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\frac{4}{5}+|-\frac{2}{7}|
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{4}{5} is \frac{4}{5}.
\frac{4}{5}+\frac{2}{7}
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{2}{7} is \frac{2}{7}.
\frac{28}{35}+\frac{10}{35}
Least common multiple of 5 and 7 is 35. Convert \frac{4}{5} and \frac{2}{7} to fractions with denominator 35.
\frac{28+10}{35}
Since \frac{28}{35} and \frac{10}{35} have the same denominator, add them by adding their numerators.
\frac{38}{35}
Add 28 and 10 to get 38.