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\frac{35}{90}+\frac{3}{90}
Least common multiple of 18 and 30 is 90. Convert \frac{7}{18} and \frac{1}{30} to fractions with denominator 90.
\frac{35+3}{90}
Since \frac{35}{90} and \frac{3}{90} have the same denominator, add them by adding their numerators.
\frac{38}{90}
Add 35 and 3 to get 38.
\frac{19}{45}
Reduce the fraction \frac{38}{90} to lowest terms by extracting and canceling out 2.