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Q31.

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Found in: Page 15

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# Name the property illustrated by each equation. 31. $\left[5+\left(-2\right)\right]+\left(-4\right)=5+\left[-2+\left(-4\right)\right]$

Name of the property illustrated is Associative Addition.

See the step by step solution

## Step 1 - Write properties of real numbers

Properties of real numbers are written in following table:

 For any real numbers $a,b,$ and $c:$ Property Addition Multiplication Commutative $a+b=b+a$ $a·b=b·a$ Associative $\left(a+b\right)+c=a+\left(b+c\right)$ $\left(a·b\right)·c=a·\left(b·c\right)$ Identity $a+0=a=0+a$ $a·1=a=1·a$ Inverse $a+\left(-a\right)=0=\left(-a\right)+a$ If $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$ Distributive $a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$

## Step 2 - Substitution in given values

Substitute a for 5, b for $-2$ and c for $-4$ in given equation.

Now equation becomes $\left(a+b\right)+c=a+\left(b+c\right)$

## Step 3 - Identify the property

From the table of properties of real numbers, $\left(a+b\right)+c=a+\left(b+c\right)$ is the property of associativity in addition

Thus, associative addition is illustrated by given equation.