91Ó°ÊÓ

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

Suppose a, b, and c is three real numbers.

Associative property of Multiplication

Property: $\text{(a}  ·  \text{b)}  ·  \text{c}=\text{a}  ·  ( \text{b}  ·  \text{c} )$

If you are multiplying three real numbers, the product is always the same regardless of their grouping.

Example: $\text{(6}  ·  \text{4)}  ·  \text{3}=\text{6}  ·  ( \text{4}  ·  \text{3} )  =  72$

Associative property of Multiplication states thatif you are multiplying three or four real numbers, the product is always the same regardless of their grouping.

Property:$\text{(a}  ·  \text{b)}  ·  \text{c}=\text{a}  ·  ( \text{b}  ·  \text{c} )$

Example: $\text{(6}  ·  \text{4)}  ·  \text{3}=\text{6}  ·  ( \text{4}  ·  \text{3} )  =  72$

So, we can multiply the numbers in any order

$\begin{array}{l}4\text{ }\left(20\right)\text{ }\left(25\right)\text{ }(−\text{ }5)\\ (\text{ }4\text{ â¶Ä‰}·\text{ â¶Ä‰}20\text{ })\text{ â¶Ä‰}(25\text{ â¶Ä‰}·\text{ â¶Ä‰}−5\text{ })\text{ â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰Grouping}\\ (80\text{ â¶Ä‰}·\text{ â¶Ä‰}25)\text{ â¶Ä‰}·\text{ â¶Ä‰}−\text{ â¶Ä‰}5\text{ â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰Associative â¶Ä‰Property â¶Ä‰of â¶Ä‰Multiplication â¶Ä‰}\\ 80\text{ â¶Ä‰}·\text{ â¶Ä‰}(\text{ â¶Ä‰}25\text{ â¶Ä‰}·\text{ â¶Ä‰}−5)\text{ â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰â€‰â¶Ä‰Associative â¶Ä‰Property â¶Ä‰of â¶Ä‰Multiplication â¶Ä‰}\\ 80\text{ â¶Ä‰}·\text{ â¶Ä‰}−125\text{ â¶Ä‰}=\text{ â¶Ä‰}−10000\end{array}$

$4\text{ }\left(20\right)\text{ }\left(25\right)\text{ }(−\text{ }5)\text{ â¶Ä‰}=\text{ â¶Ä‰}−\text{ â¶Ä‰}10000$