Name the property that justifies each step.
[(2 * 100) + (3 * 10)]+ [(1 * 100) + (5 * 10)]
= (2 * 100) + [(3 * 10)+ (1 * 100)] + (5 * 10)__________ property
= (2 * 100) + [(1 * 100)+ (3 * 10)] + (5 * 10)___________ property
= [(2 * 100) + (1 * 100)]+ [(3 * 10) + (5 * 10)]__________ property
= [(2 + 1) * 100]+ [(3 + 5) * 10] ____________property
I am confused on this, trying to figure out if commutative, distributive,etc.
To determine the property that justifies each step in the given arithmetic expression, let's break it down:
Step 1: [(2 * 100) + (3 * 10)]+ [(1 * 100) + (5 * 10)]
Property: Associative Property of Addition
Explanation: In this step, we are grouping the terms within parentheses by adding them. The Associative Property of Addition allows us to regroup the terms as long as the order of the terms is maintained.
Step 2: (2 * 100) + [(3 * 10)+ (1 * 100)] + (5 * 10)
Property: Associative Property of Addition
Explanation: Again, we are rearranging the grouping of terms within parentheses. The Associative Property of Addition allows us to change the grouping without changing the result.
Step 3: (2 * 100) + [(1 * 100)+ (3 * 10)] + (5 * 10)
Property: Commutative Property of Addition
Explanation: In this step, we are swapping the positions of two addition operations. The Commutative Property of Addition states that the order of terms in an addition operation does not affect the result.
Step 4: [(2 * 100) + (1 * 100)]+ [(3 * 10) + (5 * 10)]
Property: Distributive Property of Addition
Explanation: Now we are applying the Distributive Property of Addition. This property allows us to distribute the addition operation over the terms in parentheses.
Step 5: [(2 + 1) * 100]+ [(3 + 5) * 10]
Property: Associative Property of Multiplication
Explanation: Here, we have simplified the expressions within parentheses by performing the multiplications and additions. The Associative Property of Multiplication allows us to regroup the operands of multiplication, as long as the order is preserved.
In summary, the properties used in each step are:
Step 1: Associative Property of Addition
Step 2: Associative Property of Addition
Step 3: Commutative Property of Addition
Step 4: Distributive Property of Addition
Step 5: Associative Property of Multiplication.