Question

Which equation shows an example of the associative property of addition?

Answer 1

The associative property states that we can regroup the terms of an expression and obtain the same result.

We have then:

$a + (b + c) = (a + b) + c$

The expression that complies with this property is given by:

$(-4 + i) + 4i = -4 + (i + 4i)$

Answer:

An equation that shows an example of the associative property of addition is:

a. (- 4 + i) + 4i = -4 + (i + 4i)

Answer 2

The correct option is $\boxed{\bf option (a)}$ i.e., $\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}$.

Further explanation:

Concept used:

The associative property of the addition states that the addition of numbers cannot affect by the grouping of the number.

$\boxed{A+\left({B+C}\right)=\left({A+B}\right)+C}$

Here, in the above equation the value of $A+\left({B+C}\right)$ is always equal to the value of $\left({A+B}\right)+C$ whether the grouping of number is changes or not.

Calculation:

Now check the option to get the answer.

First check option (a)

$\left({-4+i}\right)+4i=-4+\left({i+4i}\right)$

In the above equation the grouping of the number is changed.

Now check the values of left hand side and right hand side.

$\begin{aligned}\left({-4+i}\right)+4i&=-4+\left({i+4i}\right)\\-4+5i&=-4+5i\end{gathered}$

The value of LHS is same as RHS.

Therefore, option (a) is correct.

Now check option (b)

$(-4+i)+4i=4i+(-4i+i)$

The term $i$ should be associated with $4i$ but it is associated with $-4i$.

Therefore the option (b) is incorrect.

Now check option (c)

$4i\times (-4i+i)=(4i-4i)+(4i\times i)$

The above expression does not follow any property.

Therefore the option (c) is incorrect.

Now check option (d)

$(-4i+i)+0=-4i+i$

The above expression follows additive property not associative property.

Therefore the option (d) is incorrect.

Thus, the correct option is $\boxed{\bf option (a)}$ i.e., $\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}$.

Learn more:

1. A problem on simplification: brainly.com/question/573729

2. A problem on domain and range: brainly.com/question/3412497

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Simplification

Keywords: Associative property, equation, property, addition, associative property of Addition, additive property, grouping terms, left hand side, right hand side, LHS, RHS.