1. **Problem:** Rewrite the number 24 as an expression using addition, subtraction, multiplication, and division exactly once each. 2. **Step 1: Understand the operations** We need to use addition (+), subtraction (-), multiplication (\times), and division (\div) each exactly once to form the number 24. 3. **Step 2: Set up the expression** Let’s try to find numbers and operations that satisfy: $$ a + b - c \times d \div e = 24 $$ where each operation (+, -, \times, \div) is used once. 4. **Step 3: Trial and error with simple numbers** Try the expression: $$ 6 \times 4 - 8 \div 2 $$ Calculate stepwise: $$ 6 \times 4 = 24 $$ $$ 8 \div 2 = 4 $$ Then: $$ 24 - 4 = 20 $$ This is 20, not 24. 5. **Step 4: Adjust numbers** Try: $$ 8 \times 4 - 6 \div 3 $$ Calculate: $$ 8 \times 4 = 32 $$ $$ 6 \div 3 = 2 $$ Then: $$ 32 - 2 = 30 $$ Still not 24. 6. **Step 5: Try another arrangement** Try: $$ 12 + 6 \times 4 \div 3 - 2 $$ Calculate multiplication and division first: $$ 6 \times 4 = 24 $$ $$ 24 \div 3 = 8 $$ Then addition and subtraction: $$ 12 + 8 = 20 $$ $$ 20 - 2 = 18 $$ Not 24. 7. **Step 6: Find a working expression** Try: $$ 6 \times 4 + 8 \div 2 - 4 $$ Calculate multiplication and division: $$ 6 \times 4 = 24 $$ $$ 8 \div 2 = 4 $$ Then addition and subtraction: $$ 24 + 4 = 28 $$ $$ 28 - 4 = 24 $$ 8. **Step 7: Verify operations used once each** Operations used: +, -, \times, \div each once. 9. **Final answer:** $$ 6 \times 4 + 8 \div 2 - 4 = 24 $$