1. **State the problem:** Using numbers 1 through 10 and the number 119, find expressions to get the numbers 4, 30, 36, 52, and 57. 2. **Important rules:** We can use addition, subtraction, multiplication, and division with numbers 1 to 10 and 119 to form the target numbers. 3. **Find 4:** We can use subtraction: $$119 - 115 = 4$$ Since 115 is not directly from 1 to 10, try another way: $$4 = 8 - 4$$ (using numbers 1 to 10 directly) 4. **Find 30:** Using multiplication: $$30 = 5 \times 6$$ Both 5 and 6 are between 1 and 10. 5. **Find 36:** Using multiplication: $$36 = 6 \times 6$$ 6. **Find 52:** Try addition and multiplication: $$52 = 10 \times 5 + 2$$ 7. **Find 57:** Try addition and multiplication: $$57 = 10 \times 5 + 7$$ **Summary:** - 4 = 8 - 4 - 30 = 5 \times 6 - 36 = 6 \times 6 - 52 = 10 \times 5 + 2 - 57 = 10 \times 5 + 7 These use only numbers 1 through 10 and basic operations to get the target numbers.