Final answer:
The associative property of multiplication states that the grouping of numbers being multiplied together does not affect the result. This can be illustrated using place value disks. In the given problem 30 x 21, we can use place value disks to represent the numbers and perform the multiplication.
Step-by-step explanation:
The associative property of multiplication states that when three or more numbers are multiplied together, the grouping of the numbers does not affect the result. To illustrate this using place value disks, let's consider the problem 30 x 21.
- Represent 30 using place value disks as 3 tens and 0 ones.
- Represent 21 using place value disks as 2 tens and 1 one.
- Multiply the values represented by the disks: 3 (tens) x 2 (tens) = 6 (hundreds), 3 (tens) x 1 (one) = 3 (tens), 0 (ones) x 2 (tens) = 0 (tens), and 0 (ones) x 1 (one) = 0 (ones).
- Add up the products: 6 (hundreds) + 3 (tens) + 0 (tens) + 0 (ones) = 630.
Therefore, 30 x 21 = 630.