Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine which equation demonstrates the Associative Property of Addition, let's examine each option carefully.
Definition: The Associative Property of Addition states that the way in which numbers are grouped when adding does not change their sum. Specifically, for any numbers [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], the property can be written as:
[tex]\[ (a + b) + c = a + (b + c) \][/tex]
Now, let's analyze each option one by one:
Option A: [tex]\(3 + (17 + 11) = (3 + 17) + 11\)[/tex]
- This expression rearranges the grouping of the numbers being added without changing the order of the numbers themselves.
- It clearly shows that changing the grouping does not affect the sum:
[tex]\[3 + 28 = 20 + 11 \][/tex]
[tex]\[31 = 31\][/tex]
This is a valid demonstration of the Associative Property of Addition.
Option B: [tex]\(\frac{1}{4} \times 7 \times 8 = \frac{1}{4} \times 8 \times 7\)[/tex]
- This expression involves multiplication, not addition.
- Therefore, it cannot demonstrate the Associative Property of Addition.
Option C: [tex]\(\frac{1}{4} \times (16 \times 11) = \left(\frac{1}{4} \times 16\right) \times 11\)[/tex]
- This expression also involves multiplication rather than addition.
- Hence, it does not demonstrate the Associative Property of Addition.
Option D: [tex]\(12 + 17 + 8 = 12 + 8 + 17\)[/tex]
- This expression changes the order of the numbers being added (from [tex]\(17 + 8\)[/tex] to [tex]\(8 + 17\)[/tex]), which is the Commutative Property.
- The Associative Property only changes the grouping, not the order of the numbers.
Option E: [tex]\(4(x + 3) = 4x + 12\)[/tex]
- This expression is an application of the distributive property, not the associative property, since it distributes 4 over [tex]\(x + 3\)[/tex].
From our analysis, we see that only Option A correctly demonstrates the Associative Property of Addition. Therefore, the correct option is:
A: [tex]\(3 + (17 + 11) = (3 + 17) + 11\)[/tex].
Definition: The Associative Property of Addition states that the way in which numbers are grouped when adding does not change their sum. Specifically, for any numbers [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], the property can be written as:
[tex]\[ (a + b) + c = a + (b + c) \][/tex]
Now, let's analyze each option one by one:
Option A: [tex]\(3 + (17 + 11) = (3 + 17) + 11\)[/tex]
- This expression rearranges the grouping of the numbers being added without changing the order of the numbers themselves.
- It clearly shows that changing the grouping does not affect the sum:
[tex]\[3 + 28 = 20 + 11 \][/tex]
[tex]\[31 = 31\][/tex]
This is a valid demonstration of the Associative Property of Addition.
Option B: [tex]\(\frac{1}{4} \times 7 \times 8 = \frac{1}{4} \times 8 \times 7\)[/tex]
- This expression involves multiplication, not addition.
- Therefore, it cannot demonstrate the Associative Property of Addition.
Option C: [tex]\(\frac{1}{4} \times (16 \times 11) = \left(\frac{1}{4} \times 16\right) \times 11\)[/tex]
- This expression also involves multiplication rather than addition.
- Hence, it does not demonstrate the Associative Property of Addition.
Option D: [tex]\(12 + 17 + 8 = 12 + 8 + 17\)[/tex]
- This expression changes the order of the numbers being added (from [tex]\(17 + 8\)[/tex] to [tex]\(8 + 17\)[/tex]), which is the Commutative Property.
- The Associative Property only changes the grouping, not the order of the numbers.
Option E: [tex]\(4(x + 3) = 4x + 12\)[/tex]
- This expression is an application of the distributive property, not the associative property, since it distributes 4 over [tex]\(x + 3\)[/tex].
From our analysis, we see that only Option A correctly demonstrates the Associative Property of Addition. Therefore, the correct option is:
A: [tex]\(3 + (17 + 11) = (3 + 17) + 11\)[/tex].
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.