$$

Factor

$$\frac{3 \cdot 41}{2 \cdot 7} = 8\frac{11}{14} = 8.785714285714286$$