Mixed numbers

Solve and give the result as a mixed number:

  1. $5\dfrac{8}{9}+2\dfrac{7}{11}$
  2. $\dfrac{45}{8}-2\dfrac{1}{3}$
  3. $27\dfrac{1}{2}-\dfrac{84}{7}$
  4. $\dfrac{23}{3}+\dfrac{9}{5}$
  1. $5\dfrac{8}{9}+2\dfrac{7}{11}=(5+2)+\Big(\dfrac{8}{9}+\dfrac{7}{11}\Big)=$ $=7+\Big(\dfrac{8\cdot11}{9\cdot11}+\dfrac{7\cdot9}{11\cdot9}\Big)=7+\dfrac{88+63}{99}=7+\dfrac{151}{99}=$ $=7+1+\dfrac{52}{99}=8\dfrac{52}{99}$
  2. $\dfrac{45}{8}-2\dfrac{1}{3}=5\dfrac{5}{8}-2\dfrac{1}{3}=5-2+\Big(\dfrac{5}{8}-\dfrac{1}{3}\Big)=3+\dfrac{15-8}{24}=3+\dfrac{7}{24}=3\dfrac{7}{24}$
  3. $27\dfrac{1}{2}-\dfrac{84}{7}=27\dfrac{1}{2}-12=27-12+\dfrac{1}{2}=$ $15+\dfrac{1}{2}=15\dfrac{1}{2}$
  4. $\dfrac{23}{3}+\dfrac{9}{5}=7\dfrac{2}{3}+1\dfrac{4}{5}=(7+1)+\Big(\dfrac{2}{3}+\dfrac{4}{5}\Big)=$ $=8+\dfrac{10+12}{15}=8+\dfrac{22}{15}=8+1+\dfrac{7}{15}=9\dfrac{7}{15}$
  1. $8\dfrac{52}{99}$
  2. $3\dfrac{7}{24}$
  3. $15\dfrac{1}{2}$
  4. $9\dfrac{7}{15}$
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