Question

Use the Commutative Property to determine the missing step in proving the equivalence of 12a+10+a=10+a+12a .

Step 1: [missing]

Step 2: 10+13a=10+13a

Step 3: The expressions are equivalent because they both equal the same value.

Responses

12a+10+a−a=10+a+12a−a
d plus 10 plus a equals 10 plus a plus d

12a+10+a−10=10+a+12a−10
d plus 10 plus a equals 10 plus a plus d

10+12a+a=10+13a
d plus 10 plus a equals 10 plus a plus d

12a+10=10+12a

Answer 1

To determine the missing step in proving the equivalence \( 12a + 10 + a = 10 + a + 12a \), we can start with the left side and use the Commutative Property of addition, which states that changing the order of addends does not change the sum.

Here's how we can fill in the missing step:

1. **Step 1:** \( 12a + 10 + a = (12a + a) + 10 \) (grouping like terms)

Then, in Step 2, we can combine the like terms:

- **Step 2:** \( 10 + 13a \) (because \( 12a + a = 13a \))

Finally, you have:

**Step 3:** \( 10 + 13a = 10 + 13a \)

So, the missing step to write would be:

- If we're specifically looking for how to rearrange the initial expression using the Commutative Property, the correct answer is **Option 3: \( 10 + 12a + a = 10 + 13a \)**.

To summarize:
- Original: \( 12a + 10 + a \)
- Reorganized using Commutative Property: \( 10 + 12a + a \)
- Combine like terms in Step 2 to get: \( 10 + 13a \)
- Conclude in Step 3 that both sides are equivalent.