We must find the common denominator.
It's LCM of 9 and 6.
Multiples of 6: 0, 6, 12, 18, 24, ...
Multiples of 9: 0, 9, 18, 27, ...
LCM(6, 9) = 18
18 = 3 · 6
18 = 2 · 9
[tex]\dfrac{4}{9}=\dfrac{4\cdot2}{9\cdot2}=\dfrac{8}{18}\\\\\dfrac{5}{6}=\dfrac{5\cdot3}{6\cdot3}=\dfrac{15}{18}\\\\\dfrac{4}{9}+\dfrac{5}{6}=\dfrac{8}{18}+\dfrac{15}{18}=\dfrac{8+15}{18}=\dfrac{23}{18}=\dfrac{18+5}{18}=1\dfrac{5}{18}[/tex]
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Other method:
[tex]\dfrac{4}{9}+\dfrac{5}{6}=\dfrac{4\cdot6}{9\cdot6}+\dfrac{5\cdot9}{6\cdot9}=\dfrac{24}{54}+\dfrac{45}{54}=\dfrac{24+45}{54}=\dfrac{69}{54}=\dfrac{54+15}{54}\\\\=1\dfrac{15}{54}=1\dfrac{15:3}{54:3}=1\dfrac{5}{18}[/tex]
