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Question

The Commutative Property Quick Check
3 of 53 of 5 Items
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.

(1 point)
Responses

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

12a+10=10+12a
12 a plus 10 equals 10 plus 12 a

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

12a+10+a−10=10+a+12a−10

Answer 1

To use the Commutative Property in this case, the goal is to rearrange the terms in the expression. Given that you're starting with \(12a + 10 + a\) and want to show that it's equivalent to \(10 + a + 12a\), a good missing step would involve a simple rearrangement of the terms.

Here is the appropriate missing step:

Step 1: \(10 + 12a + a = 10 + a + 12a\)

In this step, we've rearranged the original expression to move the terms around, demonstrating the Commutative Property, which allows us to add terms in any order.

So the complete reasoning looks like this:

• Step 1: \(10 + 12a + a = 10 + a + 12a\) (using the Commutative Property)
• Step 2: \(10 + 13a = 10 + 13a\) (combining like terms)
• Step 3: The expressions are equivalent because they both equal the same value.

Hence, the answer that matches the structure of your question is:

10+12a+a=10+13a (this would be option 3 from your responses).