How do you use partial products to multiply?

Understand the Problem

The question is asking for an explanation of the partial products method in multiplication, which is a way to multiply numbers by breaking them down into parts or components, facilitating easier calculation.

Answer

The product of 23 and 15 is $345$.

Steps to Solve

Introduce the Partial Products Method In this method, we break down each number into its place value components. For instance, when multiplying 23 by 15, we can look at 23 as (20 + 3) and 15 as (10 + 5).
Calculate the Partial Products Next, we multiply each part of one number by each part of the other number.

For 23 and 15, we do:

(20 \times 10 = 200)
(20 \times 5 = 100)
(3 \times 10 = 30)
(3 \times 5 = 15)

Add the Partial Products Together Now, we sum all the partial products to find the total. We have:

$$200 + 100 + 30 + 15 = 345$$

So, (23 \times 15 = 345).

The product of 23 and 15 using the partial products method is (345).

More Information

The partial products method is helpful for understanding multiplication at an elementary level. It emphasizes the importance of place value and makes calculations simpler, especially for larger numbers. This technique allows students to visualize multiplication and can be especially useful in mental math practices.

Tips

Forgetting to add all parts: A common mistake is neglecting to add all the calculated partial products together.
Misplacing values: Ensure that when breaking down numbers, each component is accurately calculated according to its place value.

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