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
10+12a+a=10+13a
d plus 10 plus a equals 10 plus a plus d
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
12a+10=10+12a
Step 1: 12a+10+a=10+a+12a (Commutative Property)
Step 2: 10+a+12a=10+a+12a
Step 3: The expressions are equivalent because they both equal the same value.
To use the Commutative Property in this proof, you need to rearrange the terms to show that addition is commutative. The missing step in proving the equivalence of 12a+10+a=10+a+12a can be found by rearranging the terms using the Commutative Property, which states that the order of addition does not affect the sum.
Step 1: 12a+10+a = 10+a+12a (Missing step)
To find the missing step, we can rearrange the terms on the left-hand side of the equation using the Commutative Property:
12a+10+a = a+12a+10
Now, step 1 becomes:
Step 1: a+12a+10 = 10+a+12a
Step 2: 10+13a = 10+13a
Step 3: The expressions are equivalent because they both equal the same value.
Therefore, the missing step is: a+12a+10 = 10+a+12a
Step 1: Swap the positions of 12a and 10 on the left side of the equation.
12a+10 = 10+12a
Step 2: 10+13a=10+13a
Step 3: The expressions are equivalent because they both equal the same value.