Match each property with an expression.
A. Commutative Property of Addition
B. Identity Property of Addition
C. Multiplicative Property of Zero
D. Distributive Property
E. Associative Property of Addition
F. Identity Property of Multiplication
1. [tex]$3 x+4=4+3 x$[/tex]
2. [tex]$3+0=3$[/tex]
3. [tex]$3(0)=0$[/tex]
4. [tex]$3(x+4)=3 x+12$[/tex]
5. [tex]$3+(7+9)=(3+7)+9$[/tex]
6. [tex]$3(1)=3$[/tex]
Answer (2)
The properties are matched with the expressions as follows: Commutative Property of Addition (A) with 3 x + 4 = 4 + 3 x (1), Identity Property of Addition (B) with 3 + 0 = 3 (2), Multiplicative Property of Zero (C) with 3 ( 0 ) = 0 (3), Distributive Property (D) with 3 ( x + 4 ) = 3 x + 12 (4), Associative Property of Addition (E) with 3 + ( 7 + 9 ) = ( 3 + 7 ) + 9 (5), and Identity Property of Multiplication (F) with 3 ( 1 ) = 3 (6).
;
Commutative Property of Addition: 3 x + 4 = 4 + 3 x
Distributive Property: 3 ( x + 4 ) = 3 x + 12
Identity Property of Addition: 3 + 0 = 3
Multiplicative Property of Zero: 3 ( 0 ) = 0
Associative Property of Addition: 3 + ( 7 + 9 ) = ( 3 + 7 ) + 9
Identity Property of Multiplication: 3 ( 1 ) = 3
Explanation
Understanding the Problem We are given six properties of real numbers and six expressions. Our goal is to match each property with the expression that demonstrates it.
Matching Commutative Property of Addition The Commutative Property of Addition states that changing the order of addends does not change the sum. The expression that demonstrates this is 3 x + 4 = 4 + 3 x . So, A matches with A.
Matching Distributive Property The Distributive Property states that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products. The expression that demonstrates this is 3 ( x + 4 ) = 3 x + 12 . So, D matches with D.
Matching Identity Property of Addition The Identity Property of Addition states that adding zero to any number does not change the number. The expression that demonstrates this is 3 + 0 = 3 . So, B matches with B.
Matching Multiplicative Property of Zero The Multiplicative Property of Zero states that any number multiplied by zero is zero. The expression that demonstrates this is 3 ( 0 ) = 0 . So, C matches with C.
Matching Associative Property of Addition The Associative Property of Addition states that changing the grouping of addends does not change the sum. The expression that demonstrates this is 3 + ( 7 + 9 ) = ( 3 + 7 ) + 9 . So, E matches with E.
Matching Identity Property of Multiplication The Identity Property of Multiplication states that any number multiplied by one is that number. The expression that demonstrates this is 3 ( 1 ) = 3 . So, F matches with F.
Final Answer In summary, the matches are:
A (Commutative Property of Addition) with A ( 3 x + 4 = 4 + 3 x )
D (Distributive Property) with D ( 3 ( x + 4 ) = 3 x + 12 )
B (Identity Property of Addition) with B ( 3 + 0 = 3 )
C (Multiplicative Property of Zero) with C ( 3 ( 0 ) = 0 )
E (Associative Property of Addition) with E ( 3 + ( 7 + 9 ) = ( 3 + 7 ) + 9 )
F (Identity Property of Multiplication) with F ( 3 ( 1 ) = 3 )
Examples
Understanding these properties is crucial in algebra. For example, when simplifying expressions, the distributive property allows us to expand terms like 2 ( x + 3 ) into 2 x + 6 , making the expression easier to work with. The commutative property lets us rearrange terms in an equation, such as changing 5 + x = 9 to x + 5 = 9 without affecting the solution. These properties are the foundation for solving more complex algebraic problems.
