Division Simplification
**Bo'linishni bajaring:**
1. $3 \frac{1}{2} : 2 \frac{1}{3} = \frac{7}{2} \div \frac{7}{3} = \frac{7}{2} \times \frac{3}{7} = \frac{3}{2}$
2. $10 \frac{4}{5} : 5 \frac{2}{5} = \frac{54}{5} \div \frac{27}{5} = 2$
3. $12 \frac{1}{2} : 5 = \frac{25}{2} \div 5 = \frac{25}{2} \times \frac{1}{5} = \frac{5}{2} = 2 \frac{1}{2}$
4. $2 \frac{5}{8} : 1 \frac{3}{4} = \frac{21}{8} \div \frac{7}{4} = \frac{21}{8} \times \frac{4}{7} = \frac{3}{2} = 1 \frac{1}{2}$
5. $\frac{5}{6} : 1 \frac{2}{3} = \frac{5}{6} \div \frac{5}{3} = \frac{5}{6} \times \frac{3}{5} = \frac{1}{2}$
6. $13 : 2 \frac{4}{11} = 13 \div \frac{26}{11} = 13 \times \frac{11}{26} = \frac{143}{26} = 5 \frac{13}{26} = 5 \frac{1}{2}$
7. $5 \frac{1}{9} : 7 \frac{2}{3} = \frac{46}{9} \div \frac{23}{3} = \frac{46}{9} \times \frac{3}{23} = \frac{2}{3}$
8. $3 \frac{1}{7} : \frac{4}{7} = \frac{22}{7} \div \frac{4}{7} = \frac{22}{7} \times \frac{7}{4} = \frac{22}{4} = 5 \frac{1}{2}$
9. $1 : \frac{1}{15} = 1 \div \frac{1}{15} = 15$
10. $4 \frac{1}{9} : 3 \frac{2}{3} = \frac{37}{9} \div \frac{11}{3} = \frac{37}{9} \times \frac{3}{11} = \frac{37}{33} = 1 \frac{4}{33}$
11. $\frac{15}{38} : 1 \frac{1}{19} = \frac{15}{38} \div \frac{20}{19} = \frac{15}{38} \times \frac{19}{20} = \frac{285}{760} = \frac{57}{152}$
12. $7 \frac{1}{2} : 12 \frac{1}{4} : \frac{49}{8} = \frac{15}{2} \div \frac{49}{4} \div \frac{49}{8} = \frac{15}{2} \times \frac{4}{49} \times \frac{8}{49} = \frac{15 \times 4 \times 8}{2 \times 49 \times 49} = \frac{480}{4802} = \frac{240}{2401}$
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**Oddiy kasrlar ustida to'rt amalga doir mashqlar** (1 savol namunasi):
1. $\left( \frac{7}{10} + \left(1 \frac{1}{3} - \frac{2}{9}\right) \div \left( \frac{1}{2} \frac{2}{9} + 2 \frac{1}{2} \left( \frac{1}{3} + \frac{1}{6} \right) \right) \right)$
Yechim bosqichlari:
1. $1 \frac{1}{3} = \frac{4}{3}$; $\frac{4}{3} - \frac{2}{9} = \frac{12}{9} - \frac{2}{9} = \frac{10}{9}$
2. $\frac{1}{2} \frac{2}{9} = \frac{1}{2} \times \frac{2}{9} = \frac{1}{9}$
3. $2 \frac{1}{2} = \frac{5}{2}$; $\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$
4. $\frac{5}{2} \times \frac{1}{2} = \frac{5}{4}$
5. $\frac{1}{9} + \frac{5}{4} = \frac{4}{36} + \frac{45}{36} = \frac{49}{36}$
6. $\frac{10}{9} \div \frac{49}{36} = \frac{10}{9} \times \frac{36}{49} = \frac{360}{441} = \frac{40}{49}$
7. $\frac{7}{10} + \frac{40}{49} = \frac{343}{490} + \frac{400}{490} = \frac{743}{490} = 1 \frac{253}{490}$
Natija: $1 \frac{253}{490}$
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**Tenglamani yeching (1 ta misol namunasi):**
1. $x - 3 \frac{1}{4} \cdot 1 \frac{3}{13} = 10$
Bosqichlar:
1. $3 \frac{1}{4} = \frac{13}{4}$, $1 \frac{3}{13} = \frac{16}{13}$
2. $\frac{13}{4} \times \frac{16}{13} = 4$
3. Tenglama: $x - 4 = 10$
4. $x = 10 + 4 = 14$
Natija: $x=14$