Yes, multiplication is associative for rational numbers. This means that when you multiply three or more rational numbers, the way in which the numbers are grouped does not affect the product.
To explain this, let’s take three rational numbers: a, b, and c. According to the associative property of multiplication, we can say:
(a × b) × c = a × (b × c)
This means that if we first multiply a and b, and then multiply the result by c, we will get the same outcome as if we first multiplied b and c and then multiplied a by that result.
For example, let’s say we have the rational numbers 1/2, 1/3, and 1/4. We can demonstrate the associative property as follows:
(1/2 × 1/3) × 1/4 = (1/6) × 1/4 = 1/24
Now let’s group them differently:
1/2 × (1/3 × 1/4) = 1/2 × (1/12) = 1/24
Both methods give us the same result, which confirms that multiplication is associative for rational numbers. Regardless of how we group the numbers, we arrive at the same product.