Which properties were used to write the numeric statement? Select all that apply.
(
18
−
5
)
+
(
432
×
15
)
=
(
15
×
432
)
+
(
18
−
5
)
A.
Associative Property of Addition
B.
Commutative Property of Addition
C.
Distributive Property
D.
Commutative Property of Multiplication
E.
Associative Property of Multiplication
F. None of the above.
Why did the math book hire a comedian? Because it needed some comic relief from all those numbers!
C. Distributive Property
To determine which properties were used to write the numeric statement, let's analyze each option:
A. Associative Property of Addition: This property states that changing the grouping of numbers being added does not change the sum. In the given numeric statement, there are no changes in the grouping of numbers being added, so the Associative Property of Addition is not applied.
B. Commutative Property of Addition: This property states that changing the order of the numbers being added does not change the sum. In the given numeric statement, the order of numbers being added is not changed, so the Commutative Property of Addition is not applied.
C. Distributive Property: This property states that multiplying a number by a group of numbers added together is the same as multiplying the number by each term individually and then adding. In the given numeric statement, we have (432 × 15), which can be rewritten as (15 × 432) due to the Commutative Property of Multiplication. This manipulation shows that the Distributive Property is used.
D. Commutative Property of Multiplication: This property states that changing the order of the numbers being multiplied does not change the product. In the given numeric statement, we have (15 × 432) which can be rewritten as (432 × 15) due to the Commutative Property of Multiplication. Thus, the Commutative Property of Multiplication is used.
E. Associative Property of Multiplication: This property states that changing the grouping of numbers being multiplied does not change the product. In the given numeric statement, there are no changes in the grouping of numbers being multiplied, so the Associative Property of Multiplication is not applied.
Based on the analysis, the properties used to write the numeric statement are:
- Distributive Property
- Commutative Property of Multiplication
Therefore, options C and D are the correct answers.