Rewrite each statement using the indicated property. a. 2+5=...

Rewrite each statement using the indicated property. a. $2+5=$ ________ ; Commutative property of addition b. $2 \cdot 5=$ _________ ; Commutative property of multiplication c. $3+(10+2)=$ _______ ; Associative property of addition d. $3 \cdot(10 \cdot 2)=$ ___________ ; Associative property of multiplication

Rewrite each statement using the indicated property.
a. $2+5=$ ________ ; Commutative property of addition
b. $2 \cdot 5=$ _________ ; Commutative property of multiplication
c. $3+(10+2)=$ _______ ; Associative property of addition
d. $3 \cdot(10 \cdot 2)=$ ___________ ; Associative property of multiplication

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Key Concepts

Associative Property of Multiplication

This property means that the grouping of factors in a multiplication expression does not change the product. For instance, (a × b) × c is the same as a × (b × c). This helps in reorganizing multiplication expressions for easier calculation.

Commutative Property of Multiplication

This property asserts that the order of factors in a multiplication can be switched without affecting the product. That is, for any two numbers a and b, a × b equals b × a. This principle is crucial for simplifying and rewriting multiplication expressions.

Commutative Property of Addition

This property states that the order of the addends does not affect the sum. In other words, for any two numbers a and b, a + b equals b + a. This fundamental principle allows the rearrangement of terms in an addition expression without changing the result.

Associative Property of Addition

This property indicates that when adding three or more numbers, the way in which the numbers are grouped does not influence the overall sum. For example, (a + b) + c is equal to a + (b + c). This allows flexibility in computation and reordering of additive combinations.

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