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Q31.

Expert-verifiedFound in: Page 15

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.**

Properties of real numbers are written in following table:

For any real numbers $a,b,$ and $c:$ | ||

Property | Addition | Multiplication |

Commutative | $a+b=b+a$ | $a\xb7b=b\xb7a$ |

Associative | $\left(a+b\right)+c=a+\left(b+c\right)$ | $\left(a\xb7b\right)\xb7c=a\xb7\left(b\xb7c\right)$ |

Identity | $a+0=a=0+a$ | $a\xb71=a=1\xb7a$ |

Inverse | $a+\left(-a\right)=0=\left(-a\right)+a$ | If $a\ne 0$, then $a\xb7\frac{1}{a}=1=\frac{1}{a}\xb7a$ |

Distributive | $a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$ |

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

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

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.

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