Problems from Mixed numbers

Development:

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

Solution:

1. $8{\displaystyle \frac{52}{99}}$
2. $3{\displaystyle \frac{7}{24}}$
3. $15{\displaystyle \frac{1}{2}}$
4. $9{\displaystyle \frac{7}{15}}$

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