1. **State the problem:** Starting from the number 114, use basic operations (addition, subtraction, multiplication, division) to reach the target numbers 10, 28, 30, 46, and 57. 2. **Important rules:** We can use any combination of basic arithmetic operations to transform 114 into each target number. 3. **Find each target number:** - To get 10 from 114: $$114 - 104 = 10$$ For example, $$104 = 2 \times 52$$, so one way is $$114 - 2 \times 52 = 10$$. - To get 28 from 114: $$114 \div 4 + 0 = 28.5$$ (not exact), so try subtraction: $$114 - 86 = 28$$ Since $$86 = 2 \times 43$$, we can write $$114 - 2 \times 43 = 28$$. - To get 30 from 114: $$114 - 84 = 30$$ $$84 = 7 \times 12$$, so $$114 - 7 \times 12 = 30$$. - To get 46 from 114: $$114 - 68 = 46$$ $$68 = 4 \times 17$$, so $$114 - 4 \times 17 = 46$$. - To get 57 from 114: $$114 \div 2 = 57$$ 4. **Summary of operations:** $$\begin{aligned} &114 - 2 \times 52 = 10 \\ &114 - 2 \times 43 = 28 \\ &114 - 7 \times 12 = 30 \\ &114 - 4 \times 17 = 46 \\ &114 \div 2 = 57 \end{aligned}$$ These are straightforward ways to reach each target number using basic operations starting from 114.