Final answer:
Multiplying a 2-digit number by a 1-digit number and then adding the products of the tens and ones separately demonstrates the Distributive Property of multiplication over addition.
Step-by-step explanation:
When you multiply a 2-digit number by a 1-digit number, break the 2-digit number into tens and ones. You then multiply the one-digit number with both the tens and the ones separately and add up the results. This process is known as the Distributive Property of multiplication over addition. For example, if you are multiplying 23 by 5, you can calculate (20 × 5) + (3 × 5) which simplifies to 100 + 15, ultimately giving you a sum of 115. The Distributive Property allows you to distribute the multiplication across the addition of the tens and ones.
Examples of the Distributive Property in Action:
Multiplying Tens: For calculating 20 × 5, you multiply the digit in the tens place (2) by the one-digit number (5) and then append the zero back to get 100.
Multiplying Ones: Similarly, to calculate 3 × 5, you just perform regular multiplication of the digits to get 15.
Sum of Each: Finally, add 100 (from multiplying tens) and 15 (from multiplying ones) to get the final answer, 115.