1.
X + 9 = 9 + xis an example of which property?
Correct Answer
C. Commutative property of addition
Explanation
The given equation x + 9 = 9 + x demonstrates the commutative property of addition. This property states that the order of the numbers being added does not affect the sum. In this case, whether we add x and 9 or 9 and x, the result will be the same.
2.
2( x + 3 ) = 2x + 6 is an example of which property?
Correct Answer
B. Distributive property
Explanation
The given equation, 2(x + 3) = 2x + 6, demonstrates the distributive property. This property states that when a number is multiplied by the sum of two other numbers, it is the same as multiplying the number individually by each of the two numbers and then adding the products together. In this equation, the 2 is being distributed to both x and 3, resulting in 2x + 6 on the right side of the equation. Hence, the equation exemplifies the distributive property.
3.
X + ( y + 3 ) = x + ( 3 + y )is an example of which property?
Correct Answer
D. Commutative property of addition
Explanation
The given equation x + (y + 3) = x + (3 + y) demonstrates the commutative property of addition. This property states that the order of adding two numbers does not affect the result. In this case, the order of adding y and 3 can be interchanged without changing the overall sum.
4.
( 5 y ) • ( 1 ) = 5 yis an example of which property?
Correct Answer
A. Multiplicative identity property
Explanation
The given expression (5y) • (1) = 5y demonstrates the multiplicative identity property. According to this property, when any number is multiplied by 1, the product is equal to the original number. In this case, when 5y is multiplied by 1, the result is 5y itself, confirming the multiplicative identity property.
5.
( x y ) z = x ( y z )is an example of which property?
Correct Answer
B. Associative property of multiplication
Explanation
The given expression (x y) z = x (y z) represents the associative property of multiplication. This property states that the grouping of numbers in a multiplication operation does not affect the result. In other words, it doesn't matter how the numbers are grouped, the product will remain the same. In this case, whether we first multiply x and y and then multiply the result by z, or if we first multiply y and z and then multiply the result by x, the final product will be the same.
6.
( x + 5 ) ( 7 + x ) =
( x + 5 )•( 7 )+( x + 5 )•( x )
is an example of which property?
Correct Answer
D. Distributive property
Explanation
The given expression (x + 5)(7 + x) can be simplified using the distributive property. According to the distributive property, when a number or expression is multiplied by a sum, it can be distributed to each term of the sum. In this case, we can distribute (x + 5) to both terms of (7 + x). Therefore, the expression can be written as (x + 5)(7) + (x + 5)(x), which demonstrates the distributive property.
7.
(y + 2) + (-y + -2) = 0is an example of which property?
Correct Answer
D. Additive inverse property
Explanation
The given equation (y + 2) + (-y + -2) = 0 demonstrates the additive inverse property. This property states that for any number a, its additive inverse is -a, and when a number is added to its additive inverse, the result is always zero. In the given equation, (-y + -2) is the additive inverse of (y + 2), and when they are added together, the sum is zero. Therefore, the equation exemplifies the additive inverse property.
8.
Determine which equation illustrates the commutative property.
Correct Answer
C. A + b = b + a
Explanation
The equation "a + b = b + a" illustrates the commutative property. This property states that the order of addition does not affect the result. In this equation, no matter the values of a and b, adding them in either order will give the same result. Therefore, it follows the commutative property.