Let's solve each of the red-written expressions using only the number
4 and standard mathematical operations. The goal is to evaluate each expression step by step.
We’ll go through each one:
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32. $ 4^{\sqrt{4}} + (4 \cdot 4) $
- $ \sqrt{4} = 2 $
- So $ 4^{\sqrt{4}} = 4^2 = 16 $
- $ 4 \cdot 4 = 16 $
- Total: $ 16 + 16 = 32 $
✔ Answer: 32
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36. $ 4! + 4 + 4 + 4 $
- $ 4! = 24 $
- $ 24 + 4 + 4 + 4 = 36 $
✔ Answer: 36
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43. $ 44 - \frac{4}{4} $
- $ \frac{4}{4} = 1 $
- $ 44 - 1 = 43 $
✔ Answer: 43
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44. $ 44 \times \frac{4}{4} $
- $ \frac{4}{4} = 1 $
- $ 44 \times 1 = 44 $
✔ Answer: 44
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48. $ 4! + 4! + (4 - 4) $
- $ 4! = 24 $
- So $ 24 + 24 = 48 $
- $ 4 - 4 = 0 $
- $ 48 + 0 = 48 $
✔ Answer: 48
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56. $ 4! + 4! + 4 + 4 $
- $ 4! = 24 $
- $ 24 + 24 = 48 $
- $ 4 + 4 = 8 $
- $ 48 + 8 = 56 $
✔ Answer: 56
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64. $ 44 + 4! - 4 $
- $ 4! = 24 $
- $ 44 + 24 = 68 $
- $ 68 - 4 = 64 $
✔ Answer: 64
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72. $ 44 + 4! + 4 $
- $ 4! = 24 $
- $ 44 + 24 = 68 $
- $ 68 + 4 = 72 $
✔ Answer: 72
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76. $ 4! + 4! + 4! + 4 $
- $ 4! = 24 $
- $ 24 + 24 + 24 = 72 $
- $ 72 + 4 = 76 $
✔ Answer: 76
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80. $ 4(4!) - (4 \cdot 4) $
- $ 4! = 24 $
- $ 4 \cdot 24 = 96 $
- $ 4 \cdot 4 = 16 $
- $ 96 - 16 = 80 $
✔ Answer: 80
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Summary Table:
| Problem | Expression | Answer |
|--------|------------|--------|
| 32 | $ 4^{\sqrt{4}} + (4 \cdot 4) $ | 32 |
| 36 | $ 4! + 4 + 4 + 4 $ | 36 |
| 43 | $ 44 - \frac{4}{4} $ | 43 |
| 44 | $ 44 \times \frac{4}{4} $ | 44 |
| 48 | $ 4! + 4! + (4 - 4) $ | 48 |
| 56 | $ 4! + 4! + 4 + 4 $ | 56 |
| 64 | $ 44 + 4! - 4 $ | 64 |
| 72 | $ 44 + 4! + 4 $ | 72 |
| 76 | $ 4! + 4! + 4! + 4 $ | 76 |
| 80 | $ 4(4!) - (4 \cdot 4) $ | 80 |
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Final Note:
These problems are part of a classic "Four 4s" puzzle, where you use exactly four 4s (and sometimes more than four) with operations to generate numbers. Here, the expressions are designed to produce the number shown in the left column using combinations of 4s.
All calculations are correct and consistent.
✔
Let me know if you'd like to see how to make other numbers using only four 4s!
Parent Tip: Review the logic above to help your child master the concept of four fours worksheet answers.
