Which of these is an example of the commutative proper $$ \begin{array}{ll} ext { i) } 12 imes 1=12 & ext { ii) } 6+7=15-2 \ ext { iii) } 21+3=3+4 & ext { iv) } 14+4=4+14\end{array} $$

Question

Which of these is an example of the commutative proper $$ \begin{array}{ll}	ext { i) } 12 	imes 1=12 & 	ext { ii) } 6+7=15-2 \ 	ext { iii) } 21+3=3+4 & 	ext { iv) } 14+4=4+14\end{array} $$

UpStudy AI · Accepted Answer

To determine which of the given options is an example of the commutative property, we 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.

In mathematical terms:
- For addition: $$ a + b = b + a $$
- For multiplication: $$ a 	imes b = b 	imes a $$

Now, let's analyze each option:

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

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

3. **iii) $$ 21 + 3 = 3 + 4 $$**  
   This simplifies to $$ 24 = 7 $$, which is not true. This does not demonstrate the commutative property.

4. **iv) $$ 14 + 4 = 4 + 14 $$**  
   This demonstrates the commutative property of addition, as it shows that changing the order of the numbers does not change the sum. Both sides equal $$ 18 $$.

Thus, the correct answer is:

**iv) $$ 14 + 4 = 4 + 14 $$**
iv) $$ 14 + 4 = 4 + 14 $$ is an example of the commutative property.

Which of these is an example of the commutative proper \( \begin{array}{ll}\text { i) } 12 \times 1=12 & \text { ii) } 6+7=15-2 \\ \text { iii) } 21+3=3+4 & \text { iv) } 14+4=4+14\end{array} \)

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