Andrew is showing his work in simplifying (−5.7 + 2.2) − 1.1.
Step 1: (2.2 − 5.7) − 1.1
Step 2: 2.2 − (5.7 + 1.1)
Step 3: 2.2 − (6.8)
Step 4: −4.6
Which statement is true? (1 point)
In step 1, Andrew used the commutative property.
In step 2, Andrew used the distributive property.
In step 3, Andrew used the associative property.
In step 4, Andrew's answer is incorrect.
In step 1, Andrew used the commutative property.
In step 1, Andrew used the commutative property.
The statement "In step 3, Andrew used the associative property." is true.
To understand why, let's break down each step:
Step 1: (2.2 − 5.7) − 1.1
In this step, Andrew rearranges the order of subtraction using the commutative property. He changes the order from (−5.7 + 2.2) to (2.2 − 5.7). However, the question specifically asks for the correct statement, and this step does not involve the associative property.
Step 2: 2.2 − (5.7 + 1.1)
In this step, Andrew uses the distributive property. The distributive property states that a multiplication or division operation distributes over addition or subtraction. In this case, Andrew distributes the subtraction operation to both numbers inside the parentheses: 2.2 minus 5.7, and 2.2 minus 1.1.
Step 3: 2.2 − (6.8)
In this step, Andrew uses the associative property. The associative property allows you to group numbers differently without changing their value. In this case, Andrew groups the numbers 5.7 and 1.1 together, and then subtracts them from 2.2. By doing this, he simplifies the equation to 2.2 minus 6.8.
Step 4: −4.6
In this step, Andrew arrives at the final answer, which is -4.6. Since we are only analyzing the steps used, this statement does not apply.
Therefore, the correct statement is "In step 3, Andrew used the associative property."