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When working with mixed numbers it is usually easier to convert to improper fractions, work with the numbers and convert any resulting improper fraction back to a mixed number:
3 5/11 + 7 2/3 = (3×11+5)/11 + (7×3+2)/3
= 38/11 + 23/3
= (38×3)/(11×3) + (23×11)/(3×11)
= 114/33 + 253/33
= 367/33
= (11×33+4)/33
= 11 4/33
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