Question

If a, b and c are the rational numbers, then associativity of rational numbers under multiplication is given by​

Answer 1

Associative Property is followed by rational numbers.

Step-by-step explanation:

If a,b and c are the rational numbers then it follows associative property for multiplication.

$\bold {a\times (b\times c)= (a\times b)\times c}$

We will show this property by taking an example.

By considiring three rational numbers $\frac{1}{2}, \frac{5}{2},\frac{16}{8}$

Here, $\frac{1}{2}\times (\frac{5}{2}}\times {\frac{16}{8}})$

         = $\frac{1}{2}\times (5)$

         = $\frac{5}{2}$

Now,$(\frac{1}{2}\times \frac{5}{2})\times \frac{16}{8}$

    = $\frac{5}{4}\times \frac{16}{8}$

   = $\frac{5}{2}$

Since,L.H.S=R.H.S

Hence Associative Property is followed by rational numbers.

Answer 2

• Associative property means that if an operation is carried out on a set of numbers, the resulting value will not change irrespective of the order in which the operations are carried out.
• Multiplication is one such operation, i.e., a X (b X c) = (a X b) X c
• For example, let a = 5, b = -4, c = 8
• Then, a X (b X c) = 5 X (-4 X 8) = -160 and (a X b) X c = (5 X -4) X 8 = -160