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Paul [167]
2 years ago
8

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

Mathematics
2 answers:
Nat2105 [25]2 years ago
6 0

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)

Eduardwww [97]2 years ago
4 0

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.

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