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Answer :
To solve the question of which expression is equivalent to [tex]\(157 + 243\)[/tex] by the Commutative Property of Addition, let's understand what this property means.
The Commutative Property of Addition states that changing the order of the numbers being added does not change the sum. In other words, if you have [tex]\(a + b\)[/tex], it is the same as [tex]\(b + a\)[/tex].
Given the original expression [tex]\(157 + 243\)[/tex], to find an equivalent expression using the Commutative Property, you simply switch the order of the numbers. Therefore, [tex]\(243 + 157\)[/tex] is equivalent.
Now, let's review the options provided:
A. [tex]\(144 + 256\)[/tex] - The numbers have changed completely.
B. [tex]\(230 + 170\)[/tex] - Again, different numbers.
C. [tex]\(243 + 157\)[/tex] - This is the same sum as the original, just with switched places.
D. [tex]\(170 + 230\)[/tex] - Different numbers once more.
So, the correct expression equivalent to [tex]\(157 + 243\)[/tex] by the Commutative Property of Addition is option C: [tex]\(243 + 157\)[/tex].
The Commutative Property of Addition states that changing the order of the numbers being added does not change the sum. In other words, if you have [tex]\(a + b\)[/tex], it is the same as [tex]\(b + a\)[/tex].
Given the original expression [tex]\(157 + 243\)[/tex], to find an equivalent expression using the Commutative Property, you simply switch the order of the numbers. Therefore, [tex]\(243 + 157\)[/tex] is equivalent.
Now, let's review the options provided:
A. [tex]\(144 + 256\)[/tex] - The numbers have changed completely.
B. [tex]\(230 + 170\)[/tex] - Again, different numbers.
C. [tex]\(243 + 157\)[/tex] - This is the same sum as the original, just with switched places.
D. [tex]\(170 + 230\)[/tex] - Different numbers once more.
So, the correct expression equivalent to [tex]\(157 + 243\)[/tex] by the Commutative Property of Addition is option C: [tex]\(243 + 157\)[/tex].
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