Which of these is an example of the commutative propert $$ \begin{array}{ll}12 imes 1=12 & ext { ii) } 6+7=15-2 \ 21 \div 3=3+4 & ext { iv) } 14+4=4+14 \ ext { Which of these does not show } & ext { the commutative property? } \ 22 imes 4=4 imes 22 & ext { ii) } 12-4=2 imes 4 \ 5+6=11=6+5 & ext { iv) } 31+72=72+31\end{array} $$

Question

Which of these is an example of the commutative propert $$ \begin{array}{ll}12 	imes 1=12 & 	ext { ii) } 6+7=15-2 \ 21 \div 3=3+4 & 	ext { iv) } 14+4=4+14 \ 	ext { Which of these does not show } & 	ext { the commutative property? } \ 22 	imes 4=4 	imes 22 & 	ext { ii) } 12-4=2 	imes 4 \ 5+6=11=6+5 & 	ext { iv) } 31+72=72+31\end{array} $$

UpStudy AI · Accepted Answer

To determine which of the given statements does not show the commutative property, we first need to understand what the commutative property is. The commutative property states that the order in which two numbers are added or multiplied does not change the result.

### Let's analyze each option:

1. **$$ 12 	imes 1 = 12 $$**: This is a true statement but does not demonstrate the commutative property since it involves only one number and does not show a change in order.

2. **$$ 6 + 7 = 15 - 2 $$**: This simplifies to $$ 6 + 7 = 13 $$, which is not true. This does not demonstrate the commutative property.

3. **$$ 21 \div 3 = 3 + 4 $$**: This simplifies to $$ 7 = 7 $$, which is true but does not demonstrate the commutative property.

4. **$$ 14 + 4 = 4 + 14 $$**: This demonstrates the commutative property of addition, as changing the order of addition does not change the result.

5. **$$ 22 	imes 4 = 4 	imes 22 $$**: This demonstrates the commutative property of multiplication, as changing the order of multiplication does not change the result.

6. **$$ 5 + 6 = 11 = 6 + 5 $$**: This demonstrates the commutative property of addition, as changing the order of addition does not change the result.

7. **$$ 31 + 72 = 72 + 31 $$**: This demonstrates the commutative property of addition, as changing the order of addition does not change the result.

### Conclusion:
The statements that do not show the commutative property are:

- **$$ 12 	imes 1 = 12 $$** (does not show order change)
- **$$ 6 + 7 = 15 - 2 $$** (not a valid commutative property example)

Thus, the answer is that the first and second options do not show the commutative property.
The first and second options do not demonstrate the commutative property.

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