Responses
5z9+8a=8a+5z9
5 z superscript 9 baseline plus 8 a equals 8 a plus 5 z superscript 9 baseline
z9⋅5=5z9
z superscript 9 baseline times 5 equals 5 z superscript 9 baseline
5+8=4+9
5 plus 8 equals 4 plus 9
0+5z9=5z9
11 answers
The correct demonstration of the Commutative Property of Addition is:
5z⁹ + 8a = 8a + 5z⁹
The Commutative Property of Addition states that changing the order of the addends does not change the sum. Thus, \(a + b = b + a\) for any numbers \(a\) and \(b\).
The expression that correctly demonstrates the Commutative Property is:
3x ⋅ 9y ⋅ 6 = 9y ⋅ 6 ⋅ 3x
The Commutative Property states that the order in which you multiply numbers does not affect the product, so \(a \cdot b = b \cdot a\) for any numbers \(a\) and \(b\). In this case, the multiplication of \(3x\), \(9y\), and \(6\) is rearranged, which shows the Commutative Property.
The other options do not correctly reflect the Commutative Property.
According to the Associative Property of Addition, the way in which numbers are grouped does not change their sum. This means that you can rearrange the grouping of the addends without changing the result.
The expression \((b+c) + a + d\) can be rewritten in any of the following equivalent forms:
All of these expressions are valid under the Associative Property.
Thus, any of the choices you provided that represent a valid regrouping of the original expression is correct. However, since you are looking for equivalence to \((b+c) + a + d\), choice (b + c) + d + a is also valid under regrouping, showing that all listed options are indeed correct representations of the original expression according to this property.
If choosing just one option to highlight, d + (b + c) + a or (b + c) + d + a fits neatly into illustrating the Associative Property as they still retain the original structure without altering the sum.
To find the difference between the expressions \((3x + 4x) + 2x\) and \(3x + (4x + 2x)\), we can simplify both expressions.
Simplifying \((3x + 4x) + 2x\): \[ 3x + 4x = 7x \ (7x) + 2x = 9x \]
Simplifying \(3x + (4x + 2x)\): \[ 4x + 2x = 6x \ 3x + (6x) = 9x \]
Both expressions simplify to \(9x\).
Now, let's find the difference between the two simplified expressions: \[ 9x - 9x = 0 \]
So, the answer is 0.
The equation that demonstrates the Associative Property is:
3x ⋅ (4x ⋅ 5) = (3x ⋅ 4x) ⋅ 5
The Associative Property applies to addition and multiplication and states that the way in which numbers are grouped does not change their product or sum. Here, it shows that regardless of how you group the factors (either \(3x\) with \(4x\) or \(4x\) with \(5\)), the result remains the same.
The other equations either do not correctly represent the Associative Property or involve a mix of addition and multiplication incorrectly.
To evaluate the expression \((3r ⋅ 5) ⋅ (−3 ⋅ 8)\), let's simplify it step by step:
Simplify each part:
Now put it all together: \[ (3r ⋅ 5) ⋅ (−3 ⋅ 8) = 15r ⋅ (-24) \]
Now calculate the product: \[ 15r ⋅ (-24) = -360r \]
Now let's check each response for equivalency to \(-360r\):
The expression that is equivalent to \((3r ⋅ 5) ⋅ (−3 ⋅ 8)\) is:
24r ⋅ (5 ⋅ −3).
