multiplication is association in rational numbers explain with an example
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Answer:
In rational numbers, multiplication is associative, which means that the way we group the numbers that we are multiplying does not affect the result.
For example, let's consider the rational numbers $\frac{2}{3}, \frac{3}{4}$ and $\frac{4}{5}$:
$\left(\frac{2}{3} \cdot \frac{3}{4}\right) \cdot \frac{4}{5} = \frac{1}{2} \cdot \frac{4}{5} = \frac{2}{5}$
$\frac{2}{3} \cdot \left(\frac{3}{4} \cdot \frac{4}{5}\right) = \frac{2}{3} \cdot 1 = \frac{2}{3}$
As we can see, the way we group the numbers does not affect the result of the multiplication. This is true for any three rational numbers, and can be extended to any number of rational numbers being multiplied.
So, in general, if we have rational numbers $a_1, a_2, \ldots, a_n$, then we can multiply them in any order and the result will be the same:
$a_1 \cdot a_2 \cdot \ldots \cdot a_n = (a_1 \cdot a_2) \cdot a_3 \cdot \ldots \cdot a_n = a_1 \cdot (a_2 \cdot a_3) \cdot \ldots \cdot a_n = \ldots$
This is because multiplication is associative in rational numbers.