Video Transcript
Which of the following illustrates
the associative property of addition? Is it (A) 𝑧 plus 41 is equal to 41
plus 𝑧? (B) 41 plus 𝑧 plus four is equal
to 41 plus 𝑧 plus four? (C) 41 plus 𝑧 plus four is equal
to 41 plus four plus 𝑧 plus four? (D) 41 multiplied by 𝑧 multiplied
by four is equal to 41 multiplied by 𝑧 multiplied by four? Or (E) 41 plus 𝑧 multiplied by
four is equal to 41 multiplied by four plus 𝑧 multiplied by four?
The associative property of
addition states that when three or more numbers are added, that sum is the same
regardless of the grouping. For example, two plus three in
parentheses plus four is the same as two plus three plus four in parentheses. It doesn’t matter which order we
add our numbers. The correct answer is, therefore,
option (B). When adding 41, 𝑧, and four, we
can add 41 and 𝑧 first or 𝑧 and four first. We could also have added 41 and
four first.
Option (A) demonstrates the
commutative property of addition. This states that when two numbers
are added, the sum is the same regardless of the order.
Option (D) looks similar to the
correct answer of option (B). This demonstrates the associative
property of multiplication. As with addition, when three or
more numbers are multiplied, the product is the same regardless of the grouping.
Option (E) demonstrates the
distributive property of multiplication. The sum of two numbers multiplied
by a third is equal to the sum of each number inside the parentheses multiplied by
the third number. In this case, we can multiply 41 by
four and 𝑧 by four. We then add these values.
Option (C) is actually an incorrect
equation. 41 plus 𝑧 plus four is not equal
to 41 plus four plus 𝑧 plus four.
The correct answer, as previously
stated, is option (B). 41 plus 𝑧 plus four is equal to 41
plus 𝑧 plus four illustrates the associative property of addition.
