1. **Stating the problem:** We need to perform division algorithms with remainders for the following divisions: 164 ÷ 19, 179 ÷ 24, and 171 ÷ 23. Then, solve two word problems involving buying jerseys and tennis shoes with given budgets. 2. **Division algorithm formula:** When dividing a dividend $D$ by a divisor $d$, we find quotient $q$ and remainder $r$ such that: $$D = q \times d + r$$ where $0 \leq r < d$. 3. **Division calculations:** - For $164 \div 19$: - $19 \times 8 = 152$ - Remainder $r = 164 - 152 = 12$ - So, $164 = 8 \times 19 + 12$ - For $179 \div 24$: - $24 \times 7 = 168$ - Remainder $r = 179 - 168 = 11$ - So, $179 = 7 \times 24 + 11$ - For $171 \div 23$: - $23 \times 7 = 161$ - Remainder $r = 171 - 161 = 10$ - So, $171 = 7 \times 23 + 10$ 4. **Word problem 2.1:** - Team has 16 players and 165 money units. - Each jersey costs 12. - Total cost for 16 jerseys: $16 \times 12 = 192$ - Since $165 < 192$, they cannot buy jerseys for all players. 5. **Word problem 2.2:** - Federation gave 387 money units. - Each pair of tennis shoes costs 23. - Number of players: 16 - Total cost for 16 pairs: $16 \times 23 = 368$ - Since $387 \geq 368$, they can buy one pair for each player. **Final answers:** - $164 \div 19 = 8$ remainder $12$ - $179 \div 24 = 7$ remainder $11$ - $171 \div 23 = 7$ remainder $10$ - Jerseys: Cannot buy for all players. - Tennis shoes: Can buy for all players.