91Ó°ÊÓ

When two or more numbers are multiplied together, it gives a number. The numbers that are being multiplied are called the factors. And the result of the multiplication of numbers is called the product of those numbers.

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

To evaluate the expression$33xy$, substitute the value of x as – 5 and the value of y as 3 and z as 2 and multiply the numbers as shown below,

$\begin{array}{l}\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}15\text{ â¶Ä‰}x\text{ }y\text{ }z\text{ â¶Ä‰}\\ =\text{ â¶Ä‰}15\text{ }·\text{ }(−5)\text{ }·\text{ }3\text{ }·\text{ }2\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰Substitute â¶Ä‰}x=−5,\text{ â¶Ä‰}y=3\text{ â¶Ä‰and â¶Ä‰}z=2\\ =\text{ â¶Ä‰}−75\text{ }·\text{ }3\text{ }·\text{ }2\\ =\text{ â¶Ä‰}−75\text{ â¶Ä‰}·\text{ â¶Ä‰}(3\text{ â¶Ä‰}·\text{ â¶Ä‰}2)\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰}(\text{Associative â¶Ä‰Property â¶Ä‰of â¶Ä‰Multiplication)}\\ =(−75\text{ â¶Ä‰}·\text{ â¶Ä‰}3)\text{ â¶Ä‰}·\text{ â¶Ä‰}2\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰}(\text{Associative â¶Ä‰Property â¶Ä‰of â¶Ä‰Multiplication)}\\ =\text{ â¶Ä‰}−225\text{ â¶Ä‰}·\text{ â¶Ä‰}2=−\text{ â¶Ä‰}450\end{array}$

Thus, the value of the expression is$15\text{ â¶Ä‰}x\text{ }y\text{ }z\text{ â¶Ä‰}=\text{ â¶Ä‰}−\text{ â¶Ä‰}450$